Finite-buffer polling systems with threshold-based switching policy

We consider a system of two separate finite-buffer M/M/1 queues served by a single server, where the switching mechanism between the queues is thresholdbased, determined by the queue which is not being served. Applications may be found in data centers, smart traffic-light control and human behavior. Specifically, whenever the server attends queue i (Qi ) and the number of customers in the other queue, Q j (i, j = 1, 2; j = i), reaches its threshold level, the server immediately switches to Q j whenever Qi is below its threshold. When a served Qi becomes empty we consider two scenarios: (i) non-work-conserving; and (ii)work-conserving.Wepresent occasions where the non-work-conserving policy is more economical than the workconserving policy when high switching costs are involved. An intrinsic feature of the process is an oscillation phenomenon: when the occupancy of Qi decreases the occupancy of the other queue increases. This fact is illustrated and discussed. By formulating the system as a three-dimensional continuous-time Markov chain we provide a probabilistic analysis of the system and investigate the effects of buffer sizes and arrival rates, as well as service rates, on the system’s performance. Numerical examples are presented and extreme cases are investigated. B Efrat Perel [email protected] Kostia Avrachenkov [email protected] Uri Yechiali [email protected] 1 Inria, Sophia Antipolis, Valbonne, France 2 Afeka, Tel-Aviv Academic College of Engineering, Tel-Aviv, Israel 3 Department of Statistics and Operations Research, School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv, Israel