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Low-Latency Upstream Scheduling in Multi-Tenant, SLA Compliant TWDM PON

Arijeet Ganguli and Marco Ruffini

School of Computer Science and Statistics, Trinity College Dublin, Ireland

<EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

We present a multi-tenant multi-wavelength upstream transmission scheme for
virtualised PONs, enabling compliance with latency-oriented Service Level
Agreements (SLAs). Our analysis highlights an important trade-off between
single-channel vs. multi-channel PONs, depending on ONUs tuning time.

##  1 Introduction

Over the past decade, network architectures have transitioned from closed
systems to open and disaggregated systems. Software Defined Networking (SDN)
and Network Function Virtualization (NFV) have played a key role, offering
programmability, cost efficiency and flexibility. Passive Optical Networks
(PONs) have experienced a similar transition towards virtualisation [2, 3],
which enables dynamic software-based control of scheduling algorithms and
multi-tenancy. This means independent Virtual Network Operators (VNOs) are
able to run multiple independent upstream scheduling algorithms in a shared
PON.

In order to support 5G and beyond use cases and business applications
(including fronthaul for different type of mobile services), which require low
latency guarantee, PONs will need to support Service Level Agreements (SLAs).
This means that capacity sharing cannot be achieved at the expense of latency
performance. This issue has been addressed by work in [3], where DBA
algorithms can be modified to suit specific applications, and in [4], with the
development of a virtual Dynamic Bandwidth Allocation (vDBA) architecture,
which allows tenants to specify indiviual allocation grant with microsecond
precision.

In this work we extend our vDBA concept to a multi-channel PON network, where
the merging of Bandwidth Maps (BMaps) is carried out across multiple
wavelength channels. The OLT, besides indicating the time at which the ONUs
can transmit, it also indicates the wavelength channel. The key objective is
to define a number of SLAs, expressed in terms of maximum latency and
compliance level, and to propose an algorithm that can operate the Bandwidth
Map merging operation, minimising the probability to breach SLAs, across all
VNOs.

The evaluation of our work is based on two key performance analysis. First we
compare the latency for systems using different line rates and number of
channels. Assuming an overall PON capacity of 200Gb/s, we consider a system
with 8 channels at 25Gb/s, one with 4 channels running at 50Gb/s, and one with
a single channel at 200Gb/s (being single channel there is no multi-wavelength
allocation for the 200Gb/s option). Then we show how the difference in
performance changes when we consider different tuning times for the ONU
transmitters. For this we compare the case of negligible tuning time (i.e., if
the system implements channel bonding, [5], so that the ONU has more than one
transceiver always ready to transmit at least at another wavelength); the case
of Class 1 transmitters (i.e., tuning time $<10\mu s$) [6], with tuning time
of 250 ns (i.e., close to the burst overhead time) and 1 us; and a Class 2
transmitters (i.e., tuning time $>10\mu s$ but $<25ms$), with tuning time of
15 us. Class 3 devices are not considered has they have tuning times longer
than 25 ms, which is more than two order of magnitudes higher than the PON
frame, and would in practice represent a semi-static allocation.

Our results show that our proposed multi-wavelength algorithm is capable of
maintaining high percentage of SLA compliance, even for high network load. In
addition, we highlight an important trade-off between the latency of multi-
channel systems and the transmitters’ tuning time. If the tuning time is
negligible compared to the burst overhead, the multi-channel system has better
latency performance. This is due to the fact that the burst overhead tends to
have similar time duration independently of the line rate [7], thus higher
line rate channels require a proportionally larger amount of bits than lower
line rate channels. However as the ONU tuning time increases, the single
channel system outperforms the multi-channel ones.

##  2 System architecture

The use case and architecture addressed in this work is shown in Fig. 2. In
our approach, multiple VNOs run different schedulers in parallel (vDBAs), each
forwarding a virtual Bandwidth Map (vBMap), which allocates upstream
transmission slots to a group of ONUs. This for example allows multiple mobile
operators to run fronthaul services (i.e., 7.2 RAN split), using independent
Cooperative Transport Interfaces (CTI) The scheduling hypervisor (or merging
engine) collects all such virtual bandwidth maps to create a single physical
bandwidth map, resolving any collisions between slots overlapping in time.
Such collisions can be resolved by delaying some of the grants (at the risk of
breaching SLAs). In this multi-wavelength approach, the OLT also has the
option to select transmission over different channels, to minimise grant
delay, although this is constrained by the ONU tuning time. Our merging engine
makes these decisions based on specific Service Level Agreements (SLAs), so
that it minimises the probability of breaching SLAs (which is key for
supporting 5G and future 6G services). The use of a stateful algorithm, which
takes into consideration the history of a service flow when making scheduling
prioritisation decisions, is preferred to stateless algorithms[8]. This is
because a stateful algorithm can prioritise flows depending on how close they
are to breaching their specific SLA target [9].

Thus in this work, we propose a heuristic stateful TWDM scheduling algorithm.
The objective of the algorithm is to maximise the SLA compliance across all
the flows during upstream transmission. We focus specifically on the
additional latency introduced by the multi-sharing aspect of the PON. An SLA
breach occurs when a given flow accumulates a number of delayed upstream slots
that is above its target SLA threshold. For example for an SLA with maximum
merging delay of 25 $\mu s$ with 99% compliance, every time an upstream slot
is delayed by more than 25 $\mu s$ with respect to the requested time slot in
the virtual BMap, we increment a counter. If the counter goes above the non-
compliance rate (in this case 100-99=1%), calculated over a number of frames
(i.e., we use a 1ms window, which is the time duration of a 5G sub-frame),
then we consider that an SLA breach has occurred.

The problem can be formulated as Mixed Integer Programming (MIP) as shown in
Fig. 2. Equation (1) calculates the maximum delay of any given allocation to
remain within the target threshold for SLA breach. We maintain a 4 dimensional
binary decision variable matrix X where the objective function is explained as
follows - the inner truth value function calculates the packet level breach
and the outer truth value function calculates the flow level breach across
each virtual BMap. Equation (3) is the constraint that any particular channel
at any time slot transmits at most 1 BMap allocation. Equation (4) is the
constraint that all BMap allocations are alloted unique channel time-slot
pairs. Equation (5) checks the conservation of BMap allocations within each
virtual BMap.

Fig. 1: TWDM multi-tenant upstream scheduling algorithm

Fig. 2: MILP Notations and Equations

The algorithm maintains a few key data structures. A flow-breach likelihood
table keeps track of how far each traffic flow is from breaching its SLA
(i.e., going above non-compliance rate); this is important to minimise SLA
breach, as the algorithm will prioritise scheduling for the flows that are
closer to breach their SLA. A channel freetime table maintains and updates the
earliest free time of each channel over time, i.e., when the channel can be
reallocated to a different BMap allocation. We also keep track of the earliest
free time of the various transceivers of the ONUs (i.e., depending on the ONU
tuning time).

With reference to Fig. 7, the algorithm first calculates the allocation
maxtime which is the latest time an allocation can be scheduled within its
latency target (code lines 1 to 3). Then, it starts allocating slots to the
various allocations according to the time assigned by their originating
virtual BMaps (code lines 5 to 6). Next, it resolves collisions (lines 8 to
21) by allocating slots first in increasing order of non-compliance rate (line
18), then increasing order of their maxtimes (line 19) and finally increasing
order of their sizes (line 20). Lines 22 to 43 traverse the sorted BMap and
allocates channel and scheduling time for the allocations. Lines 23 to 26
first get the allocation ONU id, then use it to get the free times of all the
transceivers of the respective ONU, then allocates the earliest free
transceiver and receiver for transmission of the BMap allocation. Line 27
checks the channel free time table and allocates the earliest free wavelength
for transmission. Lines 29 to 34 check if tuning of the transceiver to a new
channel is required. Lines 35 and 36 calculate the earliest transceiver and
receiver free times, respectively. Lines 37 to 40 calculate the scheduling
time for transmission according to whether tuning is required or not and lines
41 to 43 assign the transceiver id, receiver id and scheduling time memory
variables of the BMap allocation object. Finally, the lines 44 to 47
recalculate the non-compliance rate of all the flows and updates the flow-
breach table for scheduling of the allocations in the next time frame.

##  3 Performance Evaluation

In order to set up the simulation environment, we generate input BMaps from
different VNOs. The allocation load on the shared PON was considered for 20%,
50% and 80% of the total upstream capacity (i.e., 200Gb/s across all channels
considered). For each of this allocation loads, we then varied the percentage
allocated to SLA-driven flows from 10% to 100% of the total load (the
remaining part is allocated to best effort flows). We consider 5 VNOs (each
one generating a virtual BMap every frame (125 $\mu s$)) and 2 types of SLAs:
one requiring 90% compliance with a latency target of 12.5 $\mu s$ and one
requiring 95% compliance with a latency target of 25 $\mu s$. Each bandwidth
map has a uniformly distributed set of allocations, with average burst size
set at 6% of the total frame size for a 25Gb/s line rate (the same ONU is also
allowed to provide multiple burst per frame). An empty time slot of 0.33 $\mu
s$, is introduced between allocations to account for guard time between
upstream transmissions. Each ONU has one transceiver, which is tunable on any
of the available channels, and constrained by a tuning time, which is a
simulation parameter. As mentioned above, the system under investigations, are
8 x 25Gb/s, 4 x 50Gb/s and 1 x 200Gb/s channels. The tuning times considered
span from negligible to 250 ns, 1 $\mu s$ and 15 $\mu s$.

The experiment was run for 5000 time frames and the average number of SLA
breaches is recorded. The results show the ability of the system to comply
with the SLAs (y axis) versus the percentage of total flows that require SLA.
The different plots in the same figure consider PON loads of 20%, 50% and 80%
of the total capacity.

The plot in Fig. 7 reports the ability to meet SLA for negligible channel
tuning time. We can see that up to 50% load there is always full compliance
(except a slight drop for SLA flows above 90%). For 80% load, compliance
starts dropping from 60% of SLA traffic for the 8X25G and 4x50G systems and
from 50% for the 1x200G. As mentioned above the multi-channel approaches
outperform the single channel as at 200G rate the burst overhead is
proportionally larger (i.e., in terms of bits required). As the tuning time
increases, in Fig. 7, 7 and 7, we see that the latency performance of the
multi-channel system decreases, as the algorithm progressively looses the
ability to avoid scheduling delays by tuning on different channels.

Fig. 3: Pseudocode for TWDM

Fig. 4: Tuning time: 0s

Fig. 5: Tuning time: 250ns

Fig. 6: Tuning time: 1$\mu s$

Fig. 7: Tuning time: 15$\mu s$

##  4 Conclusions

In this work, we presented a heuristic stateful algorithm for upstream
scheduling in a TWDM multi-tenant PON, capable of satisfying SLAs. We show the
role that ONU tuning time plays in terms of latency performance in the trade-
off between higher capacity single channel and lower capacity multi-channel
systems. While we believe that there is room for improvement in multi-channel
scheduling algorithms for longer tuning times, the current results show that
tuning times between 250 ns and 1 $\mu s$ would be required to maintain
satisfactory performance in multi-tenant, multi-channel PON systems.

Acknowledgments. Support from SFI grants 12/RC/2276_p2, 17/CDA/4760 and
13/RC/2077_p2 is acknowledged.

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##  Appendix A Overview of subgrid physics models

###  A.1 NewHorizon

NewHorizon uses the adaptive mesh refinement code (AMR) RAMSES (Teyssier,
2002). Star formation is set to occur in regions with hydrogen gas number
density higher than $10$ cm-3, following the Schmidt law:
$\dot{\rho_{\star}}=\epsilon_{\star}\rho_{\rm{g}}/t_{\rm{ff}}$, which relates
the star formation rate mass density, $\rho_{\star}$, to the gas mass density,
$\rho_{\mathrm{g}}$, local free fall time of the gas, $t_{\rm{ff}}$ and lastly
a varying star formation efficiency, $\epsilon_{\star}$ (Kimm et al., 2018;
Trebitsch et al., 2021). The star formation efficiency is computed following
the prescriptions of Hennebelle & Chabrier (2011), which account for the
turbulence of the gas. H and He gas are modelled using an equilibrium
chemistry model with a homogeneous UV background. This gas is allowed to cool
to $\simeq 10^{4}$K through collisional ionisation, excitation, recombination,
Bremsstrahlung, and Compton cooling. This gas, if metal enriched is allowed to
further cool down to 0.1 K using the rates from Dalgarno & McCray (1972) and
Sutherland & Dopita (1993).

The impact of supernovae (SNe) on the gas and therefore, star formation is
another process below the resolution limit of cosmological simulations.
NewHorizon models each SNe as an explosion releasing $10^{51}$ erg of energy
into the surrounding baryons, with a minimum of 6 M⊙ needed in a star to go
SN, they model a specific SNe rate of 0.03 M${}_{\scriptstyle\odot}^{-1}$
using the mechanical SN feedback scheme described in Kimm & Cen (2014) and
Kimm et al. (2015).

NewHorizon implements two modes of active galactic nuclei (AGN) feedback,
thermal and kinetic (radio and quasar), depending on the accretion rate of the
supermassive black hole (following Dubois et al., 2010; Teyssier et al.,
2011). AGN feedback can help remove gas from the galaxy and/or heat it up
making it unsuitable for star formation.

###  A.2 EAGLE

EAGLE runs on the Lagrangian Smooth Particle Hydrodynamic (SPH) code GADGET-3.
Star formation is implemented stochastically, following the pressure law
scheme of Schaye & Dalla Vecchia (2008), implementing the observed Kennicut-
Schmidt (Schmidt, 1959; Kennicutt, 1998) relation into the simulation. Star
formation is set to occur in regions with a metallicity-dependent hydrogen
mass density threshold, formulated by Schaye (2004), to account for the more
efficient radiative transfer in metal-rich gas clouds. Stellar particles are
assumed to follow a Chabrier IMF (Chabrier, 2003), with stars spanning from
0.1-100 M⊙. EAGLE accounts for stellar winds, radiation and SNe feedback by
implementing their collective feedback through thermal heating, distributing
the energy produced at each timestep by a stellar particle to the neighbouring
particles using the stochastic thermal feedback scheme of Dalla Vecchia &
Schaye (2012).

The radiative cooling and heating rates of gas resolution elements at a given
density, temperature and redshift are computed with the software CLOUDY
(Ferland et al., 1998). The gas is assumed to be optically thin, in an
ionisation equilibrium and exposed to the cosmic microwave background and a
spatially homogeneous UV/X-ray background that evolves over time (Haardt &
Madau, 2001; Wiersma et al., 2009). EAGLE implements one mode of AGN feedback
through stochastic heating, following the prescriptions of Dalla Vecchia &
Schaye (2008) and Booth & Schaye (2009).

###  A.3 IllustrisTNG

TNG used the moving mesh code AREPO (Springel, 2010), which differs from AMR
code (e.g. RAMSES) and SPH code (e.g. GADGET-3) in that it uses an
unstructured mesh defined by a Voronoi tessellation of a set of discrete
points. This alternative methodology was formulated to address issues with AMR
and SPH, which impact their accuracy in particular situations (e.g.
suppression of fluid instabilities in SPH and lack of Galilean invariance and
overmixing present in AMR codes).

TNG models star formation stochastically, treating the star formation and
pressurisation of a multi-phase interstellar medium following Springel &
Hernquist (2003). In the model by Springel & Hernquist (2003), cold gas above
a density threshold of $0.1$ H cm-3 forms star particles following the
empirically defined Kennicutt-Schmidt relation (Schmidt, 1959; Kennicutt,
1998) and the Chabrier IMF (Chabrier, 2003). Under the Springel & Hernquist
(2003) prescription, SNe pressurises the gas and can lead to enhanced star
formation. The stellar winds produced by star formation can carry and inject
kinetic energy into the surrounding gas. They are modelled as described in
Vogelsberger et al. (2013) and Pillepich et al. (2018a).

The radiative cooling of gas is modelled accounting for its metal enrichment
(following Wiersma et al., 2009), and a time-evolving homogeneous UV
background with self-shielding corrections in dense interstellar medium
(following Katz et al., 1992; Faucher-Giguère et al., 2009). Following the
models of Vogelsberger et al. (2013), radiative cooling is further influenced
by the nearby radiation fields of AGN.

TNG implements subgrid AGN feedback with a radio and quasar mode. For
accretion rates below 5% of the Eddington limit, the radio-mode feedback is
active, injecting bursty thermal energy into a $\sim 50$ pc bubble displaced
away from the host galaxy (Sijacki et al., 2007). For higher accretion rates
the quasar mode is active, injecting thermal energy continuously into the
adjacent gas (Springel et al., 2005a; Di Matteo et al., 2005) The details of
all subgrid physics can be found in Weinberger et al. (2017); Pillepich et al.
(2018a) and Nelson et al. (2019).

###  A.4 Magneticum

Magneticum Pathfinder simulations are a suite of cosmological hydrodynamical
simulations, ranging in box size from $25.6^{3}$ to 38183 cMpc3. We use the
Box4-uhr simulation, which models the physics of dark matter and baryons in a
$68^{3}$ cMpc3 box. Magneticum Pathfinder has been performed with a modified
version of the Lagrangian Smooth Particle Hydrodynamic (SPH) code GADGET-3,
with modifications on the viscosity and treatment of the kernel functions
following Dolag et al. (2005), Donnert et al. (2013), and Beck et al. (2016).
Star formation and the stellar wind-driven kinetic feedback are modelled
following Springel & Hernquist (2003). Each star particle represents a stellar
population following a Chabrier IMF (Chabrier, 2003) and each gas particle can
form up to 4 stars. Star formation and metal enrichment from supernova
feedback and Asymptotic Red Giant Branch stars is modelled following the
Springel & Hernquist (2003) as well as the local metallicity dependent
processes (Wiersma et al., 2009; Dolag et al., 2017). The radiative cooling
and heating rates of gas resolution elements at a given density, temperature
and redshift are computed with the software CLOUDY (Ferland et al., 1998). The
radiative cooling accounts for a UV/X-ray background following the
prescriptions of Haardt & Madau (2001) and Wiersma et al. (2009).

The subgrid physics treatment of supermassive black holes and their AGN
feedback is implemented as described by Fabjan et al. (2010) and Hirschmann et
al. (2014). The implemented black holes feedback scheme accounts for a
transition from quasar to radio mode according to (Sijacki et al., 2007). Note
that the black holes in this simulation are not pinned to the potential
minimum. Thermal conduction is implemented according to Dolag et al. (2004)
but following Arth et al. (2017), with 1/20 of the classical Spitzer value
(Spitzer, 1962). The details of all subgrid physics are described by Teklu et
al. (2015) and Hirschmann et al. (2014).

##  Appendix B Tidal feature detection limits

Figure 13: The maximum stellar mass from the host galaxy that in the same
region as the tidal feature without making it undetectable as a function of
the tidal feature stellar mass. For a tidal feature to be detectable it has
SNR$>5$. Figure 14: The $r$-band surface brightness of the model tidal
features as a function of their radii and the corresponding maximum possible
surface brightness of the light from the host galaxy within the tidal features
area such that the tidal feature is still detectable. The tidal features panel
shows the surface brightness of each tidal feature as a function of the radius
of the circle the light is spread over. The remaining panels show the maximum
surface brightness of the light from the host that can be within the same
region as the tidal feature without making it undetectable for each
simulation. The colours correspond to the stellar masses of the tidal
features, $10^{6}$, $10^{7}$, $10^{8}$, $10^{9}$ and $10^{10}$ M⊙. The LSST 10
year $r$-band, $3\sigma$, $10^{\prime\prime}\times 10^{\prime\prime}$,
limiting surface brightness is shown in Rubin Turquoise.

The stellar mass resolutions of our simulations as well as the surface
brightness limits of our mock images limits the minimum stellar masses of the
tidal features we can resolve. Through some simple modelling we investigate
the tidal feature detection limits for each of our simulations. Following
Martin et al. (2022) we calculate the signal-to-noise ratio for a tidal
feature against its background galaxy and take a SNR${}_{\mathrm{tidal}}>5$ as
the range for a detectable tidal feature.

$\mathrm{SNR}_{\rm tidal}=\frac{n_{\rm tidal}}{\sigma_{\rm
tidal}}=\frac{n_{\rm tidal}}{\sqrt{2n_{\rm host}+n_{\rm tidal}}}$ (4)

Here, $n_{\rm tidal}$ is the number of particles that comprise a tidal
feature, $n_{\rm host}$ is the number of particles from the host in the same
region as the tidal feature. Using this equation and the simulation mass
resolutions (Table 1) we determined for each of our simulations, given a tidal
feature of a specific stellar mass, what was the maximum amount of stellar
mass from the host that could be in the same region without making the tidal
feature undetectable. The results of this calculation are shown in Figure 13,
where we show the maximum host stellar mass contamination in the same region
as the tidal feature as a function of tidal feature stellar mass. We can see
that each simulation has a drop off corresponding to where its mass resolution
is limiting its ability to resolve tidal features with SNR$>5$ without there
being virtually no contamination from the host galaxy. From this calculation
we can predict that NewHorizon is able to resolve tidal features that are
$\gtrsim 2$ orders of magnitude less massive than in the other three
simulations. NewHorizon should also be able to resolve tidal features with
much greater contamination from the host galaxy when compared to the other
three simulations.

To investigate the minimum mass galaxy that can be tidally disrupted and
detected in our mock images, we must construct a model for the surface
brightnesses of tidal features stemming from different stellar mass hosts. We
build a simple model assuming the following:

  * •

the mass-to-light ratio for the stellar particles is 1,

  * •

the light from a tidal feature is homogeneously distributed across a square
region.

While mass-to-light ratios vary as a function of galaxy morphology (e.g. de
Zeeuw et al., 2002; Emsellem et al., 2004; Cappellari et al., 2007) and could
vary significantly across a galaxy (e.g. Mehrgan et al., 2024), 1 is a
physical mass-to-light ratio and eases computation substantially. The
homogeneous distribution of light across a square area is a simplifying
assumption that allows us to compute the surface brightness of tidal features
without simulating features of varying light distributions and regions. If the
mass-to-light ratio for the tidally disrupted galaxy is above 1 or the
distribution of the light is inhomogenous resulting in some regions that are
brighter than the average brightness of the tidal feature, the resultant tidal
features would be detectable despite having lower stellar mass than our
estimates.

We convert from the physical surface brightness of the stellar particles in
L${}_{\scriptstyle\odot}\text{ pc}^{-2}$ to LSST r-band surface brightness in
mag arcsec-2 using the following relationship:

$\mu_{r}=-2.5\log_{10}(\mathrm{SB}(\mathrm{L}_{\scriptstyle\odot}\mathrm{\>pc}^{-2}))+M_{\scriptstyle\odot,\mathrm{r}}+5\log_{10}\bigg{(}\frac{648000}{10\pi}\bigg{)}$
(5)

where we use the estimated absolute AB magnitude of the Sun in the LSST
$r$-band, $M_{\scriptstyle\odot,\mathrm{r}}=4.64$ (Willmer, 2018).

The left most panel in Figure 14 shows the surface brightness with tidal
feature extent for tidal features of stellar masses $10^{6}$, $10^{7}$,
$10^{8}$, $10^{9}$ and $10^{10}$ M⊙. The surface brightness profiles in
remaining panels of Figure 14 indicate the maximum allowed host brightness
within the same area to still allow the tidal feature to be resolved against
the host background contamination. We compute these assuming a minimum
SNR${}_{\rm tidal}>5$ and again assuming the host light is distributed evenly
in the background. Our results highlight that even tidal features from
galaxies that are 106 M⊙ are above the mock image surface brightness limits
provided their radius remains within $\sim 6$ pkpc. However, only NewHorizon
has the sufficient resolution to resolve them so long as the light from the
host galaxy in the same region as the tidal feature is of a similar brightness
or fainter. The surface brightness profile for the maximum allowed host
contamination indicates that the these features are only detectable if there
is a similar amount of light from the host in this region. From Figure 13 we
can estimate that NewHorizon will resolve a $10^{6}$ M⊙ feature within the
survey detection limits if there is $\lesssim 1.5\times 10^{6}$ M⊙ of stellar
mass from the host within the same region, provided the feature is no more
extended than $\sim 6$ pkpc. For the larger cosmological simulations, we can
detect tidal features of stellar mass $\gtrsim 10^{8}$ M⊙ even if they have
been disrupted over extents $\gtrsim 50$ pkpc, so long as the host stellar
contamination is $\lesssim 1.5\times 10^{8}$ M⊙ within the same region. As the
tidal features become more massive than these lower limits, the maximum
surface brightness of the host galaxy within the same region as the tidal
feature increases for each of the simulations.


# Cost Optimisation of an Instrument Suite at an Accelerator-Driven Spallation
Source

P.M. Bentley  European Spallation Source ESS AB, P.O. Box 176, 221 00 Lund,
Sweden  Department of Physics and Astronomy, Uppsala University, Box 256, 751
05 Uppsala, Sweden<EMAIL_ADDRESS>C.S. Zendler  European Spallation
Source ESS AB, P.O. Box 176, 221 00 Lund, Sweden  O. Kirstein  European
Spallation Source ESS AB, P.O. Box 176, 221 00 Lund, Sweden  Department of
Physics and Astronomy, Uppsala University, Box 256, 751 05 Uppsala, Sweden
School of Mechanical Engineering, University of Newcastle, Australia

###### Abstract

This artcile presents an optimisation of performance and cost of neutron
scattering instrumentation at the European Spallation Source. This is done by
trading detailed cost functions against beam transmission functions in a
multi-dimensional, yet simple, parameter space. On the one hand, the neutron
guide cost increases as a power of the desired beam divergence, and inversely
with the minimum wavelength, due to the supermirror coating needed. On the
other hand, the more neutrons are transported to the instrument the greater
are the shielding costs to deal with the gamma rays that result from the
eventual absorption of the neutrons. There are additional factors in that many
of the parameters defining the neutron guide geometry are continuous
variables, and the straightness of the guide increases the transmission of
high energy spallation products, which affect the specifications of
particularly heavy hardware, such as heavy shutters and additional shielding,
beam stops etc. Over the suite of 16 instruments, a maximum potential cost
saving is identified in the vicinity of 20 M€ , with negligible penalties on
instrument performance and bandwidth, by trading minimum neutron wavelength
$\lambda$ against total optical costs and shielding costs. Finally, these cost
calculations are shown to be consistent with those at real world, existing
spallation source facilities.

###### pacs:

##  I Introduction

Modern neutron scattering instruments at spallation sources are expensive,
costing in the region of 12-20 M€. Typically, an instrument has a working
lifetime of approximately 10-20 years. At the time of writing, the budget for
the instrument suite of 16 instruments at the ESS, including ramping up all of
the suport functions, is around 211 M€, from a total facility budget of 1 843
M€.

It is imperative that facilities of this scale strike the appropriate balance
of cost and performance, to maximise the return on investment and create as
large a benefit as possible from the available resources.

It will be shown later in this report that a significant fraction of the cost
of each instrument, around 30-50%, is spent on shielding and neutron optical
components ESS-CostCatWorkshop . Indeed, shielding is the main cost driver,
costing around 30% of the total budget. Shielding is directly linked with
instrument background noise — and hence instrument user quality — along with
safety and regulatory factors. As such, one might expect that this area of
expertise would receive more attention in the neutron scattering community
than it does.

In the past, shielding and optics tended to be optimised somewhat
independently. We show in this article that successful cost optimisation and
instrument background reduction is considerably easier if the whole system is
designed and optimised together as a single task for an expert team. Indeed,
at the European Spallation Source (ESS), Sweden, and the Paul Scherrer
Institut (PSI), Switzerland, a core risk and cost minimisation strategy is to
design the optics and shielding systems together by co-located personnel using
a common set of tools and with thorough cross-checking in place.

In this article, an initial stage of this work is summarised. Preliminary
specifications and requirements are identified for the instrument suite
beamline systems, and the cost of those systems is minimised to a critical
performance metric value to be defined shortly. Systems exceeding this metric
value could be defined as being over-engineered, and systems below this value
as under-performing. This allows us to define an optimum cost for the
instrument suite.

Finally, it will be shown that by strategically selecting a subset of
“primary” instruments, which are fully optimised, and reducing the
specifications of the remainder into the under-engineered category, a further
set of cost savings are possible with a viable suite, with a small decrease in
performance.

##  II Input Data and Cost Estimates

There are two beam scenarios to consider in this initial study. The first
evaluates the shielding costs for a direct beam with line of sight back to the
source, and the latter is with part of the beam line curved out of line of
sight.

###  II.1 Line of Sight Option

This shielding is thick, since it must protect against scattered high energy
(MeV - GeV) neutrons and gamma rays. We use a rough cost estimate for an
enhanced concrete instrument cave for straight beamlines, based on the PSI
instrument “BOA”, increased in thickness to 2 metres, and accomodating
$5\times 5\times 5$ m3 of instrument space. These specifications were for a
generic instrument, based partly on calculations of minimum thickness for a MW
spallation source with a GeV proton beam, and partly on measurements at PSI
and SNS on fast neutron transmission and prompt pulse backgrounds, which
usually adversely affects instrument performance.

A completely straight beamline also requires a heavy chopper — commonly known
as “$T0$”, “$t$-zero”, or “Prompt Pulse Suppression” (PPS) choppers: these are
heavy choppers that attenuate the high-energy particles during proton
illumination of the spallation target. The cost of these T0 choppers was
estimated roughly and somewhat optimistically by the ESS Chopper group,
assuming some economy of scale by manufacturing multiple units and minimising
development costs.

The instrument also requires a heavy shutter, capable of blocking the high
energy beam and allowing access to the sample area. A study performed by the
ESS engineering department for an SNS-style cylindrical drum shutter was
completed in 2013, which provided the cost estimates for this item. Note that
a guillotine-style shutter outside the monolith is not recommended due to the
vertical streaming paths this would generate next to the short instruments.

###  II.2 Out of Line of Sight

This option has a similar cost of guide shielding as that of an instrument at
a reactor source. A thickness of 60 cm of regular concrete was found via
preliminary Monte-Carlo calculations to attenuate the radiation sufficiently
to safe levels (1.5 $\mu$Sv/h total simulated dose rate 111The requirement is
actually 3$\mu$Sv/h. A factor of 2 between simulated dose rate and actual
requirement is used to compensate for discrepancies between computer models
and engineering designs.). 60 cm of concrete is slightly thicker than other
lower power facilities but not excessive. For example, on TS2 at ISIS, 35 cm
of concrete shielding is sufficient, although in that case a heavy shutter can
be closed if there is a safety hazard on a beamline.

###  II.3 Concept Neutral Costs

For the instrument cave, we assume an enclosure similar to those at the LET
and OFFSPEC instruments on TS2 at ISIS, in the UK. These are hollow steel cans
filled with borated paraffin wax.

The cost of concrete comes from ESS Conventional Facilities Department, and is
the price for reinforced concrete, cut and shaped and installed.

The cost of raw metals come from the London Metal Exchange.

In all beamlines, it is anticipated to use at least three laminate collimation
blocks within the shielding bunker and/or curved sections, to reduce the
streaming of fast neutrons into the guide system downstream. These may be
conceptually similar to the collimator on the CHIPIR beamline at ISIS, or
indeed much smaller, and spread between multiple units. Other names for these
devices could include “horse-collars” or “fast neutron scrapers”. For the
purposes of this study, we assume these to be three units of 1 m3 of copper
with a small channel cut through the centre.

A summary of the items can be constructed as follows:

ISIS-TS2 Wax Cave

based on LET and OFFSPEC, for thermal beams out of line of sight. Cost: 950
kGBP several years ago, rounded to 1.5 M€.

PSI Concrete Cave

based on BOA, for beams with direct line of sight: 2 M€.

Heavy beam shielding

for beam areas within line of sight: approx. 7770 €$/m$.

Light beam shielding

for thermal beams out of line of sight: approx. 2600 €$/m$.

Laminate collimation blocks

initially costed as 100% copper: 47 k€per unit, 3 units per beam.

T0/PPS Chopper

: only necessary for straight beamlines with line of sight of source, 750 k€.

Heavy shutter

: only necessary for straight beamlines with line of sight of source, 750 k€.

Not included in this budget estimate are the ESS guide bunker and target
shielding, which absorb a large fraction of the radiation dose. We only
include shielding items outside the common shielding areas. This has a
potential cost-saving from the perspective of the instrument project, since —
if the geometry loses line of sight within the bunker — the instrument only
needs thermal beam shielding in its budget.

The optical system costs are evaluated for the full length of the beamline.
However, curving out of line of sight quickly, with a radius of 1.5 km for
example, increases the optical cost compared to a gentle curvature of several
km, because the neutron supermirrors need to be engineered to reflect at
larger grazing angles. At still tighter radii, of a few hundred metres, the
neutron guides are normally divided into several thin channels known as
“multi-channel benders”. These require more precision manufacturing, with a
greater surface that needs to be coated with supermirrors. It should be clear
that, whilst curving out of line of sight quickly can reduce the shielding
cost, the optical cost is increasing against the shielding cost saving. These
two costs are traded against each other in our optimisation.

Optical component cost equations were provided to ESS as part of a market
survey, and these are commercial-in-confidence details that cannot be widely
shared. However, they are comparable to costs of items at similar facilities,
as nothing in the market has changed significantly in recent years.

##  III Requirements and Matched Optical Solutions

Instrument requirements were extracted initially from the ESS Technical Design
Report (TDR) ESS-TDR-2013  and gradually refined with requirements described
in the respective instrument proposals. The minimum wavelength band of the
instrument suite is shown in figure 1. Here we can see that there are three
categories of instrument: those who are interested in wavelengths at and just
below 1 Å and above; those interested in 2 Å neutrons and above, and those
interested only in cold neutrons of 4 Å wavelength and longer.

Subdividing into long (150 m) and medium (60 m) instruments is informative.
The minimum wavelength band of the long instruments is shown in figure 2c,
where we see that the long instruments are split almost 50:50 into 2Å and
$\sim$1Å instruments.

For the medium-length instruments, the wavelength bands are shown in figure 3.
In that subset, there are two instruments requiring wavelengths around 1 Å,
and a third requiring 5 Å.

The shorter instruments follow a similar process, except with the 15 m
instruments who are considered to be so short that they are either straight or
use a multi-channel bender.

We can now begin to construct a critical performance/cost ratio transport
system as a standard, to compare with the baseline systems from the instrument
teams. There are four curved guide systems to consider: two sets of curved
guides for the 150 metre instruments for the two wavelength ranges; two sets
of curved guides for the 60 metre instruments for the two wavelength ranges.
Similarly, there are four types of benders for the two lengths and two
wavelength ranges. The 150 metre instruments can have a 20 metre long bender
within the bunker, and the 60 metre instruments can have a 15 metre long
bender, and each of these is designed for different wavelength bands.

###  III.1 Standard Guide Concept

To compare with the proposed optical systems, a more minimalist neutron guide
concept was developed at ESS for these kinds of studies. In this “ESS Standard
Guide”, elliptic geometries are replaced with constant cross section
geometries or ballistic geometries. Supermirror $m$ values are capped at $m=4$
for 12 m long ballistic focussing sections, and $m=1.5$ everywhere else. Note
that this concept still provides more than 50% of the neutron flux at 1 Å if
the guides are curved, due to the large radii involved with such long guides.
The maximum dimensions of the guide are limited to below 4 cm in the curved
sections.

###  III.2 Curved Guides

A number of curved guide options will be considered. The performance estimates
follow the work of Mildner MILDNER-CURVED-GUIDE-ACCEPTANCE-DIAGRAMS  which is
reliable for the low-divergence parts of the guide systems with low-$m$
values, which is the strategy in this case.

All the guides in the low cost options will be considered to have a maximum
size of 200 mm in horizontal and vertical extent. The curved guides have an
additional constraint that the curved parts have a width of 4 cm.

The parallel section of the guides is capped at $m$=1.5. If we restrict
ourselves to guarantee the phase space homogeneity at 1.5 Å then, with 12 m
long compression/expansion sections at the ends of the ballistic guides, we
only require $m$=4 coatings. This still provides a maximum beam divergence of
1∘. The transmission of this guide system is shown in figure 2c. For the 60
metre guides, a higher $m$ is required to get out of line of sight in a
shorter distance. The transmission of this guide system is shown in figure 3.

###  III.3 Multi-Channel Bender Options

These items are necessary to get out of line of sight quickly in the bunker.
The first solution matches the requirements of transmitting 1 Å neutrons, and
is described in table 1.

The second version of this item is designed to transmit 2 Å neutrons, and is
described in table 2.

Figure 1: Wavelengths requested by each instrument on the reference suite at
ESS.

(a)

(b)

(c)

Figure 2:
(a) Wavelengths requested by the 150 m long instruments at ESS.
(b) Transmission of a multi-channel bender designed to transmit 1 Å neutrons
to the 150 m long instruments at ESS. The specifcations of this bender are
given in table 1
(c) Transmission of a multi-channel bender designed to transmit 2 Å neutrons
to the 150 m long instruments at ESS. The specifcations of this bender are
given in table 2

.

(a)

(b)

(c)

Figure 3:
(a) Wavelengths requested by the 60 m medium length instruments at ESS. “Fund”
corresponding to “Fundamental physics” requests 5 Å.
(b) (b) Transmission of a multi-channel bender designed to transmit 1 Å
neutrons to the 60 m long instruments at ESS. The specifcations of this bender
are given in table 3.
(c) Transmission of a multi-channel bender designed to transmit 4 Å neutrons to the 60 m long instruments at ESS. The specifcations of this bender are given in table 4. Table 1: 150 metre bender specifications for efficient transmission of 1 Å neutrons. Parameter | Value
---|---
150 m bender width | 4.0 cm
150 m bender length | 20 m
150 m channel width | 0.5 cm
150 m bender m | 3.0
150 m nchannels | 8.0
150 m bender radius | 1250.0 m
150 m transmission at 1 Å | 80%
150 m Cost | 1.444 M€
Table 2: 150 metre bender specifications for efficient transmission of 2 Å neutrons. Parameter | Value
---|---
150 m bender width | 4.0 cm
150 m bender length | 20 m
150 m channel width | 2 cm
150 m bender m | 2.5
150 m nchannels | 2
150 m bender radius | 1250.0 m
150 m transmission at 2Å | 88%
150 m Cost | 341 k€
Table 3: 60 m bender for 1 Å neutrons. Parameter | Value
---|---
60 m bender width | 3.0 cm
60 m bender length | 15 m
60 m channel width | 0.5 cm
60 m bender m | 3.0
60 m nchannels | 6.0
60 m bender radius | 937.5 m
60 m transmission at 1Å | 73%
60 m Cost | 742 k€
Table 4: 60 m bender for 4 Å neutrons. Parameter | Value
---|---
60 m bender width | 4.0 cm
60 m bender length | 15 m
60 m channel width | 2 cm
60 m bender m | 1.5
60 m nchannels | 2
60 m bender radius | 703.0 m
60 m transmission at 4Å | 85%
60 m Cost | 193 k€

##  IV Suite Cost Totals

The cost per instrument as a function of instrument length is shown for the
standard instrument options in figure 4 on page 4.

Figure 4: Cost of each instrument using the standard ESS guide concept, to
isolate the cost delta for the different curving options (therefore omitting
the baseline suite).

There it is clear that a general strategy of curving all the guides is cheaper
overall. The cheapest possible method is using simple curved guides, since the
additional cost of multi-channel benders is not offset by the cost savings in
shielding outside the bunker. On the other hand, these marginal differences
between the curved guides and benders are a small increment to pay for likely
improvements in the instrument backgrounds.

Furthermore, we also see that the total cost delta for a straight guide _vs_ a
curved guide is 1-2 M€ per instrument, on average. This seems approximately
correct, considering the main cost drivers in the cost delta, namely a $T0$
chopper, heavy shutter, and enhanced instrument cave.

The total instrument suite cost for the full suite is shown in figure 5 on
page 5 for each option, and the potential savings in figure 6 on page 6.

Figure 5: Total cost for the instrument suite considered. Figure 6: Total cost
saving for the instrument suite considered, for each of the options, relative
to the baseline of as-proposed optics geometry.

In these figures, the following options are costed:

  * •

“Baseline” which is the total of the instrument proposal costs, corrected
where necessary (explanation in next paragraph)

  * •

“Standard” which is a reduction of the optical specifications towards a
standard ESS guide

  * •

“Std Curved” which forces all beamlines to be curved out of line of sight,
losing line of sight 50% of the way down the beamline, in addition to
following the ESS standard guide design

  * •

“Std Bender” which follows the ESS standard guide design and has a multi-
channel bender to lose line of sight in the bunker.

One can see that, relative to the baseline, the standard curved guide concept
is likely to save 24 M€ across the suite, with minimal impact on the
instrument performance.

##  V Costing Validation

For any publicly funded project it is important to get an as good as possible
cost indication early and refine estimations as soon as more detailed
information becomes available. The instruments described in ESS-TDR-2013
allowed for an indicative cost, which is part of the total ESS construction
cost of 1.843 B€ established in 2013.

Over the last 3 years, the instrument concepts were refined primarily in terms
of scientific requirements but not so much in terms of costs. On the other
hand it is the central facility’s responsibility to manage the available
budgets as efficiently as possible to maximise the scope for and involvement
of in-kind partners throughout Europe. In order refine the cost of neutron
instrument components (aka beamline components or instrument components or
simply components), a workshop was held in early 2014, which involved partners
from ISIS in the UK, PSI from Switzerland, and JCNS from Germany, all of which
have an extensive and excellent track record of building world-class neutron
instruments .

During the workshop, a list of around 20 components with indicative costs —
based on recent projects such as ISIS TS-II ISIS-TS2  or the JCNS spin-echo
instrument BL-15 at SNS JCNS-SNS  — was established, which included e.g.
shutters, benders, instrument caves but also services for installation or
staff/labour costs ESS-CostCatWorkshop . Although the scope of the instrument
programme was not defined at that time, the components were used to

  1. 1.

Better estimate the costs of the TDR reference suite,

  2. 2.

To gradually refine costs as instrument concepts became better defined, and

  3. 3.

To independently assess costs to obtain the best “value-for-money” for all the
partner countries involved in the instrument build programme, and consequently
the tax payers within the partner countries.

From ESS-CostCatWorkshop , a cost distribution for instruments as shown in
fig. 7 can be obtained.

Figure 7: Approximate cost distribution of components for neutron scattering
instruments considered to be built at the ESS.

While — for good reason — a lot of focus is currently on e.g. detector systems
for ESS instruments due to the difficulty to acquire large quantities of 3He
gas ESS-Detector-Strategy , it may come as a surprise that around 47% of the
total costs fall into the categories “Shielding” and “Optics”, with 31% and
16%, respectively. For the instruments described in the TDR — with adjustments
to consider improvements in the scientific requirements/specifications — one
would arrive at an overall cost of around 290 M€. While the reference suite
comprises 22 instruments, the current scope of the instrument build programme
is 16 (it is worthwhile noting that the 16 instruments are part of the ESS
Construction Programme; plans have been developed and will be refined over the
next 2-3 years to arrive at 22 public instruments described in ESS-TDR-2013 ).

For a suite of 16 instruments one would estimate costs of 211 M€. As indicated
by fig. 7 the majority of the costs are associated with shielding/optical
components, and amongst those components the main cost drivers are instrument
caves (initially valued at 2.5 M€) and neutron guides (initially valued at
30k€/m; including not only the glass components but also required shielding).
A simplistic approach ignoring any cost-benefit analysis would require for
only instrument caves and guide systems of 16 instruments a budget of around
83 M€, which is consistent within an error of around 10% with the baseline
cost indicated in fig. 6. The arguments provided earlier in terms of
optimising e.g. instrument caves as a function of ‘curved/straight’
immediately changes cost requirements for only instrument caves from around 40
M€ to 26 M€ thus giving a potential cost saving of 14 M€. Similar arguments
can be applied for different guide geometries, curvatures resulting in approx.
1 M€ per instrument, and a total of 16 M€ $+$ 14 M€$=$ 30 M€, which is — again
within a 10% error — consistent with results discussed in the context of fig.
6.

In terms of project management one could also use the results indicated in
fig. 6 to perform an indicative PERT (e.g. PERT-ESTIMATION ) estimation with

  * •

the Std Curved option saving being the optimistic estimation

  * •

the Standard option being the pessimistic estimation

  * •

the Std Bender option being the best guess estimation

Usually, a PERT analysis is used to regulate optimism and pessimism in
schedule estimates, but we can also apply the same logic here for cost option
extrema, resulting in a potential saving of 17 M€.

###  V.1 Approximate Benchmarking

For the moment it is assumed that the cost per instrument can be reduced from
14.5 M€ to 13.5 M€ using the more conservative PERT estimation. At ESS the
average length of an instrument is 90 m due to the long pulse design. At short
pulse spallation sources such as SNS or ISIS instruments are on average around
50 m long, resulting in an average cost of around 12.2 M€${}_{\\_}{2015}$.

ISIS’ recent TS2 project was established with an budget of 145 M£, out of
which 100.5 M£ were allocated to the core project and 27 M£ for the instrument
project with the remaining 17.5 M£ for instruments coming from the EU and
collaborating European countries ISIS-TS2-BC , a similar model that is used
for the phase 2 upgrade of TS2 ISIS-TS2 . The initial scope of TS2 included 7
instruments or an average cost of 6.4 M£. A conservative estimation of
inflation would assume a cost increase of around 20% since 2005 EuropeanHCIP
resulting in 7.7 M£${}_{\\_}{2015}$. Over the last years the average exchange
ration between € and £ was 1:1.28 HistoricConverter  giving 9.8
M€${}_{\\_}{2015}$ for an average instrument of around 50 m length. The main
difference between the 12.2 M€${}_{\\_}{2015}$ and the 9.8 M€${}_{\\_}{2015}$
can easily be explained by a slightly higher-level of complexity of ESS
instruments due to the different source characteristics, but also due to the
fact that ESS is a green field site. Also, it can be assumed that additional
effort, in particular with regard to installation, is required to due to the
in-kind nature of the project.

While all the numbers are only indicative — details matter after all — they
nevertheless show that proper strategies and analyses such as benchmarking,
component breakdown, cost-benefit analysis or efficient standardised technical
solutions via optimised non-recurrent engineering designs have the potential
to optimise costs, which is not a surprise in itself. Although the focus here
is on optical and shielding components any cost optimisation has two major
consequences: obviously, it reduces overall costs, which is in the interest of
the project governance and the funding agencies; but secondly, because
standardised systems are proposed with almost no or minimal impact on
performance, costs related to installation, maintenance and spare parts are
being reduced, which in turn will lower the operational costs. As the
operational costs are estimated to be typically 4 times the initial investment
cost in case of a scientific facility, this has a significant effect over the
lifetime of the facility.

It may actually be more appropriate to refer to a cost optimisation of x M€
because the aim is not to minimise the costs by all means but to rather use
the available budget more intelligently and focused by e.g. redistributing
costs into areas such as computing, installation or contingency if required,
but also to compensate for any shortfalls of the initial assumptions when
creating the list of components. It is also worthwhile noting that at this
point no significant de-scoping of instruments in terms of their scientific
performance or functionality is discussed. This is an alternative project
management tool that, whilst popular and utilised in large scale scientific
projects, nonetheless can have a devastating impact on the scientific output
of a facility, and the methodology presented here should probably be used
_before_ removing scope from the instrument projects themselves.

##  VI Conclusions

We have used neutron optics geometry combined with a cost-benefit analysis
balancing shielding costs, to propose an optimisation of the ESS instrument
suite budget. Cost savings in the order of 20 M€ are identified compared to
the baseline budget as defined in the adjusted instrument proposal costs. This
cost saving has been compared with instrument costs at existing facilities,
and found to be within reasonable agreement. While this approach is common in
industry, it is perhaps less widely used in scientific projects, and the
management challenge to unlock these savings, at any facility, is to establish
a strong central coordination mechanism: to supply standard concepts and
systems such as the ones described here; to provide a core team to manage the
suite optimisation; and to intervene when deviations from the standards are
being pursued, particularly in the cases where small performance increases are
accompanied by large cost impacts.

###### Acknowledgements.

The information and support given by our partners and colleagues from ISIS,
PSI and JCNS, in particular with regard to establishing a cost baseline for
instrument components, is greatly appreciated. We are also extremely grateful
for the feedback given at various ESS project reviews on this work,
particularly K. Herwig, D. Mildner, E. Iverson, M. Fitzsimmons, S. Kennedy, T.
Sato and T. Krist. Useful discussions with the rest of the Neutron Optics and
Shielding Group during 2013-2014 were invaluable, particularly C. Zendler, D.
Martin Rodriguez, D. DiJulio, N. Cherkashyna, and C. Cooper Jensen.

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