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A sample path analysis of the delay in the M/G/C system

  • Sridhar Seshadri (a1)
Abstract

Using sample path analysis we show that under the same load the mean delay in queue in the M/G/2 system is smaller than that in the corresponding M/G/1 system, when the service time has either the DMRL or NBU property and the service discipline is FCFS. The proof technique uses a new device that equalizes the work in a two server system with that in a single sterver system. Other interesting quantities such as the average difference in work between the two servers in the GI/G/2 system and an exact alternate derivation of the mean delay in the M/M/2 system from sample path analysis are presented. For the same load, we also show that the mean delay in the M/G/C system with general service time distribution is smaller than that in the M/G/1 system when the traffic intensity is less than 1/c.

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Corresponding author
Postal address: Department of Statistics and Operations Research, Leonard A. Stern School of Business, New York University, NY 10012, USA.
References
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Cox, D. R. and Smith, W. L. (1961) Queues. Wiley, New York.
Daley, D. J. and Rolski, T. (1984) Some comparability results for waiting times in single- and many-server queues. J. Appl. Prob. 21, 887900.
Mori, M. (1975) Some bounds for queues. J. Operat. Res. Soc. Japan 18, 151181.
Stoyan, D. (1983) Comparison Methods for Queues and Other Stochastic Models. Wiley, New York.
Suzuki, T. and Yoshida, Y. (1970) Inequalities for the many-server queue and other queues. J. Operat. Res. Soc. Japan 13, 5977.
Wolff, R. W. (1989) Stochastic Modeling and the Theory of Queues. Prentice Hall, New York.
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Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
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