Queuing (Waiting Line) Basics

SCM 301

QUEUING (WAITING LINE) BASICS

INTRODUCTION

Queuing (or Waiting Line) examines the characteristics of queues in various circumstances. For example:

* Is it a good idea to have one line for each retail (or bank, or supermarket, or car wash) service facility or have one line where the next one in line goes to the next of several service facilities?

* Is it a good idea, if you are going to double service rates, to double the speed of the current service facility or build a second facility of equal capacity?

These questions assume that those in the waiting line come from an infinite source, arrival is random, those in line are patient and do not leave the queue once they enter it, the queue has infinite length, that those in line are served on a first come first served basis, and that the service rate is constant.

The assumptions in the previous paragraph work well in many situations. However, other considerations may occur if arrivals are in batches, if those in line grow inpatient and leave, if service discipline is not first come first served (such as shortest processing time, reservations first, emergencies first), if the service rate is not constant, or if there is a need for re-service and resulting queue reentry.

Some of the issues of queuing theory might be managed by scheduling of arrivals, service times, and departures.

Two models will be discussed. First, a single service facility will be examined. Second, a multiple facility will be discussed.

SINGLE SERVICE FACILITY, ARRIVALS FROM AN INFINATE POPULATION

Assumptions for this scenario are infinite source, uncontrollable single arrivals that are patient, a single waiting line, first come first served discipline, and a low probability of exit. Variables are as follows:

A = average arrival rate

S = average service rate

n = total number of customers in the system (waiting and being served)

nq = total number of customers in the waiting line

P0 = probability of no...