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

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.