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A LOSS SYSTEM WITH SKILL-BASED SERVERS UNDER ASSIGN TO LONGEST IDLE SERVER POLICY

Published online by Cambridge University Press:  08 June 2012

Ivo Adan  and
Gideon Weiss
Ivo Adan
Affiliation:
Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands E-mail: iadan@tue.nl
Gideon Weiss
Affiliation:
Department of Statistics, The University of Haifa, Mount Carmel 31905, Israel E-mail: gweiss@stat.haifa.ac.il
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Abstract

We consider a memoryless loss system with servers = {1, …, J}, and with customer types = {1, …, I}. Servers are multi-type: server j works at rate μj, and can serve a subset of customer types C(j). An arriving customer will go to the longest idling server which can serve him, or be lost. We obtain a simple explicit steady-state distribution for this system, and calculate various performance measures of this system in steady state. We provide some illustrative examples. We compare this system with a similar system discussed recently by Adan, Hurkens, and Weiss [1]. We also show that this system is insensitive, the results hold also for general service time distributions.

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 26 , Issue 3 , July 2012 , pp. 307 - 321
Copyright
Copyright © Cambridge University Press 2012

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References

1.Adan, I.J.B.F., Hurkens, C., & Weiss, G. (2010). A reversible Erlang loss system with multitype customers and multitype servers. Probability in Engineering and Informational Sciences 24: 535–548.CrossRefGoogle Scholar
2.Adan, I.J.B.F. & Weiss, G. (2011). Exact FCFS matching rates for two infinite multi-type sequences. Operations Research to appear.Google Scholar
3.Busic, A., Gupta, V., & Mairesse, J. (2010). Stability of the bipartite matching model, Preprint, arxiv:1003.3477v1 [cs.DM].Google Scholar
4.Caldentey, R., Kaplan, E.H., & Weiss, G., (2009). FCFS infinite bipartite matching of servers and customers. Advances in Applied Probability 41: 695–730.CrossRefGoogle Scholar
5.Sevastyanov, B.A. (1957). An ergodic theorem for Markov processes and its application to telephone systems with refusals Theory of Probability and its Applications 2: 104–112.CrossRefGoogle Scholar
6.Talreja, R. & Whitt, W. (2008). Fluid models for overloaded multi-class many-service queueing systems with FCFS routing. Management Science 54: 1513–1527.CrossRefGoogle Scholar
7.Visschers, J.W.C.H., Adan, I.J.B.F., & Weiss, G. (2011). A product form solution to a system with multi-type customers and multi-type servers. Queueing Systems 70: 269–298.CrossRefGoogle Scholar