The optimal number of servers in a many server queuing system

Abstract

Classical queuing theory may be described as a branch of applied probability theory dealing with a model denoted by GI|G|S and with special cases and variants of this model. In the model GI|G|S we assume that customers arriving according to a renewal process want to be served by one of S identical server, requiring service times which are independent and identically distributed if customers cannot be served immediately they join a queue to wait for service. Several queue disciplines (i.e. the order in which customers are served) may be considered. Moreover, one can think of any different configurations (network) of servers, in parallel or in series or both, which are of practical interest. For such models one usually study the distributions of quantities like the waiting time, the queue length of a busy period. In this approach the question of optimality does not come up immediately. In practice, however, queuing models are applied for making good or preferably optimal decisions. These decisions may concern the queuing system itself, e.g. one may vary one or more parameters or change the queue discipline or the configuration of servers; they may also influence the arrival or queuing behavior of the customers