Analysis of a two-class continuous-time queueing model with two tandem dedicated servers

Abstract

Mélange et al. (2016) investigated a continuous-time queueing system with two types of customers each having their own dedicated server, where the two dedicated servers are in parallel and have different service rates, meanwhile, the system adopts a global First-Come-First-Served (gFCFS) service discipline, i.e., all new arrivals queue together in a common FCFS queue, regardless of their types. In the present paper, we aim to give a further study on this queueing model, in which the two dedicated servers are accommodated in series. By using matrix analytic method and spectral expansion method, steady state probabilities are derived to make the straightforward computation of performance measures and the sojourn time of an arbitrary customer. Finally, some numerical examples are provided to show the effect of several system parameters on performance measures.