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

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