A Priority Queueing Model for a Mixture of Two Types of Customers

Abstract

In this paper a queueing model is developed for a system serving two types of customers. Primary customers with a negative exponential service distribution arrive randomly to a group of servers. When all servers are busy with other primary customers new arrivals are assumed to leave without service. Secondary customers with a general distribution of service times can be served only by servers which are not occupied by a primary customer and join a queue if all servers are busy. Primary customers have preemptive priority and are always served ahead of secondary customers. The buffer containing the service required by the delayed secondary customers empties at a rate proportional to the number of servers not occupied by primary customers. Recursive formulas are derived for the distribution and the moments of the content of the buffer in statistical equilibrium. Numerical examples are presented.

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