Waiting times in polling systems with Markovian server routing

This study is devoted to a queueing analysis of polling systems with a probabilistic server routing mechanism. A single server serves a number of queues, switching between the queues according to a discrete time parameter Markov chain. The switchover times between queues are nonneghgible. It is observed that the total amount of work in this Markovian polling system can be decomposed into two independent parts, viz., (i) the total amount of work in the corresponding system without switchover times and (ii) the amount of work in the system at some epoch covered by a switching interval. This work decomposition leads to a pseudoconservation law for mean waiting times, i.e., an exact expression for a weighted sum of the mean waiting times at all queues. The results generalize known results for polling systems with strictly cyclic service