# Performance of CSMA in multi-channel wireless networks

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## Abstract

We analyze the performance of CSMA in multi-channel wireless networks, accounting for the random nature of traffic. Specifically, we assess the ability of CSMA to fully utilize the radio resources and in turn to stabilize the network in a dynamic setting with flow arrivals and departures. We prove that CSMA is optimal in the ad-hoc mode, when each flow goes through a unique dedicated wireless link from a transmitter to a receiver. It is generally suboptimal in infrastructure mode, when all data flows originate from or are destined to the same set of access points, due to the inherent bias of CSMA against downlink traffic. We propose a slight modification of CSMA that we refer to as *flow-aware* CSMA, which corrects this bias and makes the algorithm optimal in all cases. The analysis is based on some time-scale separation assumption which is proved valid in the limit of large flow sizes.

## Keywords

Wireless network Interference graph CSMA Flow-level dynamics Time-scale separation Stability## Mathematics Subject Classification

68M20 68M12 60J28## References

- 1.Barakat, C., Thiran, P., Iannaccone, G., Diot, C., Owezarski, P.: Modeling internet backbone traffic at the flow level. IEEE Trans. Signal Process.
**51**, 2003 (2003) CrossRefGoogle Scholar - 2.Ben Fredj, S., Bonald, T., Proutière, A., Régnié, G., Roberts, J.W.: Statistical bandwidth sharing: a study of congestion at flow level. In: Proceedings of ACM SIGCOMM, pp. 111–122 (2001) Google Scholar
- 3.Berger, A.W., Kogan, Y.: Dimensioning bandwidth for elastic traffic in high-speed data networks. IEEE/ACM Trans. Netw.
**8**(5), 643–654 (2000) CrossRefGoogle Scholar - 4.Billingsley, P.: Convergence of Probability Measures, 2nd edn. Wiley Series in Probability and Statistics. Wiley, New York (1999) CrossRefGoogle Scholar
- 5.Bonald, T.: Insensitive traffic models for communication networks. Discret. Event. Dyn. Syst.
**17**(3), 405–421 (2007) CrossRefGoogle Scholar - 6.Bonald, T., Feuillet, M.: On the stability of flow-aware CSMA. Perform. Eval.
**67**, 1219–1229 (2010) CrossRefGoogle Scholar - 7.Bonald, T., Feuillet, M.: On flow-aware CSMA in multi-channel wireless networks. In: CISS (2011) Google Scholar
- 8.Bouman, N., Borst, S., Van Leeuwaarden, J., Proutière, A.: Backlog-based random access in wireless networks: fluid limits and delay issues. In: ITC, vol. 23 (2011) Google Scholar
- 9.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) CrossRefGoogle Scholar - 10.Feuillet, M., Proutière, A., Robert, P.: Random capture algorithms: fluid limits and stability. In: Information Theory and Applications Workshop (2010) Google Scholar
- 11.Heusse, M., Rousseau, F., Berger-Sabbatel, G., Duda, A.: Performance anomaly of 802.11b. In: INFOCOM, vol. 2, pp. 836–843 (2003) Google Scholar
- 12.Jiang, L., Shah, D., Shin, J., Walrand, J.: Distributed random access algorithm: scheduling and congestion control. IEEE Trans. Inf. Theory
**56**(12), 6182–6207 (2010) CrossRefGoogle Scholar - 13.Jiang, L., Walrand, J.: A distributed CSMA algorithm for throughput and utility maximization in wireless networks. In: The 46th Annual Allerton Conference on Communication, Control, and Computing (2008) Google Scholar
- 14.Jiang, L., Walrand, J.: Approaching throughput-optimality in a distributed CSMA algorithm: collisions and stability. In: MobiHoc S3’09, pp. 5–8. ACM, New York (2009) CrossRefGoogle Scholar
- 15.Kim, S.W., Kim, B.-S., Fang, Y.: Downlink and uplink resource allocation in IEEE 802.11 wireless LANs. IEEE Trans. Veh. Technol.
**54**, 320–327 (2005) CrossRefGoogle Scholar - 16.Kurtz, T.G.: Averaging for martingale problems and stochastic approximation. In: Applied Stochastic Analysis, US-French Workshop. Lecture notes in Control and Information Sciences, vol. 177, pp. 186–209. Springer, Berlin (1992) CrossRefGoogle Scholar
- 17.Massoulié, L., Roberts, J.W.: Bandwidth sharing and admission control for elastic traffic. Telecommun. Syst.
**15**, 185–201 (2000) CrossRefGoogle Scholar - 18.Meyn, S.: Transience of multiclass queueing networks via fluid limit models. Ann. Appl. Probab.
**5**, 946–957 (1995) CrossRefGoogle Scholar - 19.Modiano, E., Shah, D., Zussman, G.: Maximizing throughput in wireless networks via gossiping. ACM SIGMETRICS Perform. Eval. Rev.
**34**(1), 27–38 (2006) CrossRefGoogle Scholar - 20.Ni, J., Tan, B., Srikant Q-CSMA, R.: Queue-length based CSMA/CA algorithms for achieving maximum throughput and low delay in wireless networks. In: IEEE INFOCOM (2010) Google Scholar
- 21.Proutière, A., Yi, Y., Lan, T., Chiang, M.: Resource allocation over network dynamics without timescale separation. In: IEEE INFOCOM (2010) Google Scholar
- 22.Rajagopalan, S., Shah, D.: Distributed algorithm and reversible network. In: CISS, pp. 498–502 (2008) Google Scholar
- 23.Rajagopalan, S., Shah, D., Shin, J.: Network adiabatic theorem: an efficient randomized protocol for contention resolution. In: SIGMETRICS’09, pp. 133–144. ACM, New York (2009) CrossRefGoogle Scholar
- 24.Robert, P.: Stochastic Networks and Queues. Stochastic Modeling and Applied Probability Series. Springer, New York (2003) Google Scholar
- 25.Rogers, L.C.G., Williams, D.: Diffusions, Markov Processes and Martingales Vol. 2: Itô Calculus, 2nd edn. Cambridge University Press, Cambridge (2000) Google Scholar
- 26.Serfozo, R.: Introduction to Stochastic Networks. Springer, New York (1999) CrossRefGoogle Scholar
- 27.Shah, D., Shin, J.: Randomized scheduling algorithm for queueing networks. Ann. Appl. Prob.
**22**(1), 128–171 (2012) CrossRefGoogle Scholar - 28.Tassiulas, L., Ephremides, A.: Stability properties of constrained queueing systems and scheduling policies for maximum throughput in multihop radio networks. IEEE Trans. Autom. Control
**37**, 1936–1948 (1992) CrossRefGoogle Scholar - 29.van de Ven, P.M., Borst, S.C., van Leeuwaarden, J.S.H., Proutière, A.: Insensitivity and stability of random-access networks. Perform. Eval.
**67**, 1230–1242 (2010) CrossRefGoogle Scholar