Journal of Applied Probability

A queueing loss model with heterogeneous skill based servers under idle time ordering policies

Babak Haji and Sheldon M. Ross

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Abstract

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.

Article information

Source
J. Appl. Probab., Volume 52, Number 1 (2015), 269-277.

Dates
First available in Project Euclid: 17 April 2015

Permanent link to this document
https://projecteuclid.org/euclid.jap/1429282621

Digital Object Identifier
doi:10.1239/jap/1429282621

Mathematical Reviews number (MathSciNet)
MR3336861

Zentralblatt MATH identifier
1315.60098

Subjects
Primary: 60K25: Queueing theory [See also 68M20, 90B22]
Secondary: 60J27: Continuous-time Markov processes on discrete state spaces 90B22: Queues and service [See also 60K25, 68M20]

Keywords
Heterogeneous server queueing loss system limiting probability no-memory policy method of stages reverse chain equilibrium distribution Gibbs sampler

Citation

Haji, Babak; Ross, Sheldon M. A queueing loss model with heterogeneous skill based servers under idle time ordering policies. J. Appl. Probab. 52 (2015), no. 1, 269--277. doi:10.1239/jap/1429282621. https://projecteuclid.org/euclid.jap/1429282621


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