Heterogeneous Multiserver Queues With General Input

A Bayesian Approach to Find Random-Time Probabilities From Embedded Markov Chain Probabilities

“…Notice that the third row is obtained by (5), which matches exactly row 1. In this case, q i ¼ 1 for i , N, and q i ¼ 0 otherwise.…”

“…This provided us with the joint distribution of the arrival phase and the number in the system and, from this, we obtained the P i and p i as follows. Notice that the third row is obtained by (5), which matches exactly row 1.…”

“…For instance, networks with all but one server having an exponential service time can be so analyzed, and in all these cases, the Baysian approach outlined in this article will work. Our method will also work in the case of the GI / M / c queue with heterogeneous server, a model analyzed in [5] by Markov renewal methods. In some problems, it might be difficult to find the throughput, in which case one probability cannot be determined, and the others can only be obtained up to a factor.…”

“…As a check, consider the GI/M/1 queue with l i ¼ l. In this case, U ¼ l, and (5) yields P i ¼ p i21 l/m, which matches with the formulas give in the literature (see, e.g., [8, p. 196]). In [5], an algorithm is given for finding both p i and P i , given constant interarrival times, using classical Markov renewal-type arguments. We used this algorithm to calculate p i and P i for some cases with c ¼ 2.…”

GTH Algorithm, Censored Markov Chains, and $RG$-Factorization

“…A list of publications by 1993, in which the GTH algorithm was used, can be found in Grassmann [5], including: Kohlas [15], Heyman [10], Heyman and Reeves [11], Grassmann and Heyman [6], Stewart [28], O'Cinneide [25]. The list of references closely related to the GTH algorithm, published after 1993, is so large, and only a small sample is included here: Stewart [29], Dayar and Stewart [2], Grassmann and Zhao [8],…”