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Open, Closed, and Mixed Networks of Queues with Different Classes of Customers

Baskett, Forest and Chandy, K. Mani and Muntz, Richard R. and Palacios, Fernando G. (1975) Open, Closed, and Mixed Networks of Queues with Different Classes of Customers. Journal of the ACM, 22 (2). pp. 248-260. ISSN 0004-5411.

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The joint equilibrium distribution of queue sizes in a network of queues containing N service centers and R classes of customers is derived. The equilibrium state probabilities have the general form P(S) = Cd(S) f_1(x_1)f_2(x_2)·f_N(x_N), where S is the state of the system, x, is the configuration of customers at the ith service center, d(S) is a function of the state of the model, f, is a function that depends on the type of the ith service center, and C is a normalizing constant. It is assumed that the equilibrium probabilities exist and are unique. Four types of service centers to model central processors, data channels, terminals, and routing delays are considered. The queueing disciplines associated with these service centers include first-come-first-served, processor sharing, no queueing, and last-come-first-served. Each customer belongs to a single class of customers while awaiting or receiving service at a service center, but may change classes and service centers according to fixed probabilities at the completion of a service request. For open networks, state dependent arrival processes are considered. Closed networks are those with no exogenous arrivals. A network may be closed with respect to some classes of customers and open with respect to other classes of customers. At three of the four types of service centers, the service times of customers are governed by probability distributions having rational Laplace transforms, different classes of customers having different distributions. At first-come-first-served-type service centers, the service time distribution must be identical and exponential for all classes of customers. Examples show how different classes of customers can affect models of computer systems.

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Additional Information:© 1975, Association for Computing Machinery, Inc. Received August 1972; Revised August 1974. This research was supported in part by the U.S. Army, U.S. Navy, and U.S. Air Force Joint Services Electronics Programs under Contract N-00013-67-A-0112-0044, in part by the National Science Foundation under Grants GJ-1084 and GJ-35109, and in part by the Advanced Research Projects Agency of the Department of Defense under Contract DAHC-15-69-C-0158.
Funding AgencyGrant Number
Army Research Office (ARO)UNSPECIFIED
Office of Naval Research (ONR)N-00013-67-A-0112-0044
Air Force Office of Scientific Research (AFOSR)UNSPECIFIED
Advanced Research Projects Agency (ARPA)DAHC-15-69-C-0158
Subject Keywords:networks of queues, theory of queues, queueing theory, multiprogramming, time-sharing, processor sharing, Markov processes
Issue or Number:2
Classification Code:CR Categories: 4.32, 5,5, 6.20
Record Number:CaltechAUTHORS:20190111-140309634
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:92221
Deposited By: Tony Diaz
Deposited On:12 Jan 2019 17:04
Last Modified:03 Oct 2019 20:42

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