LOGISTIC AND MODELLING

Logistic and Modelling

Logistic and Modelling

Introduction

Queues (or waiting lines) help facilities or businesses provide service in an orderly fashion. Forming a queue being a social phenomenon, it is beneficial to the society if it can be managed so that both the unit that waits and the one that serves get the most benefit. For instance, there was a time when in airline terminals passengers formed separate queues in front of check-in counters (Kleinrock, 1975: 6). We identify the unit demanding service, whether it is human or otherwise, as customer. The unit providing service is known as the server. This terminology of customers and servers is used in a generic sense regardless of the nature of the physical context. Some examples are given below (Gross & Harris, 1985: 69).

In communication systems, voice or data traffic queue up for lines for transmission. A simple example is the telephone exchange.

In a manufacturing system with several work stations, units completing work in one station wait for access to the next.

Vehicles requiring service wait for their turn in a garage.

Patients arrive at a doctor's clinic for treatment.

But now we see invariably only one line feeding into several counters. This is because of the realization that a single line policy serves better for the passengers as well as the airline management. Such a conclusion has come from analyzing the mode by which a queue is formed and the service is provided. The anlaysis is based on builidng a mathematical model representing the process of arrival of passengers who join the queue, the rules by which they are allowed into service, and the time it takes to serve the passengers. Queueing theory embodies the full gamut of such models covering all perceivable systems which incorporate characteristics of a queue.Numerous examples of this type are of everyday occurrence. While analyzing them we can identify some basic elements of the systems.

Input process. If the occurrence of arrivals and the offer of service are strictly according to schedule, a queue can be avoided. But in practice this does not happen. In most cases the arrivals are the product of external factors. Therefore, the best one can do is to describe the input process in terms of random variables which can represent either the number arriving during a time interval or the time interval between successive arrivals. If customers arrive in groups, their size can be a random variable as well (Cohen, 1982: 54).

Service mechanism. The uncertainties involved in the service mechanism are the number of servers, the number of customers getting served at any time, and the duration and mode of service. Networks of queues consist of more than one servers arranged in series and/or parallel.

System capacity. How many customers can wait at a time in a queuing system is a significant factor for consideration. If the waiting room is large, one can assume that for all practical purposes, it is infinite. But our everyday experience with the telephone systems tells us that the size of the ...