Performance bounds for nonhomogeneous queues

This paper considers nonhomogeneous M(t)/M(t)1 queues which can model systems such as communications networks. For such systems, bounds on moment-generating functions and on the tail distribution of the queue process are obtained. These bounds are useful for characterizing the quality of service a system can provide to its users. An approach utilizing the theory of differential equations is adapted. The bounds given in this paper are tighter than those previously available. In fact, the bounds can be made arbitrarily tight given sufficient computational effort.