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Monotonicity of throughput in non-Markovian networks

Published online by Cambridge University Press:  14 July 2016

Pantelis Tsoucas  and
Jean Walrand
Pantelis Tsoucas*
Affiliation:
University of Maryland, College Park
Jean Walrand*
Affiliation:
University of California, Berkeley
*
∗Postal address: Systems Research Center, University of Maryland, College Park, MD 20742, USA.
∗∗Postal address: Department of Electrical Engineering and Computer Sciences and Electronics Research Laboratory, University of California, Berkeley CA 94720, USA.
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Abstract

Monotonicity of throughput is established in some non-Markovian queueing networks by means of pathwise comparisons. In a series of · /GI/s/N queues with loss at the first node it is proved that increasing the waiting room and/or the number of servers increases the throughput. For a closed network of · /GI/s queues it is shown that the throughput increases as the total number of jobs increases. The technique used for these results does not apply to blocking systems with finite buffers and feedback. Using a stronger coupling argument we prove throughput monotonicity as a function of buffer size for a series of two ·/M/1/N queues with loss and feedback from the second to the first node.

Keywords

BLOCKINGCLOSED QUEUEING NETWORKS
Type
Research Papers
Information
Journal of Applied Probability , Volume 26 , Issue 1 , March 1989 , pp. 134 - 141
Copyright
Copyright © Applied Probability Trust 1989 

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References

[1] Altiok, T. M. and Stidham, S. (1982) A note on transfer lines with unreliable machines, random processing times, and finite buffers. IIE Trans. 14, 125–127.Google Scholar
[2] Van Dijk, N. M., Tsoucas, P. and Walrand, J. (1987) Simple bounds and monotonicity of the call congestion of finite multi-server delay systems. Probability in the Engineering and Informational Sciences.Google Scholar
[3] Mitra, D. and Tsoucas, P. (1987) Relaxations for the numerical solutions of some stochastic problems. AT&T Bell Labs Technical Memo.Google Scholar
[4] Shanthikumar, J. G. and Yao, D. D. (1986) The effect of increasing service rates in a closed queueing network. J. Appl. Prob. 23, 474–483.Google Scholar
[5] Tsoucas, P. (1987) Ph.D. Dissertation, Dept. of Electrical Engineering and Computer Sciences, University of California, Berkeley.Google Scholar
[6] Van Der Wal, J. (1985) Monotonicity of the throughput of a closed exponential queueing network in the number of jobs. Eindhoven University of Technology Memo. COSOR 85–21.Google Scholar
[7] Wolff, R. W. (1977) An upper bound for multi-channel queues. J. Appl. Prob. 14, 884–888.Google Scholar