On the comparison of queueing systems with their fluid limits

In this article, we study a method to compare queueing systems and their fl uid limits. For a certain class of queueing systems, it is shown that the e xpected workload (and certain functions of the workload) is higher in the q ueueing system than in the fluid approximation. This class is characterized by convexity of the value function in the state component(s) where externa l arrivals occur. The main example that we consider is a tandem of multiser ver queues with general service times and Markov-modulated arrivals. The an alysis is based on dynamic programming and the use of phase-type distributi ons. Numerical examples to illustrate the results are also given.