Distribution of Attained Service in Time-Shared Systems

A number of time-shared systems have recently been analyzed in the literature with methods from queueing theory. The quantity usually solved for is the average time spent in the system, conditioned on the total service time required (and also conditional on the priority class, if priority distinctions are considered). In this paper we consider a large class of time-shared systems and solve for the distribution of attained service for any member of this class, The attained service for an incompletely serviced customer is the number of seconds that he has so far spent in the service facility. The results are simply expressed in terms of the average conditional waiting time mentioned above, Examples of the application of this general result are also given.