Bounds on finite horizon QoS metrics with application to call admission

There exists a substantial body of work on the problem of providing guaranteed quality of service (QoS) to different service classes in B-ISDNs. We consider a discrete time, single server system in which packets arrive from a finite population of sources. Under the assumption that arrivals from each source are modulated by a Markov process, we examine the following metrics (i) the fraction of an interval during which the queue length exceeds a certain value, and (ii) the fraction of a group of packets from a single source that arrive to find the queue length above a certain value. For both metrics we derive upper and lower bounds on the probabilities that they exceed a threshold. These are important measures because they reflect more accurately the behavior perceived by applications such as networked audio and video. An application of these results to call admission is also given.