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

Masakiyo Miyazawa

19 citations0/0 files storedJournal of the Operations Research Society of Japan

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Advanced Queuing Theory Analysis Probability and Statistical Research Probability and Risk Models

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.

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1977Further Stochastic Order Relations among GI/GI/1 Queues with a Common Traffic Intensity 1983Stationary queuing systems with dependencies 2007Measuring the technological change and productivity in food, textile and chemical industries in Kuwait (1992–2002)

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