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Minimizing expected discounted cost in a queueing loss model with discriminating arrivals

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  • Haji, Babak
  • Ross, Sheldon

Abstract

We consider a queuing loss system with heterogeneous skill based servers and Poisson arrivals. We first assume that each arrival has a vector (X1,…,Xn) of independent binary random variables with Xi=1 if server i is eligible to serve that arrival. The service time at server i is exponential with rate μi. Arrivals finding no servers that are both idle and eligible to serve them are lost. Assuming the system incurs a cost of one unit for each lost customer, our goal is to find the optimal policy for assigning arrivals to idle and eligible servers so as to minimize the expected discounted cost of the system. Later, we generalize our model by considering k server pools where each pool i is eligible to serve arrivals with probability pi and all servers within this pool provide service at an exponential rate μi.

Suggested Citation

  • Haji, Babak & Ross, Sheldon, 2020. "Minimizing expected discounted cost in a queueing loss model with discriminating arrivals," European Journal of Operational Research, Elsevier, vol. 282(2), pages 593-601.
    • Handle: RePEc:eee:ejores:v:282:y:2020:i:2:p:593-601
    DOI: 10.1016/j.ejor.2019.09.026
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    References listed on IDEAS

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    1. David D. Yao, 1987. "The Arrangement of Servers in an Ordered-Entry System," Operations Research, INFORMS, vol. 35(5), pages 759-763, October.
    2. Ragavendran Gopalakrishnan & Sherwin Doroudi & Amy R. Ward & Adam Wierman, 2016. "Routing and Staffing When Servers Are Strategic," Operations Research, INFORMS, vol. 64(4), pages 1033-1050, August.
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    Cited by:

    1. Konovalov, Mikhail & Razumchik, Rostislav, 2023. "Finite capacity single-server queue with Poisson input, general service and delayed renovation," European Journal of Operational Research, Elsevier, vol. 304(3), pages 1075-1083.

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