Analysis and Applications of the Delay Cycle for the M/M/c Queueing System

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Analysis and Applications of the Delay Cycle for the M/M/c Queueing System

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Journal of the ACM (JACM) archive
Volume 25 , Issue 2 (April 1978) table of contents

Pages: 283 - 303

Year of Publication: 1978

ISSN:0004-5411

Authors

K. Omahen	ECRM, Inc., 205 Burlington Road, Bedford, MA and Purdue University, West Lafayette, Indiana
V. Marathe	Mount Sinai Hospital Services, City Hospital Center at Elmhurst, 79-01 Broadway, Elmhurst, NY and University of Illinois, Urbana, Illinois

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ACM New York, NY, USA

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Downloads (6 Weeks): 4, Downloads (12 Months): 22, Citation Count: 2

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ABSTRACT

The method of analysis employing decomposition of busy periods has, in various forms, been applied to the M/G/1 queueing system under a variety of scheduling rules This paper extends the technique of decomposition of busy periods in order to deal with the M/M/c queueing system. Particular attention is given to a special busy period referred to as a "delay cycle." The delay cycle commences with a delay period (of general distribution) in which jobs arrive but are not serviced, at the conclusion of the delay period, processing begins and continues until the system is empty. Closed form solutions are obtained for various entities such as distribution of busy period length and expected waiting time conditioned on the type of busy period in progress at the tmae of job arrival. These results are applied and extended to the analysis of six examples of multiprocessor systems.

REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	AVI-ITZHAK, B, MAXWELL, W L, AND MILLER, L W Queuemg w,th alternating pnormes Oper Res 13 (1965), 306-318
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	3	CONWAY, R W, MAXWELL, W L, AND MILLER, L W Theory of Scheduling Addison-Wesley, Reading, Mass, 1967
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	6	MAgATHE, V Priority queuemg systems with s~multaneous server reqmrements Ph.D. Th, Oper Res, Cornell U, Ithaca, N Y, May 1972
	7	MAHEN, K J Analytic models of multtple resource systems Ph.D Th., Commtttee on Inform Sct, U of Chicago, Chicago, 111, June 1973
	8	OMAHEN, K, AND MARATHE, V A queuemg model for a mult~processor system wRh partmoned memory Tech Rep CSD-TR 132, Dept of Comptr Sct., Purdue U, W Lafayette, Ind, Jan 1975.
	9	RIORDAN, J Stochastic Service Systems. Wiley, New York, 1962
	10	STRAUCH, R E When a queue looks the same to an amvlng customer as to an oba~-ver Manage Sct 17 (1970), 140-141.
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CITED BY 2

	Martin Fleury , Andrew C. Downton , Adrian F. Clark, Performance Metrics for Embedded Parallel Pipelines, IEEE Transactions on Parallel and Distributed Systems, v.11 n.11, p.1164-1185, November 2000
	Zhe George Zhang, Performance Analysis of a Queue with Congestion-Based Staffing Policy, Management Science, v.55 n.2, p.240-251, February 2009