Research Article
DOI:
xxx-xxxx-xxx
Subject:
science
KeyWords:
Fuzzy sets, Membership functions, retrial time, generalised vacation, non-linear programming, heterogeneous service.
Abstract:
This work constructs the membership function of the system characteristics of a single server retrial queues with batch arrivals, two phase of heterogeneous service and a generalised vacation time under Bernouli schedule. Here the batch-arrival rate, batch size, retrial rate, service time, vacation time are all fuzzy numbers. The α-cut approach is used to transform a fuzzy queue into a family of conventional crisp queues in this context. By means of the membership functions of the system characteristics, a set of parametric nonlinear programs is developed to describe the family of crisp-single server batch arrival
| queues. A numerical example is solved successfully to illustrate the validity of the proposed approach. Because of the system characteristics are expressed and governed by the membership function, the single server fuzzy batch arrival retrial queue with heterogeneous service and generalised vacation are represented more accurately and the analytic results are more useful for system designers and practitioners. |
