A novel model to determine the optimal number of servers in finite input source fuzzy queueing system

The finite input source queueing system has been widely used to solve many problems appearing on machine maintenance and repair systems, client-server computing, and production line operations, etc. In classical queueing models, arrival intensity is assumed to be a Poisson distribution and the service times of all servers follow a independent and identically exponential distribution, in which the arrival intensity depend on the number of units in system. Obviously, with the increasing number of servers, the waiting time of units and the utilization rate of servers are decreased, while the expected degree of acceptability are enhanced. Based on three criteria of the utilization rate of servers, the expected degree of acceptability and system cost, this paper develop a decision-making index to determine the optimal number of servers in fuzzy finite input source queueing system, which copes with the mathematical relationships of these criteria. An example show the effectiveness and the sensitivity analysis is taken.