Sojourn time distributions in modulated G-queues with batch processing

Analysis of generalized QBD queues with matrix-geometrically distributed batch arrivals and services

“…The queue length and the sojourn time analysis of the basic variant of this queue have been published in [Chakka and Harrison(2001)] and [Harrison and Zatschler(2004)], respectively. If c = 1 (single server) and there are no negative customers the system belongs to the model class presented in this paper.…”

Fast Computation of Hyper-exponential Approximations of the Response Time Distribution of MMPP/M/1 Queues

“…To this end, we compare the latency of our fast model solving technique, whose implementation still relies on Mathematica, with the latency for obtaining the queue statistics via either simulative analysis or by applying the most efficient exact solution technique (to the best of our knowledge) presented in [9], for which we have developed an implementation using again the Mathematica library. Actually, the main computational steps required by this exact solution are the following:…”

“…By these data we get that our fast model solving procedure always shows execution time lower than (or at most up to) 11 milliseconds, while the simulative solution shows latency from 5 to 10 seconds. Concerning the exact method in [9], it shows execution time on the order of 100 milliseconds only for the MMPP with 2 states. On the other hand, its performance rapidly decreases when the number of states in the MMPP arrival process gets increased.…”

Accuracy vs efficiency of hyper-exponential approximations of the response time distribution of MMPP/M/1 queues

“…On the basis of the discussions and deductions in Section 3, we have conducted the analysis while varying the parameters µ, ρ i and α i,j , as well as the number of states composing the MMPP arrival process. Also, the approximation error is evaluated by comparing the output statistics of the approximate model with those obtained by the implementation of the exact solution technique in [14]. …”

“…Compared to several other works addressing exact solution techniques for the M M P P/M/1 queue (based either on matrix geometric methods [2,24], or on generating functions [12], or on spectral expansion [6,13], or even on a combination of these approaches [14,34]), some of the approximations in [5] do not require iterative or numerical methods, e.g., for the determination of matrix eigenvalues/eigenvectors. Hence they can provide benefits for the latency of the analysis.…”