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A Queueing Loss Model with Heterogeneous Skill Based Servers Under Idle Time Ordering Policies

Part of: Markov processes Operations research and management science Special processes

Published online by Cambridge University Press:  30 January 2018

Babak Haji  and
Sheldon M. Ross
Babak Haji*
Affiliation:
University of Southern California
Sheldon M. Ross*
Affiliation:
University of Southern California
*
∗ Postal address: Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, CA 90089, USA.
∗∗ Email address: bhaji@usc.edu
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Abstract

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We consider a queueing loss system with heterogeneous skill based servers with arbitrary service distributions. We assume Poisson arrivals, with each arrival having a vector indicating which of the servers are eligible to serve it. An arrival can only be assigned to a server that is both idle and eligible. Assuming exchangeable eligibility vectors and an idle time ordering assignment policy, the limiting distribution of the system is derived. It is shown that the limiting probabilities of the set of idle servers depend on the service time distributions only through their means. Moreover, conditional on the set of idle servers, the remaining service times of the busy servers are independent and have their respective equilibrium service distributions.

Keywords

Heterogeneous serverqueueing loss systemlimiting probabilityno-memory policymethod of stagesreverse chainequilibrium distributionGibbs sampler

MSC classification

Primary: 60K25: Queueing theory
Secondary: 60J27: Continuous-time Markov processes on discrete state spaces 90B22: Queues and service

Information

Type
Research Article
Information
Journal of Applied Probability , Volume 52 , Issue 1 , March 2015 , pp. 269 - 277
Copyright
© Applied Probability Trust 

Footnotes

This material is based upon work supported by the National Science Foundation under contract/grant number CMMI1233337.

References

Adan, I. and Weiss, G. (2012). A loss system with skill-based servers under assign to longest idle server policy. Prob. Eng. Inf. Sci. 26, 307–321.CrossRefGoogle Scholar
Barbour, A. D. (1976). Networks of queues and the method of stages. Adv. Appl. Prob. 8, 584–591.CrossRefGoogle Scholar
Cooper, R. B. and Palakurthi, S.. (1989). Heterogeneous-server loss systems with ordered entry: an anomaly. Operat. Res. Lett. 8, 347–349.CrossRefGoogle Scholar
Fakinos, D. (1980). The M/G/k blocking system with heterogeneous servers. J. Operat. Res. Soc. 31, 919–927.CrossRefGoogle Scholar
Fakinos, D. (1982). The generalized M/G/k blocking system with heterogeneous servers. J. Operat. Res. Soc. 33, 801–809.CrossRefGoogle Scholar
Gopalakrishnan, R., Doroudi, S., Ward, A. R., and Wierman, A. (2015). Routing and Staffing when Servers are Strategic. Working paper.Google Scholar
Kelly, F. P. (1976). Networks of queues. Adv. Appl. Prob. 8, 416–432.CrossRefGoogle Scholar
Kelly, F. P. (1979). {Reversibility and Stochastic Networks}. John Wiley, Chichester.Google Scholar
Ross, S. M. (2014). Optimal server selection in a queueing loss model with heterogeneous exponential servers, discriminating arrivals, and arbitrary arrival times. J. Appl. Prob. 51, 880–884.CrossRefGoogle Scholar
Schassberger, R. (1976). On the equilibrium distribution of a class of finite-state generalized semi-Markov processes. Math. Operat. Res. 1, 395–406.CrossRefGoogle Scholar
Schassberger, R. (1977). Insensitivity of steady-state distributions of generalized semi-Markov processes. I. Ann. Prob. 5, 87–99.CrossRefGoogle Scholar
Schassberger, R. (1978). Insensitivity of steady-state distributions of generalized semi-Markov processes. II. Ann. Prob. 6, 85–93.CrossRefGoogle Scholar
Whitt, W. (1974). The continuity of queues. Adv. Appl. Prob. 6, 175–183.CrossRefGoogle Scholar