A linguistic approach to stochastic comparison of queuing systems

We study the problem of stochastic comparison of queuing systems. The author's previous results on stochastic comparison of supervised discrete event systems are extended to compare queuing systems with structural differences such as systems with different buffer capacities or different number of customers. This is done by comparing the languages generated by the systems. The approach has two advantages. First, it is simple because one needs only to compare the languages. Secondly, the results obtained are independent of stochastic features such as service time distributions and interarrival time distributions. After presenting the theoretical results we apply them to three queuing systems.