Abstract
Consider a multihop wireless network, with multiple source–destination pairs. We obtain a channel scheduling policy which can guarantee end-to-end mean delay for different traffic streams. We show the stability of the network for this policy by convergence to a fluid limit. It is intractable to obtain the stationary distribution of this network. Thus, we also provide a diffusion approximation for this scheme under heavy traffic. We further show that the stationary distribution of the scaled process of the network converges to that of the Brownian limit. This theoretically justifies the performance of the system. We verify the theoretical properties by means of simulations.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Billingsley, P.: Convergence of Probability Measures. Wiley, London (1968)
Bramson, M.: State space collapse with application to heavy traffic limits for multiclass queueing networks. Queueing Syst. 30(1–2), 89–140 (1998)
Budhiraja, A., Lee, C.: Stationary distribution convergence for generalized Jackson networks in heavy traffic. Math. Oper. Res. 34(1), 45–56 (2009)
Dai, J.G.: On positive Harris recurrence of multiclass queueing networks: a unified approach via fluid limit models. Ann. Appl. Probab. 5, 49–77 (1995)
Dai, J.G., Meyn, S.P.: Stability and convergence of moments for multiclass queueing networks via fluid limit models. IEEE Trans. Autom. Control 40(11), 1889–1904 (1995)
Gamarnik, D., Zeevi, A., et al.: Validity of heavy traffic steady-state approximations in generalized Jackson networks. Ann. Appl. Probab. 16(1), 56–90 (2006)
Georgiadis, L., Neely, M.J., Tassiulas, L., et al.: Resource allocation and cross-layer control in wireless networks. Found. Trends® Netw. 1(1), 1–144 (2006)
Harrison, J.: Brownian Motion and Stochastic Flow Systems. Wiley, London (1985)
Ji, B., Joo, C., Shroff, N.B.: Delay-based back-pressure scheduling in multihop wireless networks. IEEE/ACM Trans. Netw. 21(5), 1539–1552 (2013)
Krishnan, A., Sharma, V.: Distributed control and quality-of-service in multihop wireless networks. In: 2018 IEEE International Conference on Communications (ICC), pp. 1–7. IEEE, Piscataway (2018)
Krishnan, A., Sharma, V.: Quality-of-service in multihop wireless networks: diffusion approximation (2018). arXiv:1810.12209
Kumar, S.V., Sharma, V.: Joint routing, scheduling and power control providing hard deadline in wireless multihop networks. In: 2017 Information Theory and Applications Workshop (ITA). San Diego (2017)
Li, B., Srikant, R.: Queue-proportional rate allocation with per-link information in multihop wireless networks. Queueing Syst. 83(3–4), 329–359 (2016)
Meyn, S.: Control Techniques for Complex Networks. Cambridge University Press, Cambridge (2008)
Miyazawa, M.: Diffusion approximation for stationary analysis of queues and their networks: a review. J. Oper. Res. Soc. Jpn. 58(1), 104–148 (2015)
Rybko, A.N., Stolyar, A.L.: Ergodicity of stochastic processes describing the operation of open queueing networks. Problemy Peredachi Informatsii 28(3), 3–26 (1992)
Singh, R., Kumar, P.: Throughput optimal decentralized scheduling of multi-hop networks with end-to-end deadline constraints: unreliable links (2016). arXiv:1606.01608
Siram, V., Varma, K., et al.: Routing and scheduling transient flows for QoS in multi-hop wireless networks. In: 2018 International Conference on Signal Processing and Communications (SPCOM). Bangalore (2018)
Stolyar, A.L., et al.: Maxweight scheduling in a generalized switch: state space collapse and workload minimization in heavy traffic. Ann. Appl. Probab. 14(1), 1–53 (2004)
Williams, R.J.: Diffusion approximations for open multiclass queueing networks: sufficient conditions involving state space collapse. Queueing Syst. 30(1–2), 27–88 (1998)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 The Editor(s) (if applicable) and The Author(s), under exclusive licence to Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Ashok Krishnan, K.S., Sharma, V. (2020). Diffusion Approximation Analysis of MultihopWireless Networks: Quality-of-Service and Convergence of Stationary Distribution. In: Joshua, V., Varadhan, S., Vishnevsky, V. (eds) Applied Probability and Stochastic Processes. Infosys Science Foundation Series(). Springer, Singapore. https://doi.org/10.1007/978-981-15-5951-8_2
Download citation
DOI: https://doi.org/10.1007/978-981-15-5951-8_2
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-15-5950-1
Online ISBN: 978-981-15-5951-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)