Multiclass batch arrival retrial queues analyzed as branching processes with immigration
Queueing Systems: Theory and Applications
Analysis of Alternating-Priority Queueing Models with (Cross) Correlated Switchover Times
Queueing Systems: Theory and Applications
Expected waiting time in symmetric polling systems with correlated walking times
Queueing Systems: Theory and Applications
Processor sharing: A survey of the mathematical theory
Automation and Remote Control
On the discrete-time g/gi/∞ queue*
Probability in the Engineering and Informational Sciences
Foreword to the thematical issue "centenary of the queuing theory"
Automation and Remote Control
Branching processes, the max-plus algebra and network calculus
ASMTA'12 Proceedings of the 19th international conference on Analytical and Stochastic Modeling Techniques and Applications
Markov-modulated stochastic recursive equations with applications to delay-tolerant networks
Performance Evaluation
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We consider in this paper a class of vector valued processes that have the form Y n + 1 = A n ( Y n ) + B n . B n is assumed to be stationary ergodic and A n is assumed to have a divisibility property. This class includes linear stochastic difference equations as well as multi-type branching processes (with a discrete or with a continuous state space). We derive explicit expressions for the probability distribution as well as for the two first moments of state vectors at the stationary regime. We then apply this approach to derive two formalisms to describe the infinite server queue. The first is based on a branching process approach adapted to phase type service time distributions. The second is based on a linear stochastic difference equation and is adapted to independent and generally distributed service times with bounded support. In both cases we allow for generally distributed arrival process (not necessarily i.i.d. nor Markovian).