$D=0$. In the $j^{\text{th}}$ round of multicasting by node $k^{\star}_{j}$,
$D$ gets updated by adding to it the time of last node receiving the packet
successfully as:

$D=D+\max\limits_{i\in\bar{N}_{j}}t_{i},$ (3)

where $\bar{N}_{j}=\\{i\in\Pi_{u}|\delta_{i}=0\\}$, and $t_{i}$ is the minimum
access time of node $i$. The multicasting rounds continue until either i) all
unvisited nodes become visited, i.e., $\Pi_{\text{u}}=\Pi_{\text{v}}$, or ii)
When $D$ exceeds a threshold $\theta_{D}$, in that case the packet is dropped.

Reliability can be defined as the ability of the network to perform its
required functions for a certain period of time without service interruption.
A link breakage can occur due to the following reasons:

  * •

The receiver is outside of the transmission range of the transmitter

  * •

The packet is lost due to channel errors

  * •

The packet is lost due to total delay $D$ exceeding threshold $\theta_{D}$.

Assuming users are not moving, as in [324], each D2D receiver is randomly and
independently located around its corresponding transmitter with isotropic
direction and Rayleigh distributed distance with probability density function
(PDF):

$f_{\text{D}}(r)=2\pi\lambda re^{-\lambda\pi r^{2}},\text{ }r\geq 0.$ (4)

The probability that a user is outside the transmission range $R$ of the
transmitter can be calculated as
$p_{\text{R}}=1-\int_{0}^{R}{f_{\text{D}}(r)dr}=e^{-\pi\lambda R^{2}}$.

Considering log-normal shadow fading, the signal fades: (1) deterministically
with a path-loss exponent $\alpha$, and (2) stochastically represented by a
random variable with zero mean and a variance $\sigma$. Therefore, the
probability $p_{\text{e}}$ that a packet is not lost due to channel errors is
given in [325]:

$p_{\text{e}}=1-\frac{1}{2}+\frac{1}{2}\operatorname{erf}\left(\frac{\beta_{\text{th}}-\alpha\times
10\log(r)}{\sqrt{2}\sigma}\right),$ (5)

where $\beta_{\text{th}}$ is the minimum threshold required to deliver a
packet between nodes.

Finally, we combine what we have discussed to get the link reliability as:

$R_{\text{L}}=p_{\text{e}}+p_{\text{R}}+p_{\text{drop}}.$ (6)

where $p_{\text{drop}}=\mathcal{P}\left(D>\theta_{\text{D}}\right)$.

##  X Big Data Challenges and Open Issues for CPS

While ongoing research is focusing on CPS enterprise development and
applications, effective solutions to combat security flaws have not received
the enough attention, which places question marks on the foreseen integration
of CPS in critical infrastructures. This matter is made worse with CPS devices
having i) computational challenges in ensuring data confidentiality and
privacy protection; ii) the semi- or fully-autonomous security management
[326]; and iii) the high computational costs of employing cryptography [327].
Low-complexity and lightweight ciphers such as PRESENT [328] have been
developed; however research efforts should go beyond cryptography, especially
that such solutions can be costly in terms of i) latency, ii) power
consumption, and iii) key management complexity [329, 330]. Furthermore,
different CPS applications might have different security perimeters with a
multitude of interactions among devices. This complicates further the access
control decisions, the trustworthiness of entities, and their authentication
management. Therefore, there is a high need to define secure interoperation
protocols and strategies for dynamic CPS, where devices from different
applications interact together to complete specific tasks [331].

Privacy preserving is an important aspect of big data analytics and mining.
Homomorphic encryption techniques, as mentioned in Section VII-B, have been
suggested to perform analysis on encrypted data in cloud. However, they turned
out to be impractical and inefficient in terms of computational time and
overhead for large amount of datasets. Although anonymization techniques
constitute a more efficient solution for privacy protection big data
analytics, further research efforts are needed to determine their
applicability for different big data types, and their performance evaluation
and endurance in different mining techniques as outlined in Section VI-A.
Moreover, future solutions should be based on the hierarchy property of many
CPS big data applications [222]. This means that future research should be
directed towards proposing integrated privacy preserving protocols in the
modules of the CPS hierarchical structure that can perform analytical
processes on encrypted variety of big data types in a time- and cost-efficient
manner.

Correctness of CPS is another research area under the spotlight of attention.
Due to dynamic nature of physical environment, CPS need to constantly be
adapted to new situations while operating and functioning properly with little
or no human supervision [332]. The use of models can allow the early detection
of failures by simulating different components of complex designs to verify
the integration of the whole system [333, 334]. CPS components verification to
ensure they are working properly or that they meet execution time requirements
is another approach to ensure correctness [335, 336, 337]. Future research
shall focus on creating robust real-time anomaly detection and correctness
techniques that have low overhead and implementation costs.

With CPS being employed on a large scale, data access, routing, transmissions,
and processing might consume a significant amount of time, leading to real
obstacles in the way of realizing ultra-reliable and low latency
communications (URLLC), a key feature for emerging 5G technologies. In URLLC,
stringent requirements are placed on latency, throughput, and availability.
Future research should be directed towards faster data access from the clouds
with fewer data re-transmissions in order to free up resources and reduce
latency. Obviously, there is a trade-off between throughput (or end-to-end
delay) and reliability due to transmission errors that might be caused by
links failure, security policies, caching misses, scarcity of resources and so
on. For instance, cross-layer designs protocols between different CPS layers
(sensing, middleware, transmission, management and services layers) can be
used in a similar way to the wireless communication protocols to help optimize
different parameters from latency to reliability and security. An example
would be the transmission layer communicating with the sensing layer about
integrating data filtering aimed at prioritizing the sensed data in the case
of too many re-transmissions.

For faster data collection, research efforts need to shift towards devices
that do not need to preconfigure to a network with dynamic on-the-fly D2D
connectivity, and without the need of controllers or infrastructure
deployment. Furthermore, to extend the communication range among devices,
incentivized devices with tokens will replace dedicated relays [338]. In terms
of CPS computing, research directions should shift towards faster data
processing via moving data processing closer to the sources and speeding-up
big data handling. For a faster and efficient CPS analysis, research
activities need to be further conducted on information fusion techniques,
especially that information originates from heterogeneous devices with varying
capabilities. Through perfecting the fusion algorithms, related information
can be aggregated for analysis leading to higher quality information [339].

As mentioned in this survey, big data analytics is one of the most important
aspects of CPS, as it helps to pave the way for new opportunities and
services, in addition to enhancing or even optimizing systems’ performance.
However, as discussed in Section III, the sensed data can originate from a
variety of sources with unstructured formats. Merging these different data
types into single homogeneous structures is vital to ease and speed up the
analysis process so meaningful conclusions can be drawn and automated
decisions can be made [340]. How to homogenize different data sources remains
an open research issue for CPS. Moreover, different CPS applications might
need to collaborate together to achieve a specific mission. For instance, the
mobile-health application might need to collaborate with the transportation
system to get an ambulance as fast as possible in the case of patient’s
biomedical sensors revealing an emergency situation. In such scenarios, data
analytics becomes a challenging task as it requires to be able to put the
different analysis fragments from different CPS applications together to
provide broader conclusions and decisions making.

##  XI Conclusion

The emerging CPS technologies mutually benefit the technological advancements
in big data processing and analysis. When combined with artificial
intelligence, machine learning, and neuromorphic computing techniques, CPS
will bring about new applications, services and opportunities, all envisioned
to be automated with little or without human intervention. This will help
revolutionize the “smart planet” concept, where smarter water management,
smarter healthcare, smarter transportation, smarter energy, and smarter food
will create a radical shift in our lives. In this survey paper, we have
provided a broad overview of CPS big data collection, storage, access,
caching, routing, processing, and analysis to support understanding and
discovering the challenges facing CPS, the existing proposed solutions, and
the open issues that are yet to be addressed. Then, we have discussed the
security vulnerabilities of CPS and the different security solutions, as well
as how big data meet green challenges for CPS systems to address
sustainability and environmental concerns. Finally, some challenges and open
issues for CPS have been addressed.

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|  Rachad Atat received the B.E. degree (with distinction) in computer
engineering from the Lebanese American University, Beirut, Lebanon, in 2010,
the M.Sc. degree in electrical engineering from the King Abdullah University
of Science and Technology (KAUST), Thuwal, Saudi Arabia, in 2012, and the
Ph.D. degree (with Hons.) in electrical engineering from the University of
Kansas (KU), Lawrence, KS, USA, in 2017. He is currently a postdoctoral
research associate at Texas A&M University at Qatar, working on dynamic
metering allocation with integrated cybersecurity measures in smart grids. His
current research interests include smart grids, cybersecurity, and Internet of
Things. Dr. Atat was a recipient of the 2016 IEEE Global Communications
Conference Best Paper Award, the NSF Travel Grant Award in 2016, the KU
Engineering Fellowship Award, and the KAUST Discovery Scholarship Award.
---|---
|  Lingjia Liu (SM’15) received the B.S. degree in Electronic Engineering from
Shanghai Jiao Tong University, Shanghai, China, and the Ph.D. degree in
Electrical and Computer Engineering from Texas A&M University, College
Station, TX, USA. He spent more than three years working in the Standards &
Mobility Innovation Laboratory, Samsung Research America (SRA) where he
received the Global Samsung Best Paper Award twice (in 2008 and 2010,
respectively). He was leading Samsung’s efforts on multiuser MIMO, coordinated
multipoint (CoMP), and heterogeneous networks (HetNets) in 3GPP LTE/LTE-
Advanced standards. Lingjia Liu is an Associate Professor in the Bradley
Department of Electrical and Computer Engineering (ECE) of Virginia Tech (VT).
He is also serving as the Associate Director for Affiliate Relations in
Wireless@Virginia Tech. Prior to that he was an Associate Professor in the
Electrical Engineering and Computer Sciences Department, University of Kansas
(KU). His research interests include emerging technologies for Beyond 5G
cellular networks including machine learning for wireless networks, massive
MIMO, massive MTC communications, and mmWave communications. Lingjia Liu was a
recipient of the Air Force Summer Faculty Fellow from 2013 to 2017, the Miller
Scholar at KU in 2014, the Miller Professional Development Award for
Distinguished Research at KU in 2015, the 2016 _IEEE_ GLOBECOM Best Paper
Award, the 2018 _IEEE_ ISQED Best Paper Award, the 2018 _IEEE_ TAOS Best Paper
Award, and the 2018 _IEEE_ TCGCC Best Conference Paper Award.
---|---
|  Jinsong Wu (SM’11) received his Ph.D. in Electrical and Computer
Engineering from Queen’s University, Kingston, Canada. He was the leading
Editor and a co-author of the comprehensive book, entitled “Green
Communications: Theoretical Fundamentals, Algorithms, and Applications”,
published by CRC Press in September 2012. His first-authored paper won 2017
IEEE System Journal Best Paper Award. He received 3 best paper awards for IEEE
conference papers. He received IEEE Green Communications and Computing
Technical Committee 2017 Excellent Services Award for Excellent Technical
Leadership and Services in the Green Communications and Computing Community.
He also received IEEE Outstanding Leadership Award in 2013 IEEE International
Conference on Green Computing and Communications (Greencom) and 2016 IEEE
International Conference on Big Data Intelligence and Computing (DataCom),
IEEE Computer Society. He is elected Vice Chair, Technical Activities, IEEE
Environmental Engineering Initiative, a pan-IEEE effort under IEEE Technical
Activities Board (TAB). He was the founder (2011) and founding Chair
(2011-2017) of IEEE Technical Committee on Green Communications and Computing
(TCGCC). He is also the primary co-founder (2015) and founding Vice-Chair of
IEEE Technical Committee on Big Data (TCBD). He was the proposer (2012),
founder (2014) and Series Editor (2014 - 2017) of IEEE Series on Green
Communication and Computing Networks in the IEEE Communications Magazine. He
is Area Editor (2016 - present) of IEEE Transactions on Green Communications
and Networking. He was the original proposer (2012) and Series Editor
(2014-2016) of the IEEE Journal of Selected Areas on Communications (JSAC)
Series on Green Communications and Networking. He is Editor of IEEE
Communications Surveys and Tutorials, Associate Editor of IEEE Systems
Journal, Associate Editor of IEEE Access. He was the one of the earliest key
proposers and a long term promotor from Green Track to a full green symposium
in flagship conferences of IEEE Communications Society. He opened and
established Big Data Track with general and wide topic coverage in the
flagship conferences of IEEE Communications Society, starting at IEEE Globecom
2016. He has been conference chairs and main organizers in a number of IEEE
conferences and workshops.
---|---
|  Guangyu Li received the B.S. degree from China University of Mining and
Technology and M.S. degree from Tongji University, China, in 2008 and 2011,
respectively, and the Ph.D. degree in computer science from University of
Paris-Sud, Paris, France, in 2015. He is currently working as an assistant
professor with the Key Laboratory of Intelligent Perception and Systems for
High-Dimensional Information of Ministry of Education, Nanjing University of
Science and Technology, Nanjing, China. His current research interests include
routing protocol design for vehicular networks, big data transmission,
electric vehicles charging/discharging strategy design in smart grid and
traffic control.
---|---
|  Chunxuan Ye received his Ph.D. from University of Maryland, College Park in
2005. Between 2005 and 2012, he worked for InterDigital Communications, Inc.
on multiple advanced research projects in the wireless communications field.
He worked for Intel on LTE modem chipset development between 2012 and 2015. He
has been working for InterDigital Communications, Inc. as a 3GPP RAN1
standards delegate for new radios (5G) since 2015. Chunxuan Ye has more than
30 book chapters, conference and journal papers. He also has more than 60 U.S.
and international patent applications with 25 U.S. patents granted. His
specialties include wireless communications, wireless standards and
technologies, information theory, software and firmware development.
---|---
|  Yang Yi (M’09-SM’16) is an assistant professor in the Bradley Department of
Electrical Engineering and Computer engineering at the Virginia Tech. She is
an IEEE senior member. She received the B.S. and M.S. degrees in electronic
engineering at Shanghai Jiao Tong University, and the Ph.D. degree in
electrical and computer engineering at Texas A&M University. Her research
interests include very large scale integrated (VLSI) circuits and systems,
computer-aided design (CAD), neuromorphic architecture for brain-inspired
computing systems, and low-power circuits design with advanced nano-
technologies for high-speed wireless systems..
---|---