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ARPN Journal of Science and Technology >> Volume 7, Issue 1, January 2017

ARPN Journal of Science and Technology


Bulk Arrival Single Server, Bernoulli Feedback Queue with Fuzzy Vacations and Fuzzy Parameters

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Author M.Jeeva, E.Rathnakumari
ISSN 2225-7217
On Pages 492-499
Volume No. 2
Issue No. 5
Issue Date June 01, 2012
Publishing Date June 01, 2012
Keywords Batch arrival, vacation policy, a-cut, membership function, performance measures.



Abstract

This papers deals with a mathematical non-linear programming method to construct the membership function of the system characteristics of a M/G/1, bulk arrival queues with server vacations and feedback facility, in which arrival rate, service time, batch size, departure probability, and vacation time are all fuzzy numbers. A customer after getting a service, if requires another service, is taken immediately for the next service and this can be repeated any number of times. The server leaves for a vacation as soon as the system becomes empty and returns after a vacation of random duration. Both single and multiple vacation polices are considered. The a cut approach is used to transform a fuzzy queue into a family of conventional crisp queues in this context. By means of membership functions of the system characteristics, a set of parametric nonlinear programs is developed to describe the family of crisp single server bulk - arrival queues with fuzzy feedback probability and fuzzy vacation time. A man power planning problem is solved successfully to illustrate the validity of the proposed approach. Because the system characteristics are expressed and governed by the membership functions, the fuzzy bulk - arrival queues with single server are represented more accurately and analytic result are more useful for system designers and practitioners.


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