Service Service centre 3 Departures Queuing theory is concerned with the statistical description of the behavior of queues with finding e g the probability distributed of the number in the queue from which the mean and variance of queue length an probability distribution of waiting time for a customer or the distribution of a server s busy periods can be found In operational research problems involving queues investigators must measure the existing system to make an objective assessment of its characteristics and must determine how changes may be made to the system what effects of various system s kinds of changes in the system s characteristics would be and whether in the light of the queuing system under study must be constructed in this kind of analysis and the results of queuing theory are required to obtain the characteristics of the model and to assess the effects such as the addition of an extra server or a reduction in mean service time Arriving units QUEUEING SYSTEM A queuing system can be completely described by a The input or arrival pattern b The service mechanism or service pattern c The queue discipline and d Customer s behavior Queuing System Service Centre Queue or waiting time Servicing Station 0 41 system Departures a The input or arrival pattern The input describes the way in which the customers arrive and join the system Generally the customers arrive in a more or less random fashion which is not worth making the prediction Thus the arrival patteren can best be described in terms of probabilities and consequently the probability distribution for inter arrival times the time between two successive arrivals or the distribution of number customers arriving in unit time must be defined