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Bowl Shapes Are Better with Buffers–Sometimes

Published online by Cambridge University Press:  27 July 2009

Jie Ding  and
Betsy S. Greenberg
Jie Ding
Affiliation:
Management Department The University of Texas, at Austin Austin, Texas 78712
Betsy S. Greenberg
Affiliation:
Management Science and Information Systems DepartmentThe University of Texas at Austin, Austin, Texas 78712
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Abstract

We consider tandem queueing systems with a general arrival process and exponential service distribution. The queueing system consists of several stations with finite intermediate buffer capacity between the stations. We address the problem of determining the optimal arrangement for the stations. We find that considering the last two stations, the departure process is stochastically faster if the slower station is last. Our results are consistent with the “bowl shape” phenomenon that has been observed in serial queueing systems with zero buffer capacity.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 5 , Issue 2 , April 1991 , pp. 159 - 169
Copyright
Copyright © Cambridge University Press 1991

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References

Anantharam, V. (1987). Probabilistic proof of the interchangeability of. øMøl queues in series. Queueing Systems 2: 387–392.CrossRefGoogle Scholar
Chao, X., Pinedo, M. & Sigman, K. (1989). On the interchangeability and stochastic ordering of exponential queues in tandem with blocking. Probability in the Engineering and Informational Sciences 3: 223–236.CrossRefGoogle Scholar
Hillier, F.S. & Boling, R.W. (1966). The effect of some design factors on the efficiency of production lines with variable operation times. Journal of Industrial Engineering 7: 651–658.Google Scholar
Huang, C.C. & Weiss, G. (1989). On the optimal order of m machines in tandem. Operations Reseach Letters 9: 299–303.CrossRefGoogle Scholar
Lehtonen, T. (1986). On the ordering of tandem queues with exponential servers. Journal of Applied Probability 23: 115–129.CrossRefGoogle Scholar
Pinedo, M. (1982). On the optimal order of stations in tandem queues. Applied probability-Computer science: The interface, Vol. II, Disney, R.L. & Ott, T.J. (Eds.). Boston: Birkhauser, 307–325.CrossRefGoogle Scholar
Shanthikumar, J.G., Yamazaki, G. & Sakasegawa, H. (1989). Characterization of optimal order of servers in a tandem queue with blocking. To appear in Operations Research Letters.Google Scholar
Tscoucas, P. & Walrand, J. (1987). On the interchangeability and stochastic ordering of. øMøl queues in tandem. Advances in Applied Probability 19: 515–520.CrossRefGoogle Scholar
Weber, R.R. (1979). The interchangeability of tandem. øMøl queues in series. Journal of Applied Probability 16: 690–695.CrossRefGoogle Scholar
Yamazaki, G. & Sakasegawa, H. (1975). Properties of duality in tandem queueing systems. Annals of the Institute of Statistics and Mathematics 27: 201–212.CrossRefGoogle Scholar
Yamazaki, G., Sakasegawa, H. & Shanthikumar, J.G. (1989). On optimal arrangement of stations in tandem queueing systems with blocking. Berkeley, CA: University of California Press.Google Scholar