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In this, we studied and investigated IFM/IFG/1 vacation queueing system/waiting line with server breakdowns, repair and server timeout, “by using (Triangular Trapezoidal and Pentagonal) IF (Intuitionistic Fuzzy) numbers with the application of IFS (Intuitionistic fuzzy set). Here we operate single server vacation queueing system in the following manner; when the system finds empty, the server waits for fixed time ’c’ known as server timeout. At the expiration of this time, if no one arrives into the system, then server takes the vacation. If anyone arrived in the system during the timeout period as well as in vacation the server commences the service otherwise, he will go for another vacation. If the system had occurred with a breakdown, just after a break down the server undergoes for repair. After the repaired process is completed the server restarts the service to the arrived customer. By the approach of IFS properties, we develop the membership function of the system performance are of fuzzy nature. Based on IFS α-cut approach the Intuitionistic fuzzy queues are reduced to a family of ICS (Intuitionistic Crisp Set). The numerical results are illustrated to the model. |
