https://hal.inria.fr/inria-00366541Fiems, DieterDieterFiemsSMACS Research Group - UGENT - Universiteit Gent = Ghent University [Belgium]Altman, EitanEitanAltmanMAESTRO - Models for the performance analysis and the control of networks - CRISAM - Inria Sophia Antipolis - MÃ©diterranÃ©e - Inria - Institut National de Recherche en Informatique et en AutomatiqueMarkov-Modulated Stochastic Recursive Equations with Applications to Delay-Tolerant NetworksHAL CCSD2009Branching processesDelay tolerant networks[MATH.MATH-PR] Mathematics [math]/Probability [math.PR]Altman, Eitan2009-03-09 07:42:202022-06-25 19:40:352009-03-09 11:27:56enReportsapplication/pdf1We investigate Markov-modulated stochastic recursive equations. This class includes multi-type branching processes with immigration as well as linear stochastic equations. Conditions are established for the existence of a stationary solution and expressions for the first two moments of this solution are found. Furthermore, the transient characteristics of the stochastic recursion are investigated: we obtain the first two moments of the transient solution as well. Finally, to illustrate our approach, the results are applied to the performance evaluation of packet forwarding in delay-tolerant mobile ad-hoc networks.