Branching processes with random environment: theory and applications

We have been working on branching processes with random environment, not necesaarily Markovian. Our main contributions concern non-Markovian migration. This allowed us to study the role of correlation in many queueing models, such as networks of infinite server queues as well as polling models. We studied both discrete as well as continuous state models.

[1] E. Altman, Stochastic recursive equations with applications to queues with dependent vacations [ps , pdf ] Annals of Operations Research, 112(1): 43-61; Apr, 2002.
[2] R. Groenevelt and E. Altman , Analysis of Alternating-priority Queueing Models with (Cross) Correlated Switchover Times , IEEE INFOCOM, Miami, March 13-17, 2005. The full version is available at Queueing Systems, Vol. 51, pp. 199-247, 2005.
[3] E. Altman , "On stochastic recursive equations and infinite server queues , IEEE INFOCOM, Miami, March 13-17, 2005.
[4] E. Altman and D. Fiems, "Expected waiting time in symmetric polling systems with correlated vacations" postscript, pdf , Queueing Systems, , Vol 56, No. 3-4, pp. 255-265, 2007.
[5] E. Altman , "Semi-linear stochastic difference equations", pdf , Discrete Event Dynamic Systems , 19:115-136, 2008.
[6] Dieter Fiems and Eitan Altman, Markov-modulated stochastic recursive equations with applications to delay-tolerant networks , Performance Evaluation 70(11), 2013, INRIA Research Report No. 6872, 2009,

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