Analysis of an N-policy M/Ek/1 Queueing system
with Unreliable server, Multiple Vacations and
Balking

P.Jayachitra; A.James Albert

doi:https://doi.org/10.14445/22315373/IJMTT-V21P511

International Journal of Mathematics Trends and Technology

Research Article | Open Access

Volume 21 | Number 2 | Year 2015 | Article Id. IJMTT-V21P511 | DOI : https://doi.org/10.14445/22315373/IJMTT-V21P511

Analysis of an N-policy M/Ek/1 Queueing system with Unreliable server, Multiple Vacations and Balking

P.Jayachitra, A.James Albert

Citation :

P.Jayachitra, A.James Albert, "Analysis of an N-policy M/Ek/1 Queueing system with Unreliable server, Multiple Vacations and Balking," International Journal of Mathematics Trends and Technology (IJMTT), vol. 21, no. 2, pp. 77-82, 2015. Crossref, https://doi.org/10.14445/22315373/IJMTT-V21P511

Abstract

Present investigation deals with optimal control of a non reliable and removable server in an N-policy M/Ek/1 queueing system with server multiple vacations and balking. The server can be turned off and takes a vacation whenever the system is empty. If the number of units waiting in the system is less than N, the server will take another vacation. When the queue length reaches N (N≥1), the server is immediately turned on and serves the waiting units until the number of units in the system becomes empty. Arriving customers may balk with certain probability and may depart without getting service due to impatience. Lack of service occur where the server is busy or due to sudden breakdown. By applying probability generating function technique expected number of units in the system is obtained and also derived various performance measures. Further the total expected cost function is developed to determine the optimal threshold N at a minimum cost. The sensitivity analysis is performed to examine the effect of various parameters in the system.

Keywords

N-policy, M/Ek/1 queueing system, probability generating function, server vacations, balking.

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