Examples of Applications of Queueing Theory in Canada

INFOR, Nov 2008 by Mandelbaum, Marvin, Hlynka, Myron

Abstract-

As part of the 50th anniversary of the Canadian Operational Research Society, we reviewed queueing applications by Canadian researchers and practitioners. We concentrated on finding real applications, but also considered theoretical contributions to applied areas that have been developed by the authors based on real applications. There were a surprising number of applications, many not well documented. Thus, this paper features examples of queueing theory applications over a spectrum of areas, years and types. One conclusion is that some of the successful queueing applications were achieved and ameliorated by using simple principles gained from studying queues and not by complex mathematical models.

Keywords Queueing theory, applications, history.

1. INTRODUCTION

This paper is a collection of examples of applications of queueing analysis in Canada or applications by Canadian researchers and practitioners, showing their contributions since the 1950's. This paper is dedicated to the 50th anniversary of CORS (Canadian Operational Research Society)1.

We concentrated on finding applications to real queueing situations as much as possible, but we also considered theoretical contributions to applied areas that have been discovered by authors based on real applications. Hence, we were interested, to a lesser extent, in theoretical work directly motivated by real applications and done by someone closely involved, with the intent of helping the client organizations. Given that the intent was to obtain concrete and practical results, the work may not have resulted in a publication, but rather led to implementation or an internal report. Moreover, these applications often do not involve academic (or even consulting) queueing theorists. Thus, a survey of this nature can never be complete since many of the applications are silent; there may be no articles in the open literature and often there is no report or documentation, and memories of what happened long ago have faded. But our lack of completeness is also explained by the time constraints of this survey.

Queueing applications are abundant in Canada. The diverse areas where queueing analysis has been applied include: shipping and canals, grocery store checkout line count estimation, vehicle traffic flow, airline operations, airport terminal planning, forest fire management, medical wait times for surgery, patient scheduling, hospital service management, hospital emergency room management, ambulance management, banking, bus, truck, railroad and train operations, production and manufacturing, border crossings and customs, mail services, telecommunications and computer design, and call centre operations and staffing.

There is no good published description of the role of Canadians in queueing applications or theory. There are a number of papers on the birth of operational research in Canada, of which queueing was a fundamental part, and from them there is a hint at the role of Canadians in queueing research and application (Sandiford, 1963). Also there are general histories of queueing theory that include a small amount on Canadian contributions. See the queueing history link on Hlynka's Queueing Theory Page (2008).

In order to prepare the current article and given the issues of incompleteness, lack of publications and fading memories, and knowing that we could not be all inclusive, our methodology was as follows. We first issued a call for information by sending an e-mail to all current CORS members through the CORS list server and to a list of Canadian queueing researchers culled from Hlynka's Queueing Theory Page2. These attempts resulted in a very low response rate and minimal success. Using our knowledge and experience of people who worked in the held, we telephoned many practitioners directly, as well as contacted companies or organizations in areas where we thought there might be applications. Many of the people we contacted gave us information about others (living or dead, regardless of academic background) whose work included applied queueing. The interview approach with individuals, using the snowball technique, resulted in information on many of the applications discussed in this paper. We relied on the integrity of researchers and practitioners in telling us about these applications, because of the lack of documentation or references. We also had to make choices as to what was included and what we thought met the spirit of our intent. For example, what is meant by a "Canadian" application is somewhat vague. However, everything referred to in this article has some Canadian connection and we used our discretion on an individual basis as to what was included. Hence, this is a very personal and unscientific study of queueing applications from our memory and the memory of those interviewed and is not meant to be exhaustive. Accordingly, we consider dus paper as a collection of examples. We apologize in advance for any exclusions, omissions, errors, misrepresentations, or misinterpretations.