Queueing and Waiting-time Problems

Abstract

An early application of operational research methods was to the problems of queueing. The queues formed in a modern supermarket by customers waiting to pay for baskets of goods typifies quantitative problems found in other business and industrial situations. Each cash-till is approached by a single service-channel, each customer is a unit, and the service-channels and tills or service-points, to use a more general term, form a system. The fundamental problem is to strike the right balance between customers’ demands for services and the organisation’s supply of service somewhere between the extremes of excessive queueing and uneconomical manning of service-points. The first example shows that even when the arrival rates of customers and the service times are fixed — a simple situation rarely met in practice — the system is very sensitive to small changes in rates or times.