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ON THE ADAN–WEISS LOSS MODEL HAVING SKILL-BASED SERVERS AND LONGEST IDLE ASSIGNMENT RULE

Published online by Cambridge University Press:  22 January 2015

Babak Haji
Babak Haji*
Affiliation:
Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, CA 90089, USA E-mail: bhaji@usc.edu
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Abstract

We consider a queueing loss system with heterogeneous skill based servers with arbitrary distributions. We assume Poisson arrivals, with each arrival having a vector indicating which of the servers are eligible to serve it. Arrivals can only be assigned to a server that is both idle and eligible. We assume arrivals are assigned to the idle eligible server that has been idle the longest and derive, up to a multiplicative constant, the limiting distribution for this system. We show that the limiting probabilities of the ordered list of idle servers depend on the service time distributions only through their means. Moreover, conditional on the ordered list of idle servers, the remaining service times of the busy servers are independent and have their respective equilibrium service distributions. We also provide an algorithm using Gibbs sampler Markov Chain Monte Carlo method for estimating the limiting probabilities and other desired quantities of this system.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 29 , Issue 2 , April 2015 , pp. 181 - 189
Copyright
Copyright © Cambridge University Press 2015 

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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 the Engineering and Informational Sciences 24: 535–548.CrossRefGoogle Scholar
2.Adan, I.J.B.F. & Weiss, G. (2012). A loss system with skill-based servers under assign to longest idle server policy. Probability in the Engineering and Informational Sciences 26: 307–321.CrossRefGoogle Scholar
3.Barbour, A.D. (1976). Networks of queues and the method of stages. Advances in Applied Probability 8: 584–591.Google Scholar
4.Haji, B. & Ross, S.M. (2015). A queueing loss model with heterogeneous skill based servers under idle time ordering policies. Journal of Applied Probability. (accepted for publication)CrossRefGoogle Scholar
5.Ross, S.M. (2014). Optimal server selection in a queueing loss model with heterogeneous exponential servers, discriminating arrivals, and arbitrary arrival times. Journal of Applied Probability 51: 880–884.CrossRefGoogle Scholar
6.Talreja, R. & Whitt, W. (2007). 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. (2012). A product form solution to a system with multi-type jobs and multi-type servers. Queueing Systems 70: 269–298.CrossRefGoogle Scholar
8.Whitt, W. (1974). The continuity of Queues. Advances in Applied Probability 6: 175–183.CrossRefGoogle Scholar
9.Whitt, W. (2006). A multi-class fluid model for a contact center with skill-based routing. International Journal of Electronics and Communications 60: 95–102.CrossRefGoogle Scholar