Modelling Rayleigh Fading Channel in Underwater Wireless Communication Networks using Stochastic Network Calculus


  • M. R. Christhu Raj
  • Rajeev Sukumaran



Stochastic Network Calculus, Deterministic Network Calculus, Fading, Underwater Acoustics, Backlog


A fundamental issue in underwater acoustic wireless channels is in analyzing the backlog and delay bounds that directly impacts the Quality of Service (QoS) performance in networks. Modern networks have been increasingly complex over the past few years in terms of control algorithms, applications and service expectations. Deterministic Networks Calculus (DNC) is not applicable to analyze QoS for the present day packet switched multimedia networks due to their inherently random behavior. To overcome these issues, Stochastic Network Calculus (SNC) has given rise to the optimism that it can emerge as an elegant mathematical modeling tool for assessing current network performance. In this work, we develop an underwater acoustic wireless channel subject to fading eects based on SNC that obtains Stochastic Arrival Curve (SAC) and Stochastic Service Curve (SSC). Using this we also derive the stochastic performance for delay and backlog bounds in underwater acoustic fading channel. The simulation performance analysis and bounds show that this method can provide guidelines for designing transmission strategies in underwater acoustic wireless channels.


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H.Wang, J.Jiang, X.Shen, J.Bai, Modifying SNR-Independent velocity estimation method to make it suitable for SNR estimation in shallow water acoustic communication, Journal of North-western Polytechnical University, volume 27, no. 3,(2009), pp. 368-374.

F. Ciucu, A. Burchard, J. Liebeherr, Scaling properties of statistical end-to-end bounds in the network calculus, IEEE Transactions on Information Theory, volume 27, no. 6, (2006), pp. 2300-2312.

K. Wang, C. Lin, SRD service: A stochastic network calculus approach for di erentiation analysis, in Proc of IEEE International Conference on Communications, Cape Town, South Africa. (2010), pp. 1-5.

N. Dutta, I.S. Misra, Use of service curve for resource reservation in wired-cum-wireless scenario, International Journal of Computer Science and Information Security, volume. 7, no. 2 (2010), pp. 87-93.

Rajeev Sukumaran, Christhu Raj M R Modeling UWSN Simulators - A Taxonomy, Inter- national Journal of Computer, Electrical, Automation, Control and Information Engineering volume 9, no. 2 (2015), pp. 585-592.

Christhu Raj M R, Rajeev Sukumaran, Modeling and Simulation of Acoustic Link Using Mackenzie Propagation Speed Equation, International Journal of Computer, Electrical, Au- tomation, Control and Information Engineering, volume 9, no. 10 (2015), 2075-2083.

F. De Rango, F. Veltri, P. Fazio, A Multipath Fading Channel Model for Underwater Shallow Acoustic Communication, IEEE ICC Signal Processing for Communications Symposium, (2012), pp. 3811-3815.

Jess Llor and Manuel Perez Malumbres, Statistical Modeling of Large-Scale Signal Path Loss in Underwater Acoustic Networks, Sensors, volume. 13 no. 1, (2013), pp. 2279-2294.

Dilip Roy, Discrete Rayleigh Distribution, IEEE Transactions on Reliability, volume. 53, no. 2 (2004), pp. 255-260.

Jan Sijbers, Arnold J, den Dekker, Paul Scheunders, Dirk Van Dyck, Maximum?Likelihood Estimation of Rician Distribution Parameters, IEEE Transactions on Medical Imaging, vol- ume. 17, no. 3, (1998), pp. 357-361.

Amine Laouriner, Betting on Gibert-Elliot Channel, IEEE Transactions on Wireless Com- munications, volume. 9, no. 2, (2010), pp. 723-823.

Mukesh Kumar Mishra, Neetu Sood, Ajay K Sharma, Ecient Analysis of OFDM System over Nakagami-m Fading Channel, International Journal of Advanced Science and Technol- ogy, volume. 37, (2011), pp. 37-46.

Mohammad Sadeghi, Mehdi Barati, Peformance Analysis of Poission and Exponential Dis- tribution Queuing Model in Local Area Network, International Conference on Computer and Communication Engineering, (2012), pp 499-503.

Christhu Raj M R, Rajeev Sukumaran Stochastic Network Calculus for AWGN Fading in Underwater Wireless Communication networks, Australian Journal of Basic and Applied Science, volume. 9, no. 31, (2015), pp. 253-262.

Rajeev Sukumaran, Christhu Raj M R Stochastic Network Calculus for various Fading tech- niques in Underwater Wireless Communication, International journal of Applied Mathemat- ics and Statistics, volume. 55 no. 1, (2016), pp. 100-112.

Huimin She, Zhonghai Lu, Axel Jantsch, Dian Zhou, Li-Rong Zhe, Modelling and Analysis of Rayleigh Fading Channels using Stochastic Network Calculus, IEEE Conference on WCNC, (2011), pp. 1056-1061.

O. Boxma, On a tandem queueing model with identical service times at both counters part Advances in Applied Probability, volume. 11, no. 3, (1979), pp. 616-659.

Christhu Raj M R, Rajeev Sukumaran, Acoustic Link modeling using speed of sound equa- tions for Underwater wireless sensor networks applications, Australian Journal of Basic and Applied Sciences, volume. 9, no. 36, (2015), pp. 437-448.

S. Ayyorgun and W. Feng, A systematic approach for providing end-to-end probabilistic QoS guarantees, In Proceedings of the International Conference On Computer Communications and Networks (ICCCN), (2004), pp. 115-122.

F. Baskett, K. M. Chandy, R. R. Muntz, and F. G. Palacios, Open, closed and mixed networks of queues with di erent classes of customers, Journal of the ACM, volume. 22, (1975), pp. 248-260.

J. Choe and N. B. Shro , A central-limit-theorem-based approach for analysing queue be- haviour in high-speed network, IEEE/ACM Transactions on Networking, volume. 6, no. 5, (1998), pp. 659-671.

Y. J., Y. C., and M. Y, Flow interception problem with double capacitated service, China Journal of Highway and Transport, no. 17, (2004), pp. 85-88.

J.-Y. Le Boudec, Application of network calculus to guaranteed service networks, IEEE/ACM Transactions on Information Theory, volume. 44, no. 3, (1998), pp. 1087-1097.

M. Fidler, An end-to-end probabilistic network calculus with moment generating functions In proc of IEEE 14th International Workshop on Quality of Service (IWQoS), (2006), pp. 261-270.

M. Fidler, A network calculus approach to probabilistic quality of service analysis of fading channels, In Globecom, (2006).

J.-Y. Le Boudec, Application of network calculus to guaranteed service networks, IEEE/ACM Transactions on Information Theory, volume. 44, no. 3, (1998), pp. 1087-1097.

Jens B. Schmitt and U. Roedig, Sensor network calculus - a framework for worst case anal- ysis, IEEE/ACM Int. conference on Distributed Computing in Sensor Systems, (2005).

Yuming Jiang, A basic stochastic network calculus. Proceeding of ACM SIGCOMM, (2006).

C.-S. Chang, Stability, queue length and delay, Part II: Stochastic queueing networks, In Proceedings of the 31st IEEE Conference on Decision and Control, (1992 )pp. 1005-1010.

R. Cruz, A calculus for network delay, part I: Network elements in isolation. IEEE Trans- action on Information Theory, volume. 37, no.1, (1991) pp. 114-121.

R. Cruz, A calculus for network delay, part II: Network analysis. IEEE Transaction on Information Theory, volume. 37, no. 1, (1991), pp. 132-141.

Chen Xin,Xiang Xudong, WAN Jianxiong, A Stochastic Network Calculus Approach for Per- formance Evaluation of Wired-cum-wireless Networks over FAN, Chinese Journal of Elec- tronics, volume 21, no. 1, (2012), pp. 137-143.

Yuming Jiang, Stochastic Network Calculus for Performance Analysis of Internet Networks- An overview and Outlook, IEEE International Conference on Computing, Networking and Communication, (2012), pp. 638-644.

Yuming Jiang and Peder J. Emstad, Analysis of stochastic service guarantees in communi- cation networks: A server model, In Proceeding of the International Workshop on Quality of Service (IWQoS-05), (2005), pp. 233-245.

Xi Zhang, Markov-Chain Modeling for Multicast Signaling Delay Analysis, IEEE/ACM Transaction on Networking volume. 12, no. 4, (2004), pp: 667-680.

Christhu Raj M R, Rajeev Sukumaran, Stochastic Network Calculus for Gilbert-Elliot Fading in Underwater Wireless Communication, Mathematics and Statistics Journal, volume. 1, no. 5, (2016), pp. 9-18.



How to Cite

Christhu Raj, M. R., & Sukumaran, R. (2017). Modelling Rayleigh Fading Channel in Underwater Wireless Communication Networks using Stochastic Network Calculus. The Journal of the Indian Mathematical Society, 84(1-2), 29–42.