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Analysis of a Tollbooth Tandem Queue with Two-Class Customers and Two Heterogeneous Dedicated Servers

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  • Tao Jiang

    (College of Economics and Management, Shandong University of Science and Technology, Qingdao 266590, P. R. China)

Abstract

Do [European Journal of Operational Research, 247, 672–675] discussed a tollbooth tandem queue with two heterogeneous servers, where customers arrive the system according to a Poisson process and the service times at the two heterogeneous servers follow an exponential distribution. In this present paper, we aim to consider a tollbooth tandem queue with two-class customers and two heterogeneous dedicated servers, i.e., different types of customers should be served by their dedicated servers. Using matrix analytic method and spectral expansion method, we derive the steady state probabilities, which are then used for the computation of other performance measures and the Laplace–Stieltjes transform (LST) of the sojourn time of an arbitrary customer. Finally, some numerical examples are provided to illustrate the impact of several system parameters to the performance measures.

Suggested Citation

  • Tao Jiang, 2018. "Analysis of a Tollbooth Tandem Queue with Two-Class Customers and Two Heterogeneous Dedicated Servers," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(06), pages 1-21, December.
    • Handle: RePEc:wsi:apjorx:v:35:y:2018:i:06:n:s0217595918500434
    DOI: 10.1142/S0217595918500434
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    References listed on IDEAS

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    1. Bruneel, Herwig & Mélange, Willem & Steyaert, Bart & Claeys, Dieter & Walraevens, Joris, 2012. "A two-class discrete-time queueing model with two dedicated servers and global FCFS service discipline," European Journal of Operational Research, Elsevier, vol. 223(1), pages 123-132.
    2. Herwig Bruneel & Willem Mélange & Dieter Claeys & Joris Walraevens, 2017. "A two-class global FCFS discrete-time queueing model with arbitrary-length constant service times," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 164-178, April.
    3. Gu, Weihua & Cassidy, Michael J. & Li, Yuwei, 2012. "On the capacity of highway checkpoints: Models for unconventional configurations," Transportation Research Part B: Methodological, Elsevier, vol. 46(10), pages 1308-1321.
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    Cited by:

    1. Gabi Hanukov & Michael Hassoun & Oren Musicant, 2021. "On the Benefits of Providing Timely Information in Ticket Queues with Balking and Calling Times," Mathematics, MDPI, vol. 9(21), pages 1-16, October.

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