A Priority Queuing System with Server-Walking Time

Abstract

This paper is concerned with the queuing process which arises when one imposes nonzero crossover times on a nonpreemptive priority system with two classes of customers. The objective is to derive the Laplace-Stieltjes transform of the waiting-time distribution function and the queue-size generating function for each class of customers. The results are obtained by first analyzing a simple single queue model with walking time and then extending this model to fit the two queue problem by an appropriate choice of variables.

Approximate Mean Value Analysis of Process Algebra Models

“…Temporary unavailability has been termed vacation [16] or, in the case of enhanced queueing networks, second-phase service [11]. The latter terminology comes from the interpretation of the actual service as the time consumed for a typical request/reply operation during which the caller is blocked; the second phase is concerned with accessory operations (such as cleanup and logging) during which the server is still busy, but the client is released.…”

Queueing models of secondary storage devices

“…The first analysis of this model is in Skinner (1967). It has enjoyed high popularity since then; a comprehensive summary is given in .…”

“…The above analysis is implied in (Skinner, 1967). He considers the situation where following each service S there is an "inspection period" (T) after which either a service or a vacation takes place.…”

Level crossing analysis of priority queues and a conservation identity for vacation models

“…Specifically, queueing systems with server vacations have been solved using this technique by Sandhu and Posner [I 31, Shanthikumar [ 14-1 7, 19,201, and Teghem [23]. Server vacation models have a long history (e.g., Cooper [4,5], Fuhrmann and Cooper [7], and Skinner [22]) and recently the interest in such models has been further enhanced by its applicability in communication, computer and production systems. Most of the references on this topic can be found in two excellent review articles by Doshi [6] and Teghem [23].…”