A ''queue'' is a waiting line. Queues are commonly observed to form before ticket offices, cafeterias, and bus stops. Thus, to have a queue, one must have arrivals at a service facility where they often wait; for example, at a doctor's office to see the doctor in the order of their appointments. Telegrams are classified according to the order of their arrival with priority assigned to regular telegrams over night letters.Queueing theory is a branch of applied mathematics utilizing concepts from the field of stochastic processes. It has been developed in an attempt to predict fluctuating demands from observational data and to enable an enterprise to provide adequate service for its customers with tolerable waiting. However, the theory also basically improves understanding of a queueing situation, enabling better control. For example, loss of customers at a grocery store because of slow check-out-counter service may be remedied by rapid service at a larger number of counters. To put this into effect does not require a theory. But to organize airport take-off and landing operations at a minimum inconvenience does, because of the many factors entering the problem and the large size of the operation. Thus, the theory provides one with predictions about waiting times, the number waiting at any time, the length of a busy period and so fcrth...