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.

Steady-State Distribution for the Buffer Content of an $M /G/1$ Queue with Varying Service Rate

“…It is shown in [1], that under these conditions the function det (A(s)) has a zero at So O, and c 1 distinct positive zeros sl, s2, "", so_ 1. The (left) null space of A(s,) is one-dimensional for each n O, ..., c 1.…”

“…Also, a can be computed by substituting x 0 in the last equation in (1). Noting that bc 0, we get ic-acac #+ In the following we shall always assume that V is nonsingular.…”

“…The system and some of its properties. It was shown in [1] that the steadystate distributions of the buffer content Go(x),..., Gc(x) satisfy the following system of c + ordinary differential-integral equations" (1) dG. (x) -It,+ 1G,+ (x) 2,_ 1G._ I(X), is finite.…”

“…Introduction. A queueing model for a system serving two types ofcustomers was developed in [1]. In this model, primary customers receive preemptive priority service and have no provisions for queueing, while secondary customers are served only by servers which are not occupied with a primary customer.…”

Diffusion approximations for the cooperative service of voice and data messages

“…Specifically we study a queueing phenomenon which arises with the SENET network, as described by Coviello and Vena (1975) or Barbacci and Oakley (1976 This system has been studied previously by a number of researchers including Halfin and Segal (1972) , Halfin (1972) , Fischer and Harris (1976), Bhat andFischer (1976), Fischer (1977) , Chang (1977) , and Gaver and Lehoczky (1979a, b is an M/M/(c + v -V(t)) queueing system with arrival rate 6 and service rate n . We say that the V process subordinates the X process.…”