nt for many electronic systems and so modelling delays 3.1.1 Some queuing problems and finding strategies which make efficient use of the resources within these systems becomes an essential part of their design. For example if the graph represents the performance of a computer Queuing is a ubiquitous feature of electronic systems such as com- controlling a telephone exchange, one way to reduce the average puters and communication networks. Queues will build up, even if delays would be to schedule the work so as to process shorter jobs, the capacity of the system exceeds the load on it. This is an such as call set-ups and clear downs first. This procedure 'shares inevitable consequence of the fact that arrivals and services take out' delay in a sensible fashion. Longer jobs, for example those place in a random fashion. Indeed the more random the services and associated with background routines are given lower priority and the arrivals are, the more queues build up. Thus it is possible for long are held back. Telephone calls are connected as quickly as possible, queues to develop at even quite light loads arising as a consequence whilst the longer jobs take on an increase in delay which is often of sheer variability in the pattern of arrivals and services. small in comparison with the amount of time needed to process If the queue length distribution does not depend on time the queue them. is said to be in equilibrium. This is only possible if the queue's It is not always quite SO obvious what the capacity of a queuing capacity is not exceeded. In most queuing situations the equilibrium system is as it was in the example depicted in Figure 3.1, where the builds up rapidly. Even when the load itself is not constant the queue remained stable provided the arrival rate is less than the changes in it take place more slowly than in the queue SO that the service rate. A communication channel which allows a group of equilibrium is effectively 'tracked'. This means that equilibrium users to share it by means of random multip