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Optimal Markovian coupling and exponential convergence rate for the TCP process. (English) Zbl 1480.60212

Summary: In this work, by constructing optimal Markovian couplings we investigate exponential convergence rate in the Wasserstein distance for the transmission control protocol (TCP) process. Most importantly, we provide a variational formula for the lower bound of the exponential convergence rate.

MSC:

60J25 Continuous-time Markov processes on general state spaces
60K30 Applications of queueing theory (congestion, allocation, storage, traffic, etc.)
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[1] Bardet, J.; Christen, A.; Guillin, A., Total variation estimates for the TCP process, Electron. J. Probab., 18, 1-21 (2013) · Zbl 1283.68067 · doi:10.1214/EJP.v18-1720
[2] Chafaï, D.; Malrieu, F.; Paroux, K., On the long time behavior of the TCP window size process, Stoch. Proc. Appl., 120, 1518-1534 (2010) · Zbl 1196.68028 · doi:10.1016/j.spa.2010.03.019
[3] Chen, M. F., Optimal Markovian couplings and applications, Acta Math. Sin., Engl. Ser., 10, 260-275 (1994) · Zbl 0813.60068 · doi:10.1007/BF02560717
[4] Cloez, B.: Wasserstein decay of one dimensional jump-diffusions, arXiv:1202.1259v2, 2012
[5] Dumas, V.; Guillemin, F.; Robert, P., A Markovian analysis of additive-increase multiplicative-decrease algorithms, Adv. in Appl. Probab., 34, 85-111 (2002) · Zbl 1002.60091 · doi:10.1239/aap/1019160951
[6] Floyd, S., Connections with multiple congested gateways in packet-switched networks 1: One way traffic, Computer Comm. Rev., 21, 30-47 (1991) · doi:10.1145/122431.122434
[7] Guillemin, F.; Robert, P.; Zwart, B., AIMD algorithms and exponential functionals, Ann. Appl. Probab., 14, 90-117 (2004) · Zbl 1041.60072 · doi:10.1214/aoap/1075828048
[8] Meyn, S. P.; Tweedie, R. L., Markov Chains and Stochastic Stability (1993), Berlin: Springer-Verlag, Berlin · Zbl 0925.60001 · doi:10.1007/978-1-4471-3267-7
[9] Monmarché, P.: On ℌ^1 and entropic convergence for contractive PDMP. Electron. J. Probab., 20, 30 pp. (2015) · Zbl 1332.60123
[10] Padhye, J.; Firoiu, V.; Towsley, D., Modeling TCP throughput: A simple model and its empirical validation, ACM Sigconm’98 (1998), New York: ACM, New York
[11] Roberts, G.; Rosenthal, J., Quantitative bounds for convergence rates of continuous time Markov processes, Electron. J. Probab., 1, 1-21 (1996) · Zbl 0891.60068 · doi:10.1214/EJP.v1-9
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