Abstract
In this paper, the waiting time and response time processes in continuous-time two parallel queueing systems are analyzed as well as the system size process in discrete-time two parallel queueing systems. Upon arrival, each job splits into two tasks, denoted by task 1 and task 2. Task k, $k = 1,2$, is assigned to the kth queueing system to be served on a FCFS (first-come-first-served) basis. Each queueing system consists of a single server and an infinite-capacity queue. For the continuous-time queueing system, we assume that jobs arrive in a state-independent Poisson fashion with rate $\lambda $; the servers have exponential service times with rates $\mu _1 $ and $\mu _2 $, respectively. A closed-form expression for the Laplace transform of the ergodic bivariate waiting time distribution is derived. The distribution of the sum of the two waiting times is then obtained. The distribution of the response time when $\mu _1 = \mu _2 $ is derived analytically. For the discrete-time queueing systems, it is assu...
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