Transient analysis of multi-server queues with Markov-modulated Poisson arrivals and overload control

Abstract

This paper studies the transient behavior of a Markov-molulated Poisson arrival queue under overload control. The queue has finite or infinite buffer capacity with multiple exponential servers. A Markov-modulated Poisson process is used to represent an aggregated voice or video packet arrival process in integrated service networks. By overload control, we mean to properly adapt the arrival process once the buffer contents exceed a designated level. The probability distribution of queue length as a function of time is obtained. The temporal effect of the overload control is measured in two forms. While in overload, we measure the amount of time for the queue to fall into underload. While in underload, we measure the amount of time for the queue to rise to overload. A proper design of the control will not only reduce the fall time but also increase the rise time. We also explore the transient queueing behavior as affected by time stochastic properties of the underlying Markov chain for the arrival process.