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On the departure processes of M/M/1/N and GI/G/1/N queues

  • Xiuli Chao (a1)

Abstract

The purpose of this note is to point out the connection between the invariance property of M/M/1 and GI/G/1 queues (which has been reported in several papers) and the interchangeability and reversibility properties of tandem queues. This enables us to gain new insights for both problems and obtain stronger invariance results for M/M/1, GI/G/1, as well as loss systems M/M/1/N, GI/G/1/N and tandem systems.

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Copyright

Corresponding author

Postal address: Division of Industrial and Management Engineering, New Jersey Institute of Technology, Newark, NJ 07102, USA.

Footnotes

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This research is partially supported by SBR, NJIT.

Footnotes

References

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Ali, H. (1970) Two results in the theory of queues. J. Appl. Prob. 7, 219226.
Ali, H. (1990) Expected number of departures in M/M/1 and GI/G/1 queues. Adv. Appl. Prob. 22, 770772.
Chao, X. and Pinedo, M. (1991) On reversibility of tandem queues with blocking. Naval Res. Logist. To appear.
Chao, X., Pinedo, M. and Sigman, K. (1989) On the interchangeability and stochastic ordering of exponential queues in tandem with blocking. Prob. Eng. Inf. Sci. 3, 223236.
Greenberg, H. and Greenberg, I. (1966) The number served in a queue. Operat. Res. 14, 137144.
Hubbard, J. R., Pegden, C. D. and Rosenshine, M. (1986) The departure process for the M/M/1 queue. J. Appl. Prob. 23, 249255.
Muth, E. (1970) The reversibility property of production lines. Management Sci. 25, 152158.
Takács, L. (1962) Introduction to the Theory of Queues. Oxford University Press, New York.
Tembe, S. and Wolff, R. W. (1974) Optimal order of servers in tandem queues. Operat. Res. 22, 824832.
Weber, R. R. (1979) The interchangeability of tandem queues in series. J. Appl. Prob. 16, 690695.
Weber, R. R. (1992) The interchangeability of tandem queues with heterogeneous customers and dependent service times. Adv. Appl. Prob. 24, 727737.

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