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Fundamentals of Stochastic Networks by Oliver C. Ibe

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4

ADVANCED QUEUEING THEORY

4.1 INTRODUCTION

The previous chapter discussed Markovian queueing systems, which are characterized by the fact that either the service times are exponentially distributed or customers arrive at the system according to a Poisson process or both. Specifically, the chapter covered M/M/x and M/G/1 queueing systems. In this chapter we discuss M/G/1 queues with priority as well as a more general queueing system that permits the interarrival and service times to have a general distribution. As in the previous chapter, the emphasis in this chapter is on the steady-state analysis with limited discussion on transient analysis.

4.2 M/G/1 QUEUE WITH PRIORITY

Usually all customers do not have the same urgency. Some customers require immediate attention while others can afford to wait. Thus in many situations, arriving customers are grouped into different priority classes numbered 1 to P such that priority 1 is the highest priority, followed by priority 2, and so on, with priority P being the lowest priority.

There are two main classes of priority queues. These are preemptive priority and nonpreemptive priority. In a nonpreemptive priority queue, if a higher priority customer arrives while a lower priority customer is being served, the arriving higher priority customer will wait until the lower priority customer’s service is completed. Thus, any customer that enters for service will complete the service without interruption. In a preemptive priority queue, if a higher ...

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