Volume 6, Number 1 (2022)
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Home > Journals > SCIREA Journal of Information Science and Systems Science > Archive > Paper Information

Simulation Models of Modified Multiple Vacation Policy for Multi-Server Queuing Systems

Volume 6, Issue 1, February 2022    |    PP. 62-88    |PDF (1647 K)|    Pub. Date: February 12, 2022
DOI: 10.54647/isss12197    9 Downloads     713 Views  

Author(s)
Zhernovyi Yuriy, Faculty of Mechanics and Mathematics, Ivan Franko National University of Lviv, Ukraine

Abstract
We consider a multi-server vacation queueing system that operates in the modified multiple vacation policy related to the number of busy servers. The condition for the transition to vacation mode at the time of the release of the server is the lack of customers in the queue and the implementation of one of the restrictions on the number of servers currently in use by customers (CU-condition): CUU-condition is satisfied, then it takes another vacation. Using GPSS World simulation models, we studied the dependencies of the system performance measures on the following parameters: the load factor, coefficient of variation of the inter-arrival times, value of CU, duration of vacations, and number of servers. We tested the simulation models by comparing the results with the known ones obtained by an analytical method. The value of the simulation time, which makes it possible to obtain results corresponding to the stationary process, is determined. The results for systems with and without vacations are compared.

Keywords
queueing system, vacations, modified multiple vacation policy, simulation model, GPSS World

Cite this paper
Zhernovyi Yuriy, Simulation Models of Modified Multiple Vacation Policy for Multi-Server Queuing Systems, SCIREA Journal of Information Science and Systems Science. Vol. 6 , No. 1 , 2022 , pp. 62 - 88 . https://doi.org/10.54647/isss12197

References

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[ 3 ] Ibe, O., “M/G/1 Vacation Queueing Systems with Server Timeout,” American Journal of Operations Research, 5 (2). 77-88. Mar.2015.
[ 4 ] Takagi, H., Queueing Analysis: A Foundation of Performance Evaluation, Vacation and Priority Systems, Part I, Volume I; North-Holland, Amsterdam, 1991.
[ 5 ] Yadin, M. and Naor, P., “Queueing system with a removable service station,” Journ. of the Operational Research Society, 14 (4). 393-405. 1963.
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[ 7 ] Levy, Y. and Yechiali, U., “Utilization of idle time in an M/G/1 queueing system,” Manag. Sci., 22 (2). 202–211. Oct.1975.
[ 8 ] Birta, L.G. and Arbez, G., Modelling and Simulation: Exploring Dynamic System Behaviour, 3rd edition, Springer Nature, Switzerland, 2019, 491-520.
[ 9 ] Zhernovyi, Yu., Creating models of queueing systems using GPSS World: Programs, detailed explanations and analysis of results, LAP Lambert Academic Publishing, Saarbrücken, 2015, 220 p.
[ 10 ] Levy, Y. and Yechiali, U., “An M/M/s queue with servers vacations,” Information Systems and Operational Research, 14 (2). 153-163. 1976.

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