The Equivalent Group Method for Estimating the Capacity of Partial-Access Service Systems Which Carry Overflow Traffic

In telephone traffic engineering, it is frequently necessary to understand the behavior of partial-access service systems, i.e., systems in which arriving customers do not have access to all servers. T h e analysis of such systems is difficult even when the arrivals are adequately approximated by a Poisson process. However, when the arrivals are the overflows from some other service system, there are no simple methods for estimating capacity. In this note, we present a new procedure, called the E q u i v a l e n t Group method, for estimating the capacity of partial-access service systems which carry overflow traffic. T h e basic idea is to find a fullaccess group of servers which has the same capacity as the partial-access system when the arrival process is Poisson. We consider these groups 777 778 T H E BELL SYSTEM TECHNICAL JOURNAL, MARCH 1972 to be " e q u i v a l e n t " and use the capacity of the full-access group when it is offered overflow traffic to estimate the capacity of the partial-access group if it is offered the same overflow traffic. We then consider the Step-by-Step switching system, wherein the trunk groups t h a t interconnect the selectors are sometimes arranged so as to form partial-access systems called graded multiples. 1 , 2 Although graded multiples have been studied extensively, almost all of the results have had to be based on the assumption t h a t arrivals occur according to a Poisson process. W h e n graded multiples are used as alternate routes, the arrivals are not adequately approximated by a Poisson process.