Matrix analysis
Analysis of polling systems
Probability
Analysis and Control of Poling Systems
Performance Evaluation of Computer and Communication Systems, Joint Tutorial Papers of Performance '93 and Sigmetrics '93
Semi-linear Stochastic Difference Equations
Discrete Event Dynamic Systems
Probability in the Engineering and Informational Sciences
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
Spreading rumours in Euclidean space
ACM SIGMETRICS Performance Evaluation Review - Special issue on the 31st international symposium on computer performance, modeling, measurements and evaluation (IFIPWG 7.3 Performance 2013)
Markov-modulated stochastic recursive equations with applications to delay-tolerant networks
Performance Evaluation
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Polling systems have been extensively studied, and have found many applications. They have often been used for studying wired local area networks such as token passing rings and wireless local area networks such as bluetooth. In this contribution we relax one of the main restrictions on the statistical assumptions under which polling systems have been analyzed. Namely, we allow correlation between walking times. We consider (i) the gated regime where a gate closes whenever the server arrives at a queue. It then serves at that queue all customers who were present when the gate closes. (ii) The exhaustive regime in which the server remains at a queue till it empties. Our analysis is based on stochastic recursive equations related to branching processes with migration with a random environment. In addition to our derivation of expected waiting times for polling systems with correlated walking times, we set the foundations for computing second order statistics of the general multi-dimensional stochastic recursions.