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

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

Asia-Pacific Journal of Operational Research (APJOR), 2018, vol. 35, issue 06, 1-21

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.

Keywords: Tollbooth queue; tandem; two-class customers; dedicated servers (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1142/S0217595918500434

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