# Centralized QoS-Aware Resource Allocation for D2D Communications with
Multiple D2D Pairs in One Resource Block

Mohammad Hossein Bahonar†, Mohammad Javad Omidi†
† Dept. of Electrical and Computer Engineering, Isfahan University of
Technology, Isfahan, Iran 84156-83111
Emails<EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

Device-to-device (D2D) communications can result in spectral efficiency (SE)
improvement of cellular networks when interference is addressed properly. For
further improvement of overall network sum-rate, it can be assumed that
multiple D2D pairs reuse the same resource block (RB) of a cellular user
equipment (CUE). In this paper, we study a centralized joint power and
spectrum resource allocation problem to maximize the overall sum-rate of the
network while guaranteeing the quality-of-service (QoS) requirements of CUEs
and admitted D2D pairs. The proposed method uses a distance based approach to
select a CUE at each step with a distance and power based approach to increase
the number of admitted D2D pairs. A power minimization approach when the
number of admitted D2D pairs are increasing and a power maximization approach
at the end of resource allocation for each RB is proposed. Numerical results
show that the proposed algorithm significantly improves SE compared to the
situation where at most one D2D pair can reuse the RB of a CUE. It also shows
that the proposed algorithm has a slight lower performance compared to the
optimal scheme but dramatically decreases the matching complexity and
signaling overhead.

###### Index Terms:

Device-to-device communication, resource allocation, power allocation,
complexity reduction.

##  I Introduction

Due to the ever increasing data demand, a device-to-device (D2D) communication
scheme has been proposed which enables direct data transmission between two
devices in proximity without going through the base station (BS). This type of
communication can increase the overall network sum-rate and spectral
efficiency (SE). Power control [1], security, interference management [2],
caching, coverage analysis [3], and resource allocation [4] are some of the
challenges in D2D communications.

Interference management is an important issue in D2D communications since this
type of communication causes interference to existing cellular user equipment
(CUE) in underlaying schemes. The resource allocation problem can be
formulated as a constraint optimization problem with SE [5] or energy
efficiency (EE) [6] objective functions and quality-of-service (QoS)
constraints in terms of signal-to-interference-plus-noise ratio (SINR) or
achievable data rate in an uplink [7] or downlink resource reuse [8] schemes.
In [4] a 3-step optimal centralized resource allocation algorithm is proposed
that assumes at most one D2D pair in each resource block (RB). It is usually
assumed that the BS has complete channel state information (CSI) of all links
[9], in the centralized scheme. In [5] channel uncertainty is investigated and
resources are allocated in a centralized manner. Due to the high complexity of
centralized approaches, distributed approaches [10] are used with lower
complexity and signaling overhead that have some performance losses compared
to the centralized schemes. The QoS constraints of the optimization algorithm
limit the interference experienced by the CUEs. The QoS constraints can be
either related to just the CUEs since they are considered as primary users or
to both CUEs and D2D pairs [4] since the achievable data rate requirement of
D2D pairs is also of high importance. Consideration of QoS for D2D pairs makes
the optimization problem more complicated, which makes researchers to focus
more on the QoS constraints of CUEs [11].

Each CUE occupies one RB in a cellular network. It is usually assumed that at
most one D2D pair can reuse one RB, while consideration of multiple D2D pairs
in one RB can result in significant performance improvement of the network.
Consideration of multiple D2D pairs in one RB results in a dramatic increase
of complexity and a signaling overhead. Due to the high complexity and
signaling overhead of centralized schemes, it is not reasonable to consider
multiple D2D pairs in centralized scheme without complexity and signaling
overhead reduction. In [2], multiple D2D pairs in one RB are assumed and the
optimization problem is solved using a distributed approach that has a lower
performance compared to the centralized ones. The proposed method allocates
resource to each UE based on its own CSI which results in low complexity and
signaling overhead of the proposed method. It is assumed that the number of
D2D pairs is more than the number of CUEs in [12] and network capacity
optimization is considered. Resource allocation with the assumption of
multiple D2D pairs in one RB is investigated in [13], but the QoS of CUEs is
just guaranteed. The resource allocation problem is modeled as a mixed integer
programming optimization problem and solved using a subchannel sharing
protocol. Multiple D2D pairs in one RB assumption is also considered in [7],
while the QoS of CUEs is only considered and the EE of D2D links is optimized.

We formulate the resource allocation problem to allocate power and spectrum to
CUEs and D2D pairs in a cellular network in order to maximize the overall sum-
rate while the D2D pairs reuse the uplink spectrum. The problem is modeled as
a constraint optimization problem, where the QoS of CUEs and D2D pairs in
terms of SINR are considered as the optimization constraints. We propose
selecting one CUE at each step based on a distance metric and allocate the
maximum number of D2D pairs to the RB of the CUE while the optimization
problem remains feasible. The procedure of adding D2D pairs to the RB of the
selected CUE is performed at several steps. At each step a D2D pair is
selected based on a distance and power metric. Then, the power of CUEs using
the same RB is minimized in order to add more D2D pairs to the RB, that
results in further sum-rate increment. At the end of the resource allocation
to each RB, power of CUEs using the same RB is optimized to increase the
overall sum-rate. It is shown that the proposed scheme has a slight lower
performance compared to the optimal scheme but it dramatically decreases the
matching complexity and signaling overhead of resource allocation.

The rest of the paper is organized as follows. System model consisting of the
network model and the achievable data rate alongside with the notation of used
symbols are introduced in section II. Problem formulation for power and
spectrum allocation to CUEs and D2D pairs with multiple D2D pairs in one RB is
presented at section III. The proposed centralized resource allocation
algorithm is given in section IV. Complexity and signaling overhead is
analyzed in section V. Numerical results are presented at section VI and
section VII concludes the paper.

##  II System Model

The system bandwidth is divided into N orthogonal RBs. Considering a fully
loaded cellular scenario, $N$ active CUEs denoted by $C_{1},C_{2},...,C_{N}$
occupy the $N$ orthogonal channels in the cell and $M$ D2D pairs denoted by
$D_{1},D_{2},...,D_{M}$ coexist with CUEs. We use $\textbf{c}=\\{1,...,N\\}$
and $\textbf{d}=\\{1,...,M\\}$ to denote the index sets of CUEs and D2D pairs.
Each RB is allocated to one CUE and each CUE occupies one RB different from
other CUEs. Each D2D pair shares one RB with a CUE but one RB can be allocated
to multiple D2D pairs. Uplink resource sharing is considered. Since the BS is
located at the center of the cell and has a higher transmission power compared
to other UEs, downlink interference is mostly caused by the BS. This kind of
interference exists in large areas of the cell while uplink interference
exists just around the CUE that uses its corresponding RB. Each D2D
transmitter sends its data toward its corresponding receiver in the uplink RB
of a CUE. Based on the value of $M$, the number of D2D pairs might be much
larger than the number of available RBs. So it is necessary for multiple D2D
pairs to occupy the RB of one CUE simultaneously. Also each CUE and D2D pair
have their own minimum QoS requirement in terms of SINR.

The channel gain between CUE $i$ and the BS is denoted as $g_{C_{i},B}$ and
that of the D2D pair $i$ between its transmitter and receiver is denoted by
$g_{D_{i}}$. The channel gain from the transmitter of D2D pair $i$ to the BS,
from the CUE $i$ to receiver of D2D pair $j$, and from transmitter of D2D pair
$i$ to receiver of D2D pair $j$ are denoted as $h_{D_{i},B}$,
$h_{C_{i},D_{j}}$, and $h_{D_{i},D_{j}}$, respectively. The power of additive
white Gaussian noise (AWGN) on each channel is assumed to be $\sigma_{N}^{2}$
while $\sigma_{s}^{2}$ denotes the power of signal processing noise at the
receiver. Both fast fading due to multi-path propagation and slow fading due
to shadowing have also been considered.

Let $\gamma_{C_{i}}$ and $\gamma_{D_{j}}$ denote the SINR for the link between
CUE $i$ and the BS and the link between transmitter and receiver of D2D pair
$j$ respectively. Also, let $\rho_{i,j}$ be the resource reuse indicator for
CUE $i$ and D2D pair $j$, $\rho_{i,j}=1$ when D2D pair $j$ reuses the resource
of cellular user $i$; otherwise, $\rho_{i,j}=0$. Considering a total bandwidth
of $W$, the bandwidth of each RB would be $B_{\rm RB}=\frac{W}{N}$. The SINR
of CUE $i$ can be expressed as

$\gamma_{C_{i}}=\frac{P_{C_{i}}g_{C_{i},B}}{\sum_{j}\rho_{i,j}P_{D_{j}}h_{D_{j},B}+\sigma_{N}^{2}+\sigma_{s}^{2}}$
(1)

where $P_{C_{i}}$ denotes the transmission power of CUE $i$. The summation at
the denominator of (1) corresponds to interference from other D2D pairs that
use the same RB of CUE $i$. The SINR of D2D pair $i$ can be expressed as

$\gamma_{D_{i}}=\frac{P_{D_{i}}g_{D_{i}}}{\sum_{j}\rho_{j,i}[P_{C_{j}}h_{C_{j},D_{i}}+\sum_{k\neq
i}\rho_{j,k}P_{D_{k}}h_{D_{k},D_{i}}]+\sigma_{N}^{2}+\sigma_{s}^{2}}$ (2)

where $P_{D_{i}}$ denotes the transmission power of D2D pair $i$. The
summation at the denominator of (2) corresponds to interference from one CUE
and other D2D pairs using the same RB of D2D pair $i$.

##  III Problem Formulation

The purpose of this work it to maximize the sum-rate performance of all UEs in
a cell. Since there exists $N$ CUEs and $M$ D2D pairs in a cell, the sum-rate
of all UEs in a cell, $R_{\rm Total}$ can be expressed as

$R_{\rm
Total}=\sum\limits_{i\in\textbf{c}}{\log_{2}{(1+\gamma_{C_{i}})}}+\sum\limits_{i\in\textbf{d}}{\log_{2}{(1+\gamma_{D_{i}})}}$
(3)

where the first and second summations correspond to sum-rate of CUEs and D2D
pairs, respectively. A cellular link from a CUE to the BS or a D2D link
between the transmitter and the receiver of a D2D pair is set up only when
their minimum QoS requirement can be guaranteed. So the sum-rate maximization
problem is an optimization problem constrained to some QoS requirement
constraints that can be expressed as

$\displaystyle\max_{\textbf{p}_{C},\textbf{p}_{D},\bm{\rho}}\quad$
$\displaystyle R_{\rm Total}$ (4a) $\displaystyle s.t.$
$\displaystyle\gamma_{C_{i}}\geq\gamma_{C_{i},{\rm min}},\forall
i\in\textbf{c}$ (4b) $\displaystyle\gamma_{D_{j}}\geq K_{j}\gamma_{D_{j},{\rm
min}},\forall j\in\textbf{d}$ (4c) $\displaystyle
K_{j}=\sum\limits_{i\in\textbf{C}}{\rho_{i,j}}\leq 1,\forall
j\in\textbf{d},\rho_{i,j}\in\\{0,1\\},$ (4d) $\displaystyle 0\leq
P_{C_{i}}\leq P_{C,{\rm max}},\forall i\in\textbf{c}$ (4e) $\displaystyle
0\leq P_{D_{j}}\leq P_{D,{\rm max}},\forall j\in\textbf{d}$ (4f)

where $\textbf{p}_{C}=\\{P_{C_{1}},...,P_{C_{N}}\\}$ and
$\textbf{p}_{D}=\\{P_{D_{1}},...,P_{D_{N}}\\}$ are transmit power vectors
related to CUEs and transmitters of D2D pairs respectively.
$\gamma_{C_{i},{\rm min}}$ and $\gamma_{D_{j},{\rm min}}$ correspond to the
minimum required QoS of CUE $i$ and D2D pair $j$, respectively. $K_{j}$ is a
reuse indicator variable related to D2D pair $j$. When D2D pair $j$ reuses the
RB of a CUE, $K_{j}=1$ and we call the D2D pair an admitted D2D pair. When D2D
pair $j$ can not reuse the RB of any CUE, $K_{j}=0$ and we call it a denied
D2D pair. Constraints (4b) and (4c) represent the QoS requirements of CUEs and
admitted D2D pairs. According to constraint (4c), the achievable QoS related
to a denied D2D pair is equal to zero. Constraint (4d) indicates that a D2D
pair shares at most the RB of one CUE. Constraints (4e) and (4f) guarantee the
transmit powers of CUEs and D2D pairs, respectively.

##  IV Centralized Resource Allocation

The sum-rate maximization problem (4a) is a nonlinear constraint joint
optimization problem of power control and matching between D2D pairs and CUEs.
We jointly design the matching variable $\bm{\rho}$ and the power control
strategies $\textbf{p}_{C},\textbf{p}_{D}$ to maximize overall sum-rate of the
network. Considering more than one D2D pair reusing the RB of a CUE results in
increased complexity of the matching process. Also due to the centralized
resource allocation scheme and the assumption of known channel gains at the
BS, multiple D2D pairs in one RB result in increased signaling overhead of the
network, which is because of transmitting measured channel gains to the BS. We
propose increasing the overall sum-rate of the network by increasing the
number of admitted D2D pairs as a higher priority and maximizing the power of
all CUEs as a lower priority, since increasing the power of CUEs results in
logarithmic increase of its data rate. Increasing the number of admitted D2D
pairs can be done by limiting the transmission power of other UEs in the same
RB that results in smaller interference areas.

###  IV-A Matching Complexity and Signaling Overhead Reduction

The solution of the optimization problem in (4a) consists of a CUE-D2D
matching procedure and power optimization of the matched UEs in one RB. High
complexity matching process is due to the fact that the BS has to check every
possible matching state to find the optimal CUE-D2D matching. Our proposed
method is a suboptimal algorithm with a very low complexity matching procedure
that chooses one CUE at each step based on a distance metric and matches the
maximum number of denied D2D pairs with the chosen CUE based on a distance and
power based metric while QoS requirements are guaranteed.

The BS allocates power to each UE based on its desired and interference
channel gains that are computed at the UEs and transmitted to the BS. In our
system model where the number of D2D pairs is more than CUEs, a huge signaling
overhead is needed to transmit the interference gains to the BS. We propose to
estimate and transmit the channel gains related to the communication links
between UEs that are matched to the same RB at each step of the algorithm when
they are needed for power allocation.

###  IV-B First Admitted D2D Pair

In order to solve the optimization problem based on matching the maximum
possible number of D2D pairs to one specific UE, the objective function of the
optimization problem can be expressed as
$R_{Total}=\sum_{i\in\textbf{c}}\bigg{(}{\log_{2}{(1+\gamma_{C_{i}})}+\sum_{i\in\textbf{d}}{\rho_{i,j}\log_{2}{(1+\gamma_{D_{i}})}}}\bigg{)}$
where the overall sum-rate of the network, $R_{Total}$ is expressed as the
summation of $R_{i}$s that corresponds to the sum-rate of all UEs using the RB
of CUE $i$.

In the proposed algorithm, the CUEs with larger distance from the BS are
selected earlier. Let $s(A,B)$ denote the distance between A and B. We define
CUE priority vector $\bm{\alpha}=\\{\alpha_{1},...,\alpha_{N}\\}$ as the
vector of CUE indices that their distance from the BS has a descending order,
i.e.,

$s(C_{\alpha_{1}},BS)>...>s(C_{\alpha_{N}},BS)$ (5)

where $s(C_{\alpha_{i}},BS)$ denotes the distance between $C_{\alpha_{i}}$ and
the BS. CUEs are selected based on the CUE priority vector.

After selecting the CUE $\alpha_{i}$, one denied D2D pair must be selected to
reuse the RB of the CUE. Since the distance highly influences the channel gain
value and QoS constraints, we define $m_{j}$ equal to the distance of CUE
$\alpha_{i}$ from the receiver of D2D pair $j$ as in (6). The selected denied
D2D pair $j^{*}$ is the one with the largest distance from CUE $\alpha_{i}$.

$\displaystyle m_{j}$ $\displaystyle=s(C_{\alpha_{i}},D_{j,Rx})$ (6)
$\displaystyle j^{*}$
$\displaystyle=\operatorname*{arg\,max}_{j\in\mathcal{D}}{(m_{j})}$ (7)

where $\mathcal{D}$ is the set of denied D2D pairs. The resource indicator
variable is also updated, i.e., $\rho_{\alpha_{i},j^{*}}=1$ .

In order to increase the overall sum-rate of the network by maximizing the
number of admitted D2D pairs, it is necessary to lower the amount of
interference from CUE $\alpha_{i}$ and D2D pair $j^{*}$ to other denied D2D
pairs. To achieve this goal the allocated power for CUE $\alpha_{i}$ and D2D
pair $j^{*}$ is set to the minimum amount that guarantees their QoS
requirement and are derived analytically as expressed in (8). The minimum
power of CUE $\alpha_{i}$ and D2D pair $j^{*}$ must be a feasible point in the
sum-rate optimization problem.

$\left\\{\begin{matrix}P_{C_{\alpha_{i}}}^{*}=\frac{(\gamma_{C_{\alpha_{i}}}\gamma_{D_{j^{*}}}h_{D_{j^{*}},B}+\gamma_{C_{\alpha_{i}}}g_{D_{j^{*}}})(\sigma_{N}^{2}+\sigma_{s}^{2})}{g_{C_{\alpha_{i}},B}g_{D_{j^{*}}}-\gamma_{C_{\alpha_{i}}}\gamma_{D_{j^{*}}}h_{C_{\alpha_{i}},D_{j^{*}}}h_{D_{j^{*}},B}}\\\
P_{D_{j^{*}}}^{*}=\frac{(\gamma_{C_{\alpha_{i}}}\gamma_{D_{j^{*}}}h_{C_{\alpha_{i}},D_{j^{*}}}+\gamma_{D_{j^{*}}}g_{C_{\alpha_{i}},B})(\sigma_{N}^{2}+\sigma_{s}^{2})}{g_{C_{\alpha_{i}},B}g_{D_{j^{*}}}-\gamma_{C_{\alpha_{i}}}\gamma_{D_{j^{*}}}h_{C_{\alpha_{i}},D_{j^{*}}}h_{D_{j^{*}},B}}\end{matrix}\right.$
(8)

If $P_{C_{\alpha_{i}}}^{*}>P_{C,max}$ or $P_{D_{j^{*}}}^{*}>P_{D,max}$ then
the power allocation problem does not have a feasible solution which means
that the D2D pair $j^{*}$ is not an admissible D2D pair for CUE $\alpha_{i}$.

Algorithm 1 Joint power and spectrum allocation to multiple D2D pairs in one
RB underlaying a cellular network

1: Input: $\bm{C}$ (Set of CUEs), $\bm{D}$ (Set of D2D pairs)

2: Output: $\textbf{p}_{C}$ (Transmission powers of CUEs), $\textbf{p}_{D}$
(Transmission powers of D2D pairs), $\bm{\rho}$ (Resource sharing indicator)

3: Initialization: $\mathcal{D}=\bm{D},$

4: Calculate CUE priority vector $\bm{\alpha}$ from (5)

5: for all $i\in\bm{\alpha}$ do

6: Calculate $m_{j}\forall j\in\mathcal{D}$ from (6) and $j^{*}$ from (7)

7: Transmission of D2D pair $j^{*}$ channel gain to BS

8: Calculate $\mathcal{P}=(P_{\alpha_{i}},P_{D_{j^{*}}})$ from (8)

9: if $P_{\alpha_{i}}<P_{C,max}$ and $P_{D_{j^{*}}}<P_{D,max}$ then

10: $\mathcal{D}=\mathcal{D}-j^{*}$

11: repeat

12: Calculate $m^{\prime}_{j},\forall j\in\mathcal{D}$ from (9) and $j^{*}$
from (10)

13: Transmission of D2D pair $j^{*}$ channel gain to BS

14: Adjust $P_{C_{\alpha_{i}}}$ ( Section IV-C )

15: for k=1:K+1 do

16: Adjust $P_{D_{\beta_{k}}}$ according to ( Section IV-C)

17: end for

18: if $P_{C_{\alpha_{i}}}\leq P_{C,max}$ and $P_{D_{\beta_{k}}}\leq
P_{D,max}$ then

19: $\mathcal{P}=\mathcal{P}_{2}$

20: else

21: Maximize $P_{C_{\alpha_{i}}}$ ( Section IV-D )

22: for k=1:K+1 do

23: Maximize $P_{D_{\beta_{k}}}$ ( Section IV-D)

24: end for

25: end if

26: until

27: else

28: $P_{\alpha_{i}}=P_{C,max},P_{D_{j^{*}}}=0$, Continue

29: end if

30: end for

###  IV-C Increasing The Number of Admitted D2D Pairs

After selecting the first D2D pair to reuse the RB of CUE $\alpha_{i}$, other
denied D2D pairs can also reuse the RB. We propose to select one denied D2D
pair based on a distance and power metric at each step and try to allocate the
minimum possible power that guarantees QoS of UEs. If a feasible power
allocation exits, the same process will be repeated for the next selected
denied D2D pair, otherwise the power of all UEs using the same RB will be
maximized in order to maximize overall sum-rate.

CUE $\alpha_{i}$ and D2D pairs $\beta_{1},\beta_{2},...,\beta_{k}$ are using
the same RB and D2D pair $\beta_{k+1}$ may also use the same RB. We define
$m^{\prime}$ as a function of the minimum distance of CUE $\alpha_{i}$ and
transmitter of D2D pairs $\beta_{1},\beta_{2},...,\beta_{k}$ from the receiver
of denied D2D pair $j$. It is a power normalized distance metric because
larger distances and lower transmission powers of other UEs results in less
interference to the newly admitted D2D pair.

$m^{\prime}_{j}=min\\{\frac{s(C_{\alpha_{1}},D_{j,Rx})}{P_{C_{\alpha_{1}}}},\frac{s(D_{\beta_{1}},D_{j,Rx})}{P_{D_{\beta_{1}}}},...,\frac{s(D_{\beta_{k}},D_{j,Rx})}{P_{D_{\beta_{k}}}}\\}.$
(9)

The next admitted D2D pair is the one that has the largest $m^{\prime}$
parameter, i.e. the one that has the highest shortest distance from other UEs,
and is the solution of the following maxmin optimization problem.

$j^{*}=\operatorname*{arg\,max}_{j\in\mathcal{D}}{(m^{\prime}_{j})}.$ (10)

Allocation of the minimum power that guarantees the QoS of UEs in the same RB
is discussed in a $K+2$ dimension space where one CUE and $K+1$ D2D pairs are
using the same RB. The channel gains of links related to the newly admitted
D2D pairs are computed and transmitted to the BS. The power allocation
procedure starts from the an initial point in the $K+2$ dimension space that
is defined as
$\bm{\mathcal{P}}=\\{P_{C_{\alpha_{i}}},P_{D_{\beta_{1}}},...,P_{D_{\beta_{K+1}}}\
\\}$. where $P_{C_{\alpha_{i}}}$ is the transmitting power of CUE $\alpha_{i}$
and $P_{D_{\beta_{1}}},...,P_{D_{\beta_{K}}}$ are the transmitting powers of
previously admitted D2D pairs from the previous step. The value of
$,P_{D_{\beta_{K+1}}}$ is set to the maximum possible power of a D2D pair,
$P_{D,max}$. The power of CUE $\alpha_{i}$ is adjusted until its QoS gets
equal to the its minimum required QoS and the QoS constraint become an equal
active constraint. At each step, the power of one D2D pair is adjusted on a
direction that preserves the equal active constraint of previous steps. For
this purpose the increase or decrease direction of $P_{D_{\beta_{k}}}$ is set
to be along the slope of hyperplanes related to equal active QoS constraints
of other UEs in previous steps and in the same RB. In this way a previously
equal active QoS constraint remains equal active at the next steps and the
power of other D2D pairs in the next steps are adjusted in a way that their
QoS gets close to the minimum QoS requirement.

###  IV-D Increasing the Power of CUE and admitted D2D Pairs

After adding the maximum number of possible D2D pairs to the admitted D2D pair
set, the optimal power must be computed which is more than their current power
values and results in an increases in the sum-rate of the network. Assuming
that a maximum number of $K$ D2D pairs are reusing the RB of the CUE
$\alpha_{i}$, an initial point $\bm{\mathcal{P}}$ is used to start the
allocation of maximum feasible power to all UEs. This point is defined as
$\bm{\mathcal{P}}=\\{P_{C_{\alpha_{i}}},P_{D_{\beta_{1}}},...,P_{D_{\beta_{K}}}\\}$
where each the power of each UE is the minimum QoS guaranteeing power from the
previous step. The maximization of power is performed at $K+1$ steps. At the
first step, the power of CUE $\alpha_{i}$ is adjusted until the QoS constraint
related to another UE become equal to its minimum QoS requirement. Then this
procedure is repeated for all other UEs that are using the same RB of CUE
$\alpha_{i}$ at next steps. Similar to previous section at each step the power
of one D2D pair in increased on a direction that preserves the equal active
constraint of previous steps. The increase direction of $P_{D_{\beta_{k}}}$ is
set to be along the slope of hyperplanes related to QoS constraints that are
equal to their minimum QoS requirement. So the maximum feasible transmitting
power of all UEs is reached while their QoS is also guaranteed. At each step
of the algorithm, the QoS constraint of a UE with a QoS equal to its minimum
requirement is preserved and the power of other UEs are increased. Hence
overall sum-rate is maximized. The overall resource allocation algorithm is
presented at table 1.

##  V Complexity and Signaling Overhead Analysis

Considering the assumption of at most one D2D pair at each RB, there will be
$M+1$ possible matching state for each CUE. But in our system model there will
be $2^{M}$ possible matching states for each CUE. The total number of matching
states for optimal matching $N_{\rm{states,optimal}}$ will be equal to

$N_{\rm{states,optimal}}=N\sum_{k=0}^{k=M}{\binom{M}{k}}=N2^{M}$ (11)

Based on our suboptimal and low complexity proposed matching procedure, there
will be $N$ steps related to all CUEs and at most a mean number of $M/N$ D2D
pairs matched to the CUE at each step. Thus the complexity of our proposed
algorithm will be $N_{\rm{states,proposed}}\approx N(M/N)=M$. In our system
model the number of channel gains related to the optimal resource allocation
is

$N_{\rm{signaling,optimal}}=N(M+1)+2M+M(M-1)$ (12)

In our proposed method, the channel gain between UEs that are using the same
RB is just needed. Assuming a uniform load distribution, a maximum number of
$M/N$ D2D pairs are matched to one specific CUE and the signaling overhead
$N_{\rm{signaling,proposed}}$ will be equal to

$N_{\rm{signaling,proposed}}\approx N(M+1)+2M+M(M/N-1)$ (13)

##  VI Numerical Results

A single cell network with uniformly distributed CUEs is considered.
Transmitter and receiver of each D2D pair are also uniformly distributed in a
cluster with radius $r$ where different D2D pairs are located in different
clusters and each cluster is also uniformly distributed in the cell. QoS
requirements, maximum transmit power of UEs, and the number of UEs are
described at table I.

TABLE I: Simulation Parameters Parameter |  Value
---|---
Physical link type |  Uplink
Cell Radius |  400, 600 m
Noise power ($\sigma^{2}_{N}$) |  -114 dBm
Path loss exponent ($\alpha$) |  -3.5
Maximum D2D Tx power ($P_{D,max}$) |  18 dBm
Maximum CUE Tx power ($P_{C,max}$) |  24 dBm
CUE and D2D minimum QoS requirements ($\gamma_{C_{i,min}},\gamma_{D_{j,min}}$) |  Uniformly distributed in [5,20] dB
D2D cluster radius |  10,15, …, 40 (m)
Number of CUEs (N) |  5,10
Number of D2D pairs (M) |  5N
Figure 1: Sum-rate for different D2D cluster radius ($R=0.4,0.6km$, $N=5$).
Figure 2: Average number of assisted D2D pairs ($R=0.4,0.6km$ and $N=5$).
Figure 3: Average number of assisted D2D pairs ( $N=5,10$, $R=0.4km$, and
$M=25$).

Overall sum-rate and the number of assisted D2D pairs are used as performance
evaluation metrics. We compare our scheme with 3-step, AllCSI, and exhaustive
search algorithms. The 3-step algorithm is proposed in [4] and assumes that
the RB of each CUE can be shared with at most one D2D pair. This method
assumes known channel gains at the BS and computes overall sum-rate for all
matching states. The AllCSI algorithm is presented at [14] and assumes that
the channel gains of all links are known at the BS. This method has a huge
signaling overhead equal to (12) and uses a reduced complexity matching
algorithm that selects the next admitted D2D pair based on minimum
interference link gain. The exhaustive search algorithm is a generalized
approach of the 3-step algorithm that is applied to a large number of CUE-D2D
matching states. The authors of [4] have proposed the 3-step algorithm and we
have generalized their approach to consider multiple D2D pairs in one RB. This
exhaustive algorithm has a large number of matching states equal to (11) and a
huge signaling overhead equal to (12) and can be considered as an optimal
solution to the problem.

Figure 1 compares the overall sum-rate performance of the four algorithms for
different cell radii. The 3-step algorithm has the lowest overall sum-rate
since a maximum of one D2D pair can reuse the RB of each CUE. AllCSI and the
proposed algorithms have lower performances compared to optimal algorithm but
with less complex matching procedures. The optimal algorithm has an
exponential matching complexity while the matching complexity of the proposed
algorithm increases linearly with $M$. The performance of AllCSI algorithm is
slightly higher than the proposed algorithm due to its huge signaling
overhead. The signaling overhead of our proposed method is $N$ time less than
AllCSI algorithm. The performance gap between AllCSI and the proposed
algorithm is considerably reduced when the cell radius is increased.

Figure 2 discusses the number of admitted D2D pairs for different cell radii.
The number of admitted D2D pairs in the 3-step algorithm is almost equal to
the number of CUEs, while the number of admitted D2D pairs in AllCSI and the
proposed method is almost three times more than the number of CUEs. Due to
previously mentioned reasons related to complexity and signaling overhead, the
performance of exhaustive search algorithm is higher than the two other
algorithms. By increasing the radius of the cell, more D2D pairs can be
admitted.

Figure 3 considers a constant number of D2D pairs with different number of
CUEs. It can be seen that increasing the number of CUEs results in an increase
in the number of RBs. So better interference management can be done and more
D2D pairs can be admitted.

It is shown that the proposed algorithm significantly increases the overall
sum-rate compared to the situation where at most one D2D pair is admitted for
each RB and is slightly lower than the performance of optimal algorithm for
multiple D2D pairs in one RB. The matching complexity of the proposed
algorithm increases linearly respect to $M$ while it grows exponentially in
the optimal algorithm. The proposed algorithm also has smaller signaling
overhead while optimal and AllCSI algorithms have a huge signaling overhead.

##  VII Conclusion and Future Work

In this paper we have investigated joint power and spectrum allocation for D2D
communications in a centralized manner for sharing uplink resources in a fully
loaded cellular network with multiple D2D pairs reusing the same RB in order
to maximize overall sum-rate. The optimal solution of this problem has a high
complexity CUE-D2D matching and signaling overhead. We propose to allocate
resource to each CUE at one step where the maximum possible number of denied
D2D pairs are added to the admitted D2D pair set of that CUE. At each step of
adding denied D2D pairs to the admitted D2D pair set, the power of all UEs are
minimized with respect to the QoS constraints using a QoS hyperplane slope
based approach. The power of all UEs in the same RB are maximized when no more
denied D2D pair can be added. Our proposed suboptimal algorithm dramatically
reduces the matching complexity and signaling overhead. In future research, we
will consider the problem with channel uncertainty. Also deriving a close form
for power allocation related to sections IV-B and IV-C should be investigated.

## References

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  * [8] Z. Zhou, C. Gao, C. Xu, T. Chen, D. Zhang, and S. Mumtaz, “Energy-efficient stable matching for resource allocation in energy harvesting-based device-to-device communications,” _IEEE Access_ , 2017.
  * [9] D. Feng, L. Lu, Y.-W. Yi, G. Y. Li, G. Feng, and S. Li, “Qos-aware resource allocation for device-to-device communications with channel uncertainty,” _IEEE Transactions on Vehicular Technology_ , vol. 65, no. 8, pp. 6051–6062, 2016.
  * [10] S. Dominic and L. Jacob, “Distributed resource allocation for d2d communications underlaying cellular networks in time-varying environment,” _IEEE Communications Letters_ , 2017.
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  * [14] R. Khalvandi and M. Pakravan, “Improvement of resource allocation methods in device to device communication systems,” Master’s thesis, Sharif University of Technology, 2015.


# Weather of the Dorm Wi-Fi Ecosystem at the University of Colorado Boulder:
Fall Semester 2019 to Spring Semester 2020 – A Case Study of Wi-Fi including a
Campus Response to the COVID-19 Perturbation

Jake Mcgrath -Aeropace Engineering, Armen Davis -Applied Mathematics, Dr.
James Curry –Applied Mathematics, Orrie Gartner –Office of information
Technology, Glenn Rodrigues –Office of information Technology, Dr. Seth
Spielman -Office of Data Analytics, Dr. Daniel Massey -Department of Computer
Science. Contact E-mail<EMAIL_ADDRESS>Applied Mathematics,
University of Colorado, Boulder 80309-0526

(November 20, 2020)

###### Abstract

”Growing use of network-enabled technology in Institutions of Higher Education
(IHEs) among students, staff, and faculty means that there has been increasing
demand to adapt technology platforms and tools that transform student learning
strategies, faculty teaching, research modalities, as well as general
operations. In fact, many of the new modalities are a necessity for doing IHE
business. In August 2019, our research team, at the University of Colorado
Boulder, began collecting and analyzing data from the campus Wi-Fi network. A
goal of the research was to answer the question of ”what passive sensing” of
the IHE’s Wi-Fi might be able to tell you about the gross dynamics of the ”Wi-
Fi weather” in the IHE ecosystem? Or more generally, what does anonymized data
tell us about the dynamics in a IHE’s ecosystem. Anonymized data were made
available by the University of Colorado Boulder (CU) Office of Information
Technology (OIT). Our goal was to understand the campus’ dynamical ecosystem
as a reflection of its collected Wi-Fi data. Those data could then be used to
develop forecast models and an understanding of the dynamics of the university
ecosystem where the dynamics of Wi-Fi  connected device count could be used as
a proxy for the ebb and flow of large scale, and small scale, behavior in the
ecosystem. The analogy with weather prediction seemed appropriate and a viable
strategy. Starting Fall 2019, data were collected in the ’observational phase’
(data collection is ongoing). In the ’analysis phase,’ briefly touched on
here, we applied Singular Spectrum Analysis (SSA) ”eigen decomposition,” to
deconstruct Wi-Fi data from dorms, the central campus dining cafeteria, the
recreation center, and other buildings on campus. That analysis led to the
identification of clusters of buildings that behaved similarly. Several campus
buildings are dual use and they are placed in different clusters. Just as in
the case of models of the weather, a final component of this research was
forecasting. We found that weekly forecast of Wi-Fi behavior in the Fall 2019,
was straight forward using SSA and seemed to present behavior of a low
dimensional dynamical system. However, in Spring 2020, with the COVID-19
Perturbation, the campus ecosystem received a “shock” and data show that the
campus changed very quickly. We found that as the campus moved to conduct
remote learning, teaching, the closure of research labs, and the edict to work
remotely, SSA forecasting techniques not trained on the Spring 2020, data
after the shock, performed poorly. While SSA forecasting trained on a portion
of the data did better, especially SSA R-forecasting. Finally, there is a
short animation of the ’Wi-Fi Weather’ for a typical Fall 2019 day on the CU
Boulder campus, the full animation can be found at
https://youtu.be/jvygO73oNxk

###### Index Terms:

Campus ecosystem, Wi-Fi Weather forecasting, Smart Communities, Streaming
Data, Wi-Fi, Singular Spectrum Analysis, Covid-19 Perturbation.

##  1 Introduction

Examples of ”smart and connected environments” are college and university
campuses. Wi-Fi is also the most popular form of wireless technology adapted
by Institutions of Higher Educations (IHEs) to provide network services to
students, faculty and staff. At the University of Colorado Boulder (CU
Boulder) Wi-Fi officially launched around September 15th, 1999 and is
constantly evolving to yield faster data rates and better security. Wi-Fi
currently operates on unlicensed frequencies in the 2.4GHz and 5GHz band,
making it possible for any enterprise to deploy a Wi-Fi network that enables
its stakeholders to be mobile and connect to both private and public networks.
In addition, governing standards and certification bodies such as the IEEE and
the Wi-Fi Alliance continue to improve Wi-Fi standards and ensure
compatibility between Wi-Fi devices both current and anticipated. Through this
research we have worked with the Boulder Campus Office of Informational
Technology (OIT) to assess this profound perturbation in the educational
ecosystem.

The starting point of this research was August 2019 at CU Boulder (or CUB) and
has been focused on the campus Wi-Fi network usage. The larger research
question was to what extent campus buildings have discernible WiFi
characteristics and behaviors in their profiles from which we could generate
information which would provide insights into the campus ecosystem, e.g. its
”weather.” This includes information on the impact of various large and small
scale perturbations and disruptions of connected components of campus life.
The research agenda is part of a multi-year program with an initial phase
where we report on aspects of a ”year in the life of a campus” from the
perspective of Wi-Fi usage of a smart and connected community. Further, IHEs
are possibly at the epi-center of generations of the most tech savvy users and
their presence on and off campuses is motivating rethinking issues around the
emergent technology, cybersecurity, policy issues. Such issues are ultimately
being confronted by the larger society–IHEs are part of a societies cutting
edge for innovation. Wi-Fi at CUB presents a rich source of data and
information, that could anticipate and model emergent patterns. Further, this
view and the granularity of the data likely lends itself to construction of
differential data-driven prediction (DDDP) modeling, that is differential
equation models generated from data, that are akin to weather forecasting.

CUB Wi-Fi data sets typically contain 57,109,890 entries and have a point
density of 1472.42857143 points/day. It is reasonable to expect that with the
increased use of network-enabled technology among IHEs, the data density
should be expected to grow. In fact, on campus Wi-Fi deployment has resulted
in increases in the spread of technology platforms and tools to transform the
delivery of education. Many of these new learning modalities and technologies
demand network connectivity for functionality. Further, because CUB is a
research university, additional research devices are also demanding network
access. So, developing and deploying mathematical and computational tools,
methods and strategies for better understanding such data rich environment
should lead to a better understanding of other data rich connected
environments, e.g. smart communities. Research studies such as this one may
lead to advance modelling of population centers and development of their
infrastructure.

In Spring 2020, with the appearance of COVID-19 on the world stage this
research took the opportunity to examine that pressing and emergent phenomena
with the goal of both better understanding whether campus data might expose
perturbations of normal and usual patterns of the connected campus as it tried
to assess and also respond to changes in various campus environments such as
dorms, study halls, recreational facilities, eateries and lecture halls. Our
research had some success with the previously collected data in looking at the
ecosystem up to the campus response to COVID-19.

###  1.1 Overview

This research has three parts: observation, analysis, and forecasting. In what
follows, the project first gives a large scale view of the CU Boulder Wi-Fi
and presents components that may be shared with most other IHEs. We present
the raw data and make observations on the ebb and flow of campus activities
using known Wi-Fi behavior as a surrogate for population and depicting this
with a ’weather map.’ The behavior includes identifying Wi-Fi hot spots as the
campus population goes about its usual activities at the outset of the Fall
2019 academic year like attending classes, visiting the central campus
cafeteria or common study spaces, returning to dormitories, or the periodic
leavings and returns to campus. The weather maps and raw data show such
events, including Fall Break and major holidays. Unexpected, the data show
clusters of behavior. The data also shows the start of the spring semester and
some of the consequences of the spring semester COVID-19 perturbation and its
aftermath.

In the analysis we deconstruct the streaming data using Singular Spectrum
Analysis (SSA). That analysis tool allows us to identify typical behaviors,
their frequency content, and finer characteristics using the ’anonymized’
surrogate Wi-Fi data. Anonymized data means no privacy rights were breached.
The third and final component of this research presents a discussion of the
results of using averaged Wi-Fi data in SSA forecast models.

####  1.1.1 Weather Forecasting Analogy

At its core, this research work was motivated by the seminal work of [16] L.
F. Richardson as well as results from the early 1960’s of [17], [15]. In the
case of Lewis Richardson, he, and others, started with the goal of weather
forecasting [19]. This then led to the collection of data and model
development based on the data of which he was successful in building a modest
forecast. In [10], the approach was to build least squares approximations and
that led the researchers in [10] to a “differential prediction” model. Just as
in [9], their approach was novel and led to other approximation strategies for
constructing prediction. More recently, the work of Tu, Rowley, et al. [11]
was formative for the proposed research. References [10] and [11] are like [9]
in that they started with observation and moved to analysis and forecasting.
Wi-Fi ecosystems are ripe for such an approach, one consistent with our goals.
[15] was also a transformational reference because it was among the first
articles to meld dynamical systems with Singular Spectrum Analysis (SSA) of
streaming data, and especially measures of the ”dimension” of recurrent
dynamical behavior which are used here.

Observations give a picture of the ebb and flow of daily Wi-Fi traffic and
then give a snapshot of the Wi-Fi ecosystem. Because the University of
Colorado Boulder is a comprehensive research university, the focus in this
article will be limited common areas that students are likely to navigate on a
nearly daily basis dormitories, eateries, study spaces, etc. We do this by
presenting anonymized data from traces of Wi-Fi activity, and specifically
device counts. After presenting an initial trace, we focus on the ”mean data”
from dorms. This research officially started just before the launch of the
Fall 2019 semester on ”move in day.” The collected data continues through the
Fall semester break, the return of students from that break, and the second
departure in March 2020 at the start of the COVID-19 ramp down. The ramp down
was associated with the Spring 2020 semester break and the end of the academic
calendar year. In a series of graphs, we present data traces of this evolution
and identify important dates associated with official campus announcements.

With the start of Spring 2020, we present data from the return of students to
the campus, and initially of the normal return to campus modes of operations
as noted in Fall 2019. In fact, it is striking that the unprocessed raw Wi-Fi
data captures the normal semester start up until: the start of the COVID-19
perturbation. For CUB the Perturbation started around the beginning of March
2020. As with the earlier section on observation, we focus on the mean
dormitory behavior and present the mean deviation of the number of connected
Wi-Fi devices. We also note that dorms that house primarily engineering
students have a higher device count, while students in residential apartments
exhibit device behavior similar to students living off campus. Also worth
noting was that there was significant network traffic as students transitioned
to remote education from off-campus sites, from around the country, after the
official start of the enhanced COVID-19 Spring 2020 break.

So, with the available Wi-Fi sensor information ’Wi-Fi Weather’ forecast for
the campus ecosystem is possible and could be integrated into a larger multi-
layered modeling effort that could be useful for developing a better
understanding of the emerging dynamics in analogous complex ecosystems. And
with even higher resolution data collection in the future, a more detailed
local analysis of ebbs and flows should be possible. This would enable more
accurate predictions of the IHE ecosystem. We end the the article with a
summary of our findings, and concluding remarks as well as and a couple of
future directions.

##  2 SSA and Data Collection: SSA Analysis

To further understand the ebb and flow of Wi-Fi usage across campus both
mathematical and statistical techniques of time series analysis were employed.
The main analysis tool is Singular Spectrum Analysis (SSA), a well developed
time series analysis technique used to decompose, in our context, streaming
data signals into interpretable components and, ultimately, produce forecasts
using an eigenvector and eigenvalue decomposition of the data matrices. We
refer to such a deta decomposition as generating sets of $EigenTriples$. There
are several excellent references on SSA including [7], and [4], [8] see also
[10].

A critical component of this analysis is its use of the singular value
decomposition (SVD) where the core idea is to decompose the signals from the
data matrix into three components – a trend, oscillations or seasonal
variation, and a structure-less noise component [8]. Then, by ”removing the
underlying noise,” a better understanding of the ebb and flow, e.g. the
dynamical behavior of the system, can be gleaned and a ”smooth forecasts” can
be extracted. Data streams with prominent oscillatory behavior especially
benefit from SSA techniques since such oscillations can then be examined
separately from other patterns at play. With multidimensional time series, an
analogous technique called Multi-channel SSA or MSSA can be used to achieve
similar results [9].

With SVD being the dominant analysis technique used in both SSA and MSSA, data
analysis leads to a significant flexibility, and freedom, as we shall see, in
subsequent sections where details are presented. However, and as expected,
additional flexibility comes with added complexity in constraints on SSA, i.e.
how one chooses to decompose the underlying signal, indeed, parameter
selection, is more of an art and is guided by the given data streams.

As we proceeded, a potentially useful scientific metaphor that was driving our
research, because we are collecting access-point data from across campus, was
an analogue to modern-day weather forecasting. More specifically, since such
streaming data were collected at specific locations in the campus ecosystem,
and forecasts based on the spatio-temporal data was desired, we will view SSA
as being analogous to the technique of empirical orthogonal functions (EOFs)
used by [16] L.F. Richardson and also E.N. Lorenz [13] in their quest for
increasingly accurate weather predictions.

###  2.1 SSA Embedding

We start with a time series $\mathbb{X}=(x_{1},x_{2},...,x_{N})$ of length
$N\geq 2$ with at least one nonzero data point. To apply SVD to a one-
dimensional time series, a standard process referred to as embedding takes
place where the data stream is converted to a Hankel data matrix. With $N$
data points sampled in time and with a set window length $L$, we can generate
the following data matrix:

$\centering X=[X_{1}:X_{2}:...:X_{K}]=\begin{bmatrix}x_{1}&x_{2}&...&x_{K}\\\
x_{2}&x_{3}&...&x_{K+1}\\\ x_{3}&x_{4}&...&x_{K+2}\\\
\vdots&\vdots&\ddots&\vdots\\\
x_{L}&x_{L+1}&...&x_{N}\end{bmatrix}\@add@centering$ (1)

with each column being a lagged vector of the form

$\centering X_{i}=[x_{i},...,x_{i+L-1}]^{T}\thinspace,\thinspace 1\leq i\leq
K\thinspace,\thinspace K=N-L+1\@add@centering$ (2)

Note that the elements in matrix 1 are equal on the off-diagonals. Such
matrices need not be square, and are referred to in the literature as a Hankel
Matrix. This is the matrix representation we will use in the singular value
decomposition of our streaming data matrices. Also it is possible to return to
the one-dimensional time series by tracing the top/right or left/bottom edges
of the matrix in equation 1. Choosing the value of $L$ is problem specific,
and is constrained to be $2\leq L\leq N/2$. Higher values of $L$ offer more
eigen triples components in the decomposition, but at the cost of increased
computational complexity and more difficulty in the ”grouping stage” as
discussed in [8].

###  2.2 SSA - Singular Value Decomposition

The core idea behind SSA is the singular value decomposition (SVD). Like its
counterpart, principle component analysis, we aim to use SVD to decompose the
data matrix in equation 1 into its rank-one components where the positive
singular values are arranged in decreasing magnitude. We begin by factoring

$\centering X=U\Sigma V^{T}\@add@centering$ (3)

where the columns of $U$ are the eigenvectors of $XX^{T}$, the columns of $V$
are the eigenvectors of $X^{T}X$ and the entries of the diagonal matrix
$\Sigma$ are the eigenvalues of $XX^{T}$ (the singular values of $X$). Since
$X\in\mathbb{R}^{L\times K}$, it can be shown that $U\in\mathbb{R}^{L\times
L}$, $\Sigma\in\mathbb{R}^{L\times K}$ and $V\in\mathbb{R}^{K\times K}$. If we
set $d=max\\{i,\Sigma_{ii}>0\\}=rank(X)$, then it is possible to decompose the
data matrix $X$ into $d$ rank-one components

$\centering X=X_{1}+X_{2}+...+X_{d}\@add@centering$ (4)

where $X_{i}=U_{i}\Sigma_{ii}V_{i}^{T}$. In most time series,
$d=min\\{K,L\\}$, [8]. Such a component $X_{i}$ is called an Eigen Triple or
ET for short. Importantly, the singular values of $\Sigma$ are in descending
order, with the largest being in $\Sigma_{1,1}$. The columns of $U$ and $V$
must be arranged accordingly, but this is usually done automatically by most
modern software.

##  3 A snapshot of the CU Boulder Wi-Fi Ecosystem: Dorms

In the remainder of this introduction, we provide a snapshot of five of the
critical areas in the University of Colorado Boulder Wi-Fi environment.

In what follows, we present a table of some of the buildings where data were
sampled as part of the CU building ecosystem. These are buildings where large
numbers of Wi-Fi device were counted throughout typical days during the
academic year, Fall 2019 and Spring 2020.

###  3.1 Dormitories

Below is a partial list of dormitories included in this study. The data
included in the table includes building name, a tentative group of students by
major or or college, number of rooms and reported bed count. When developing
the average Wi-Fi device count, these data were helpful in understanding the
ebb and flow of average connected Wi-Fi device count. We present some of the
information that was available in the Fall 2019.

Dorm |  Students |  Rooms |  Beds
---|---|---|---
Aden |  Double Majors |  56 |  113
Bear Creek B |  2nd years + |  172 |  498
Buckingham |  Media |  110 |  205
Crossman |  Engin |  46 |  138
Smith |  Arts |  185 |  338
Stearns (E,W) |  Out of State |  418 |  855
Will Vill North |  Older Dorm |  278 |  500
Will Vill East |  New Dorm |  420 |  705
TABLE I: Dormitories examined on the CUB campus

The Center for Community (C4C) is the main campus dining hall on the CU
Boulder campus. It offers a range of food options and cuisines. The facility
opens early and closes late. Like the Norlin Library, C4C is also ”multiple
use” facility and hosts a range of meeting rooms, offices and the like.

The fact that these two facilities are multiple use implies they are
facilities that house campus offices with multiple missions. For example, the
C4C houses some offices of student services focused on how to access community
resources, medical leave, health and safety referrals, etc. More importantly,
when students take a break from campus, e.g. during November’s Fall break,
many of the service offices continue to be operational and data traces show a
small number of connected Wi-Fi devices. The same low level of connectivity is
also visible, typically over the weekends when building offices are closed.
Observations like this allowed us to establish a baseline for device count as
the campus moves into the Spring 2020 semester and the COVID-19 perturbation.

##  4 Wi-Fi Weather Maps-”WFW”

Previously, we discussed Wi-Fi density in terms of devices per bed, or more
usefully, devices per person. While this is useful for understanding device
behavior at the building level, it is also beneficial to imagine the campus as
an ecosystem. To do this, we introduce another form of Wi-Fi density:
devices/area or ”physical Wi-Fi density.” Physical Wi-Fi density is a useful
measure because it illustrates exactly where Wi-Fi traffic originates on
campus and how the macro scale traffic moves throughout the day. An apt
analogy is that each campus building can be thought of a ”weather station” in
a Wi-Fi sensor network. Then, a goal is to ”track” the weather in the
ecosystem over an extended period. (See [17] for another approach.)

###  4.1 Analogy and Methods: Building the Weather Maps

To create this illustration, we first sourced a map of the entire CU Boulder
campus that we used as a background for our density data. Next, we obtained
the pixel coordinates of every building on campus from the campus map. For any
given time, say 10/21/2019 at 8:00AM, our algorithm obtains the number of Wi-
Fi devices in each building, finds that building’s boundaries on the map, then
fills the building with one point for each device. Then we use a Gaussian
Kernel Density Estimation (KDE) function to estimate the probability density
function of Wi-Fi propagation across the map. The map is then broken into
discrete hexagons that are colored from the results of our KDE. Finally,
contour lines are calculated and overlaid onto the colored hexagons. This
process is repeated for every time step, and can be used to create animated
maps.

The result of this process looks very similar to a weather map where each
building acts like a ”weather station” observing nearby devices and reporting
their numbers back to a central server. Then, as the day progresses, we are
able to see an analogue of ”pressure” (Wi-Fi density) systems move across
campus, storms develop in certain areas, and even parts of campus that have
become devoid of Wi-Fi activity completely, see [16], [14] and [12].

###  4.2 The Physical Campus Layout

Figure 1: The CU Boulder Campus

Wi-Fi dynamics suggest that the CU Boulder Campus is separated into three main
regions outlined in figure 1. The largest, leftmost region is main campus and
consists of scattered dormitories, learning spaces, eateries, and shared
spaces like the recreation center and the library. The smaller, bottom most
region southeast of the main campus is William’s Village. It consists of high
capacity, high rise dorms, the Bear Creek Apartments, a dining hall, and a
smaller recreation center. The final section in the upper right portion of the
map is East Campus, which primarily contains buildings specialized to a
specific major like the aerospace building and some smaller eating spaces.

###  4.3 Ebb and Flow of Wi-Fi on Campus and an Animation

The following snapshots come from a larger animation showcasing the change in
Wi-Fi density across campus over a regular day in the Fall 2019 semester. An
animation of the Wi-Fi weather for a typical Fall day on the CU Boulder campus
can be found here: https://youtu.be/jvygO73oNxk

In what follows, several discrete images are provided, first of the CU Boulder
campus and subsequently of several activity hot spots that demonstrate the
dynamics of Wi-Fi density on campus. All maps are from early October 2019 and
show various Wi-Fi activity levels as the day progresses.

At 8:00AM, we observed the highest density of devices in William’s Village and
activity associated with dorms on Main Campus, including but not limited to
the engineering dorms and also other dorms bordering Farrand Field. At this
time of day there are comparatively no devices present on East Campus. This is
understandable because many classes in this area start around 8:30AM, so we
would not expect to see much activity.

Around noon, the density shifts away from William’s Village and towards East
and Main Campus. As previously stated, data suggests that many students from
William’s Village leave for the duration of the school day and focus most of
their activities on the main campus. However, we also notice a shift away from
dorms on Main Campus to educational buildings like Norlin Library, Duane
Physics, Eaton Humanities, Cristol Chemistry, the Mathematics building, and
the Engineering Center. The ”pressure” map also indicates that there are two
main hot spots on East Campus, the Aerospace Building and the Biotech
building, which are two of the larger learning spaces in that area.

At 3:00PM, we observe a shift to secondary and tertiary hot spots on main
campus. The Wi-Fi density has begun to move away from educational spaces and
back to some main campus living spaces such as Kittredge Commons, at the
southern extreme of the central campus, and the Engineering Dorms, and to
outdoor spaces like Farrand Field and Duane Field. Also, at this time, there
is still a considerable concentration of students present in the Engineering
Center and East Campus.

Figure 2: Wi-Fi Weather Map of CU Boulder Campus, 7:00 PM, Fall 2019

Finally, at 7:00PM, a shift of devices back to dorms as well as a shift in
concentration to the main campus dining hall, C4C, the Center for Community.
However, there are still notable concentrations of devices in the Engineering
Center and East Campus at this time, but overall students seem to be settling
in for the evening.

###  4.4 Interpreting the Hot Spots

The brighter yellow portions of the weather maps are ”hot spots,” more
concentrated areas of Wi-Fi devices, and thus more students. The shift of
these hot spots during the day are significant because they show popular areas
of campus and how the hive of devices migrates from place to place. It is
reasonable to expect that this notion will become increasingly important in
the Fall 2020 semester. With the rise of COVID-19, such high concentrations of
devices could be indicative of transmission vectors for the virus. During a
normal semester, these hot spots are a positive indication of a healthy
campus; students are in class, enjoying time outside, spending time in the
dining hall, and living together in unique communities. While we can’t control
where or how students move around the campus ecosystem, working to recognize
and mitigate these hot spots as best as possible might be a strategy. In Fall
2020, a more diffuse weather map may well be a better indication of a healthy
campus.

###  4.5 Granularity of Data leading to better predictions

The maps showcased in this article were generated building by building. While
this is satisfactory for understanding the campus ecosystem as a whole, finer
detail may likely be required for more accurate predictions. Our data set
supports this capability; we use spooled data on an access point level which
we later aggregated to save computational power. Then, given an architect’s
blueprint of a given building as well as the placement of associated access
points, we could generate maps of device movement on a building level. This
has numerous practical applications which include, but are not limited to the
following:

  * •

Better planning and spacing of study tables in a given building.

  * •

An understanding of which places are used and when.

  * •

A more adaptable cleaning and sanitation schedule which limits worker contact
and student disruption (particularly applicable for Fall 2020).

  * •

An understanding of how many devices are present in a given space and adapt
Wi-Fi architecture accordingly.

  * •

Understand how devices move through human designed spaces and optimize
furniture arrangement.

  * •

Maximize floor space usage.

  * •

Security applications like alerts when devices are moving in buildings and
shouldn’t be.

  * •

Find network security vulnerabilities by visualizing where and when devices
are connected to the network without human supervision (i.e vending machines
that accept credit cards, Wi-Fi thermometers, lab equipment, workout
equipment, digital picture frames, smart devices, etc.)

  * •

Controlling the density of devices in a physical space by throttling network
resources.

  * •

Limiting devices in a certain space to help reduce COVID-19 transmission
vectors.

Clearly, going forward with the Wi-Fi weather maps may provide additional
utility or insights.

##  5 Mean Dorm Behavior: Examining the Raw Data

Going forward, we will also use the notion of a ”mean dorm” in order to
understand the relationship between the typical CU Boulder student and their
Wi-Fi enabled devices. While device count does serve as a proxy representation
of flow and movement of students on campus, device count over-represents the
number of students in a given area. This is because there is a delay in the
hand-off between Wi-Fi access points and device. The landscape of the
classroom is quickly evolving and is becoming a more Wi-Fi connected
environment. Further, it is no longer the case that individual students carry
only one Wi-Fi enabled device to class. In fact, it has become increasingly
common for students to tote a smartphone, laptop computer, and even a tablet
(for taking notes). Furthermore, individual dormitories on campus seemingly
have their own Wi-Fi fingerprints both in terms of physical and student
makeup. As noted in Table 1, a CU Boulder dormitory can be as large as 850
beds or as small as 100 while some dorms even group students of similar majors
to create learning communities. The variation in dorm composition and the fact
that students often carry more than one device make it difficult to infer
building-level behavior; these difficulties can be reduced by focusing on the
average dorm, i.e. the ”Mean Dorm.”

###  5.1 Methods

While we have no way of knowing how many students are in a given classroom at
a given time, we do know roughly how many students live in a dormitory. Each
dorm has an available bed count, room count, and student grouping outlined in
Table I. We can use bed count and the knowledge that each student is given
exactly one bed to normalize each dormitory for analysis and to determine
roughly how many devices students carry with them on average.

For each data set involving a dorm, we can divide the device count by the
number of beds to obtain ”devices per bed,” or more usefully, ”devices per
person.” We now have an understanding of how the number of devices and the
device density (devices per person) changes throughout the day. We can use
this information to establish an accurate range for the number of devices a
student carries on a dorm by dorm basis, to normalize and directly compare two
unlike dorms, and then create a fingerprint of the selected dorms behavior on
average.

###  5.2 Average Device Count

We expect that different groupings of students will have different devices.
For example, the need for engineering students to have a powerful, separate
laptop for CAD and simulations while an arts and sciences major could use just
a tablet might skew the device counts of some dorms. The results of device
count range from a normal week in Fall 2019 are outlined below in Table II.

Dorm | Max (D/P) | Min (D/P) | Diff(D/P)
---|---|---|---
Will Vill North | 1.30 | 0.88 | 0.42
Sterns | 1.36 | 0.61 | 0.75
Bear Creek Ap | 1.59 | 0.63 | 0.96
Aden | 1.72 | 0.88 | 0.83
Crossmam | 1.43 | 0.72 | 0.71
Buckingham | 1.20 | 0.66 | 0.54
Smith | 1.29 | 0.70 | 0.59
Will Vill East | 1.34 | 0.51 | 0.83
Mean | 1.36 | 0.81 | 0.55
TABLE II: The maximum, minimum, and average number of devices per person for
selected dorms for CU Boulder campus.

The minimum figure outlined in the table was often met very late at night or
very early in the morning while the max was met around 8-9PM. On average, for
every ten people in a dorm, between about eight and fourteen devices will be
connected to the network. This information could be useful to those planning
the Wi-Fi architecture so the network can be better equipped to handle student
traffic.

Overall, our hypothesis that more technologically demanding majors warranted
more devices was supported. Aden Hall, concentrated with double majors, had
the highest device density at 1.72 devices/person. Buckingham Hall,
concentrated with media majors, had the lowest device density at 1.20
devices/person. The second highest density was found in Bear Creek Apartments,
upperclassman housing, at 1.59 devices/person, which can likely be attributed
to the fact that these students have larger living spaces and thus more room
for Wi-Fi creature comforts like gaming consoles or smart devices. We
similarly find the next highest density in Crossman Hall, an engineering dorm,
and the second lowest density in Smith hall, an arts dorm.

###  5.3 Some Typical Usage Patterns

Now that the notion of a mean dorm has been established, we can normalize and
compare unlike dorms over time to find deviations from the average in day to
day behavior. The graphs showcased in this section are information dense; the
purple line represents the normalized device count (devices/person) for the
dorm in question, the black line represents the mean dorm device count, the
blue shaded areas showcase the standard deviation from the mean (darker is
smaller deviation), and finally the red and green shapes across the bottom are
the difference between the dorm’s device normalized count and the mean
normalized device count (green means the dorm has a higher normalized device
count, red means a lower normalized device count).

The snapshots in this subsection were taken from a standard week in Fall 2019
and is a good representation of standard behavior for the dorms.

Figure 3: Aden Hall compared to the mean dorm behavior for a normal week in
Fall 2019. For all mean dormitories images ”Red areas” correspond to fewer
devices than the mean and ”Green areas” correspond to more devices than the
mean.

Aden Hall, figure 3, consistently has higher than average device density for a
dorm. During peak usage, Aden can climb as high as 0.5 devices per person
higher than the average, and will generally fall three standard deviations
above the mean dorm. There are occasional times when the Aden device density
drops below the mean; these often happen late at night between the hours of
11PM and 8AM indicating that students in this dorm sign off earlier than
average.

##  6 The COVID-19 Perturbation

During Spring 2020, the rise and spread of COVID-19 resulted in a series of
COVID related announcements, culminating in the campus asking students living
in the dorm to leave. Using the notion of mean dorm behavior and using Fall
2019 as a baseline, we can see what effect that COVID had on the students and
if the manner in which they left campus is considered typical or not.

Figure 4: Aden Hall compared to the mean dorm behavior for the week students
were encouraged to leave campus due to COVID-19, Spring 2020. Compare this
image with raw data presented in ”Fig. 1”

Aden hall, figure 4, did not change behavior after the first official campus
announcement of COVID-19. Device usage patterns and density remained constant
until the first case appeared on campus. Almost immediately, students began to
leave and device density in Aden hall swiftly dropped to within one deviation
above the mean. In this dorm, students left at a rate very close to average;
campus administration encouraging students to leave had no apparent effect on
the rate in which they left.

###  6.1 The Rise of COVID-19 and The Timeline

  * •

Thursday, March 5th: First announcement to CU Boulder staff, students and
faculty of COVID-19, first two cases are confirmed in Colorado.

  * •

Monday, March 9th: Information begins to spread of the possibility of campus
reaction to COVID-19 disease.

  * •

Tuesday, March 10th: Some official campus visits are cancelled.

  * •

Wednesday, March 11th: CU announces the movement to online classes, as well as
cancelling official events over 150 people for the near future.

  * •

Thursday, March 12th: The first case of COVID-19 on campus is an employee who
worked in the Center for Community Dining Center (C4C).

  * •

Friday, March 13th: In person classes cancelled.

  * •

Saturday, March 14th: Williams Village Recreation Center closes indefinitely,
Main Campus Recreation Center operating on restricted hours.

  * •

Sunday, March 15th: Main Campus Recreation Center closes indefinitely, first
CU Boulder student case confirmed.

  * •

Monday, March 16th: Sororities and Fraternities require that students move out
by Friday, March 19. Students are strongly encouraged to ”return home.”

  * •

Tuesday, March 17th: CU Boulder 2020 commencement is cancelled.

##  7 Campus Response

CU Boulder quickly responded to the pandemic, mandating that classes take an
online or remote teaching approach soon after the recorded arrival of COVID-19
in Colorado. A day or two after the first recorded case arrived on campus, in
person classes was cancelled. Subsequently, CU Boulder administration, over
the the following week, transitioned to remote and online classes. It also
encouraged students not to return to campus after the Spring 2020 break.

###  7.1 A Naive Approximation and The Return That Never Was

Our data shows that compared to a normal break, students generally left far
sooner than expected. In some dorms, students began to move out as early as
the week before break. Due to mandatory online classes, we would expect to see
a higher device count in campus dorms, while in reality we saw quite the
opposite.

A general observation is that trends in the data during the early parts of the
semester do not vary significantly from week to week. As a result, we were
able to quickly infer device behavior in a standard week from any other
standard week in the year. With the COVID-19 perturbation to campus life, we
used a quick but naive visual assessment by simply comparing one similar week
to another to look for deviation in device behavior. We easily saw that
students were leaving sooner than expected; we also quickly anticipated from
looking at the data that, while not required at the time, students would stay
away from campus after break.

As spring break drew to a close, we monitored Wi-Fi activity in the dorms to
look for any sign of returning students in anticipation of possibly needing to
inform campus administration. Again, using a naive approach, we saw no signs
of a ”typical” return from a break, that is, when students returned to campus
there was visible ramp up in device count. This was not noted for dates after
spring break.

Figure 5 represents this naive approximation in the Smith resident hall. The
white curve depicts behavior from Fall Break 2019 and how we might reasonably
expect student managed devices to behave when students leave the dorm for an
extended period of time. The magenta curve presents student device data in
early parts of Spring 2020, before the pandemic, and the red line represents a
standard week from the Fall 2019 semester. Finally, the blue area below the
three upper curves depicts device response to the COVID-19 pandemic. We see
that, in terms of general trends during ”normal” weeks, one week’s behavior is
a relatively good predictor of another week’s. The bundle of curves just
mentioned, excluding the blue area, shows the usual ebb and flow of Wi-Fi
activity at CUB. This makes the COVID-19 response look even more dramatic in
comparison.

From these data, it is clear that students left campus roughly one week before
they were expected to for spring break, but in a more gradual fashion. At the
time, move out was not required, but encouraged, and it was unclear to
students how long they would be away from their dorms. As a result, most
devices had left by the time spring break would have started (note: the
baseline of 20 devices represents Wi-Fi enabled devices that are always
connected to the network). As time progressed, the devices stayed away, and it
became apparent that the return we would expect (the white line) was nowhere
in sight.

Figure 5: Smith Hall Wi-Fi device count for four weeks: October and November
2019 and February and March 2020 and compared to the mean dorm behavior for a
normal week, Fall 2019. Analogue behavior is clearly visible for several weeks
in the Fall 2019 and Spring 2020 as compared to indicated periods in the
included box.

As we proceed, a potentially useful scientific metaphor driving our research,
because we are collecting access-point data from across campus, is an analogue
to modern-day weather forecasting. More specifically, since such streaming
data were collected at specific locations in the campus ecosystem and
forecasts based on the spatial/temporal data were desired, we will view
Singular Spectrum Analysis as being analogous to the statistical technique of
empirical orthogonal functions (EOFs) used by L.F. Richardson and E. N. Lorenz
in their quest for increasingly accurate weather predictions.

By summing the first 10 Eigen Triples in the decomposition figure we produce
the rank-10 reconstruction that best approximates the initial streaming data
and produce the image shown in the next figure.

Figure 6: Normalized mean dorm device count reconstruction for the Spring 2020
semester using the first 10 Eigen Triples from our SSA decomposition. Dates
used were January 3rd to May 13 th, all reconstructed values less than zero
were considered to be zero. Figure 7: R-Forecast and V-Forecast using SSA
analysis. Training data included portions of the COVID-19 Perturbation data.
Dates used were March 21, 2020 to April 4, 2020. SSA R-forecasting strategy
generated reasonable predictions while SSA V-Forecasting did not.
Interpolation of the data, the white curve, was most reliably followed by
R-Forecasting.

The mean dorm is one crucial aspect of estimating populations on campus, since
there must be a normalizing factor given a gross Wi-Fi connection count. After
closer inspection, it is worth noting that peak device densities occur roughly
at midnight while the lowest device densities occur roughly at midday. This is
indicative of dispersal for classes during daytime hours and plays an
important role for population estimation discussed further in later sections.
The implication being that we must consider data during the nighttime when
most students are inside their respective residence halls.

##  8  Findings, Discussion, Concluding Remarks, and Future Work

An initial goal of this research was to better understand the dynamics of the
ebb and flow of aspects of campus life in the ecosystem on a major residential
research university as reflected by Wi-Fi count dynamics. Our strategic and
operational approach was to do this by working with CUB’s Office of
Information Technology (OIT) and specifically by collecting Wi-Fi usage data
at scale. By data at scale, we mean that the volume of daily data exceeds
multiple gigabytes, and therefore there is quite a lot of Wi-Fi connected
device count data to process. This was an observable variable that was a
proxy/surrogate for campus population dynamics.

This research’s point of view is that Wi-Fi at CUB not only presents a rich
source of information, but also that its granularity could lend itself to
differential data-driven prediction (DDDP) modeling, that is differential
equation models generated from data. For example, at CUB Wi-Fi data sets
contain 57,109,890 entries and with a point density of 1472.42857143
points/day. Further, and more importantly for this research’s point of view,
it offers a surrogate for the campus population.

Many new learning modalities and technologies demand network connectivity for
functionality. Further, and because CU Boulder is a research university, more
research devices are also demanding network access. Identifying such devices
provides a baseline for activities, examples of these devices include vending
machines in the AERO Space engineering building.

###  8.1 Building Clusters

This research demonstrates that buildings in the CU Boulder ecosystem are of
two types: dorms and ”everything else.” Dorms have nearly all contribution
covered by the ”first eigen triple” (ET1), implying that they have a high Wi-
Fi baseline of devices being used. Daily and weekly oscillations are
discernible in the subsequent eigen triples, and each account for
significantly less variation. However, both are roughly equal in their
contribution to the original signal. The conclusions that we reached was that
dorms have a high baseline of devices and exhibit approximately equal
contributions due to daily and weekly variations.

Other buildings in the ecosystem (C4C, Rec, Aero, …) exhibit much less
contribution by ET1 due to the extremely high daily variation and low baseline
connectivity. Despite different numbers of Wi-Fi devices, each of these non-
dorm buildings have the same structural frequency hierarchy. Explicitly, ETs 4
and 5 always seem to account for weekly oscillations that are independent of
the building and ETs 2 and 3 are always a part of the daily oscillations,
again, independent of the building. We interpret this as suggesting that these
buildings have similar usage behavior in addition to daily oscillations being
dominant over weekly oscillations. Further, facilities that do not house
students have similar behavior even though the number of people inside can be
significantly different between them. If we only considered ETs 1 through 5,
each one of these buildings would be in clusters, i.e. have the same grouping.
Finally, a surprise for this research was the number of devices, e.g. Vending
machines, that routinely access Wi-Fi and add to a building’s ecosystem.

###  8.2 SSA Forecasting:

Material on R-Forecast and V-Forecast using SSA analysis is presented in
chapter 3 of [7]. As noted in some training data included portions of the
COVID-19 Perturbation data. In this case the SSA R-forecasting strategy
generated reasonable predictions, while SSA V-Forecasting did not. We
conjecture that it is likely that more can be done using other matrix
decompositions beyond SSA, e.g. Non-Negative factorization is a good prospect.

###  8.3 Technology, Cybersecurity, and Policy:

Wi-Fi at present is likely the most popular form of wireless technology that
is adapted by IHEs to provide network services to students, faculty and staff.
Wi-Fi officially launched at CU Boulder in September 1999 and has been
evolving ever since with faster data rates and better security. Wi-Fi
currently operates on unlicensed frequencies in the 2.4GHz and 5GHz band,
making it possible for any enterprise to deploy a Wi-Fi network that enables
its stakeholders to be mobile and to connect to the private and public
networks. As a result, data density is increasing rapidly. However, legacy Wi-
Fi installations are present and developing current maps of access points
would be worth looking into as modeling and understanding based on data
analytics becomes more valued.

As expected organizations governing standards and certification bodies , e.g.
IEEE and the Wi-Fi Alliance, continue to improve Wi-Fi standards and ensure
compatibility between Wi-Fi devices from over 800+ Wi-Fi product companies.
Due to the popularity of Wi-Fi and the ability for Wi-Fi to positively impact
GDP, the FCC is considering opening more spectrum that could leverage the Wi-
Fi investment. This means that with the eventual roll out of 5G, spectrum
sharing, and more, smart infrastructures will be developed and deployed.
Understanding the impact on not only IHEs but societal infrastructure will
become increasingly important. The interplay and connections are forcing the
emergence of new languages, new analysis tools, and ultimately better
forecasting of the ’weather’ in such ecosystems, thus leading to the
possibility of new ways of thinking about issues of Technology, Cybersecurity
and Policy.

###  8.4 Future Work

Since IHEs are at the forefront of components of emerging trends in demand for
connectivity, computation, connections, data flows, and innovations they are
excellent environments to deploy passive and active sensors an harvest data
streams. Melding the computational and mathematical tools that are emerging
almost lend themselves to a near real time understanding of these vital
ecosystem. The point of view of this research is that much can be learned
about smart and connected environments through an examination of data streams.
This research is looking forward to the ”return” of faculty staff and students
and using some of the tools mentioned here to extract further patterns of
emergence in the IHE ecosystem.

##  9  Acknowledgments

Special thanks to OIT and the Campus Chief Security Officer for helping to
make campus Wi-Fi data available for analysis and modeling. Many of the ideas
and framing were developed because of colleagues in Technology, Cybersecurity,
Policy program and from seminar presentations in that program. Special thanks
to speakers: John Scrano of Zayo, Tom Kellerman of VMware, and Professor
Kristine Kaminski of Wolf Law and Dr. Amie Stefanovic, and my colleague Dr.
Kevin Gifford. Thanks also to Joshua Park for aiding in the editorial
contributions to this article; Jackson Trust for several formative discussions
and finally, thanks to unnamed colleagues for providing feedback on earlier
versions of the manuscript.

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##  10 Biography

|  First Author. Jake McGrath is an MS. student at the University of Colorado
Boulder he holds a BS in Aerospace Engineering Sciences with minors in Applied
Mathematics and Leadership Studies with the President’s Leadership Class form
the University of Colorado Boulder.
---|---
|  Second Author, Armen Davis is a Senior at the University of Colorado
Boulder Majoring in Applied Mathematics and with a focus in the Atmospheric
Sciences.
---|---
|  Third Author Dr. James H. Curry, Professor of Applied Mathematics and
Computer Science, teaches in the Technology, Cybersecurity and Policy program
at University of Colorado, Boulder. Curry is also a Member of National
Academies Board on Mathematical Sciences and Analytics (BMSA). His research
interest include numerical methods, dynamical systems, linear algebra, data
analytics. E-mail<EMAIL_ADDRESS>
---|---
|  Fourth Author. Orrie Gartner is the Director of Operations for the Office
of Information Technology at at the University of Colorado Boulder. His focus
is the application of IT to support and advance the mission of the University
while overseeing daily operations and long term planning of reliable, high-
performance, secure and scalable infrastructure.
---|---
|  Fifth Author, Jr. Glenn Rodrigues is a Senior Mobility and Wireless
Architect at the University. Glenn leads Wi-Fi architecture design,
configuration and support for one of the largest single site deployments of
Wi-Fi in the state of Colorado. He is responsible for the vision, and driving
an innovative and high ROI wireless strategy for the campus. Glenn introduced
mapping customer mobility business needs and workflow into wireless technology
solutions.
---|---
|  Sixth Author. Dr. Seth Spielman is Associate Professor of Geography and
Director of the University of Colorado Boulder office of Data Analytics. His
research focus is spatial data, data analytics, modeling.
---|---
|  Seventh Author. Dr. Dan Massey is Professor of Computer Science and former
Director of the Technology, Cybersecurity and Policy program. His research
focuses on cybersecurity for traditional systems, emerging cyber physical
systems and the Internet of Things. Prior to joining CU, he was a Program
Manager in the Department of Homeland Security, where his programs included
denial of service defense, cyber physical system security for vehicles,
medical devices and building controls.
---|---