Simulation Models of the Bi-Level Randomized Policy and  N-Policy for Multi-Server Queueing Systems

Abstract
We consider a multi-server G/G/n queue that operates the bi-level randomized (p, N1, N2)-policy or the N-policy. This means that as soon as there are no more customers in the system, the server will be shut down immediately. If the number of arriving customers falls to a particular low threshold value N1, the server will be activated for work with a probability of p or remain turned off with a probability of 1‒p. If the number of arriving customers reaches a specified high threshold value N2 (≥N1), the server will start serving waiting customers until the system is empty again. When p=1 or p=0 or N1=N2=N, the (p, N1, N2)-policy becomes the classic N-policy. Using GPSS World simulation models, we studied the dependencies of system performance measures on the following parameters: threshold values N1, N2 or N, the load factor, coefficient of variation of inter-arrival times, and number of servers. We validated the simulation models by comparing the results with those obtained by an analytical method. We determined the simulation time required to obtain results corresponding to the stationary process. By utilizing the created simulation models, we can solve the problem of minimizing a long-run expected cost rate by selecting appropriate values for the thresholds N1 and N2.

Keywords
queueing system, N-policy, be-level randomized policy, simulation model, GPSS World

Cite this paper
Yuriy Zhernovyi, Simulation Models of the Bi-Level Randomized Policy and N-Policy for Multi-Server Queueing Systems, SCIREA Journal of Information Science and Systems Science. Vol. 7 , No. 3 , 2023 , pp. 48 - 74 . https://doi.org/10.54647/isss120287

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