Evaluation and optimization of polling systems

Throughout this internship report, polling systems play a central role. Polling systems are queueing systems consisting of multiple queues, attended by a single server. The server can only serve one queue at a time. Whenever the server moves from one queue to another, a stochastic, non-zero switch-over time is incurred. The server never idles; even when there are no customers waiting in the whole system the server keeps roving between queues. In the literature on these systems, often Poisson arrivals are assumed. In many applications, however, the Poisson assumption is not realistic. This motivates us to study polling models with renewal arrivals, which represent a far broader class of arrival streams. Firstly, an approximation of the complete waiting time distribution in polling systems with renewal arrivals is derived. This approximation may act as a basis for design decisions within polling systems. Secondly, polling systems with renewal arrivals and batch service are studied. Using characteristics of the obtained distributional approximation, the question is addressed how sizes of batches should be chosen in order to optimize the waiting time.