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

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Abstract
The transient behavior of a Markov-modulated Poisson arrival queue is studied 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 services networks. With overload control, the arrival process is properly altered 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, the amount of time for the queue to fall into underload is measured. While in underload, the amount of time for the queue to rise to overload is measured. A proper design of the control will not only reduce the fall time but also increase the rise time. The transient queuing behavior as affected by time stochastic properties of the underlying Markov chain for the arrival process is also explored.

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