STOCHASTIC ORDER RELATIONS AMONG GI/G/1 QUEUES WITH A COMMON TRAFFIC INTENSITY

Abstract

A class of queues in which the numbers of customers in systems are stochastically larger (smaller) than the one in M/M/1 with a common traffic intensity is given. This fact ensures that M/M/1 queues give safety bounds for a large class of queues. The case of M/E_k/1 (k = 2,3,・・・) or MID/1 is treated in like manner. A new type of conservation law is derived to prove these results. Stochastic order relations among M/E_k/1 (or E_k/M/1) queues (k = 1,2,・・・) are also obtained.