Abstract
This paper deals with the study of multi-server queueing model in a fuzzy environment with imposition of reneging of customers. Entry of the customers in the system is assumed to be Poisson process and exponential service time distribution under first-come-first-served basis. Specific of this investigation is to derive the various fuzzy performance measures such as fuzzy queue length, fuzzy waiting time in queue, fuzzy response time and fuzzy optimal number of servers in explicit form for the finite capacity multi-server queueing system by using recursive method. For the validity of the model we have obtained the numerical illustrations in tabular form which shows that fuzzy-queue can be more realistic than crisp queue.
Highlights
Since the birth of queueing theory concept in 1909 by the contribution of A
We develop the mathematical model of optimization of multi-server finite capacity Markovian queueing model in the fuzzy-environment under the reneging behavior of the customers
Let us consider the car-workshop with capacity of N = 8 cars at a time which are repaired/inspected by multiple mechanics and we find various following performance measures of the system
Summary
Since the birth of queueing theory concept in 1909 by the contribution of A. We develop the mathematical model of optimization of multi-server finite capacity Markovian queueing model in the fuzzy-environment under the reneging behavior of the customers. In the problems with maintenance and inventory which have a large number of states and exact information of a particular state is difficult to know and automatic machining systems have been designed in fuzzy-concepts that motivated us to study the model under investigation This model may be of the first of this kind in which optimization of model under fuzzy environment with imposition of reneging of customers has been taken under study and major objective of this work is to determine the various fuzzy performance measures such as fuzzy queue length, fuzzy waiting time in queue, fuzzy response time and fuzzy optimal number of servers
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