Application of Fuzzy System on a Server-Dependent Queue Modeled with Empirical Bayesian Estimation

Abstract

This study presents a fuzzy system by collecting membership function and rules based on a decision model that uses empirical Bayesian estimation to construct a server-dependent M /M /2 /L queue. A Markovian queue of finite capacity in which the number of servers depends upon queue length is considered. First, data on the interarrival times and service times are collected by observing a queuing system, and the empirical Bayesian method is adopted to estimate its server utilization. Second, the costs are associated with the operation of the second server and the waiting of customers, to establish a cost minimization model to determine the optimal number of customers in the system to activate the second server (N), and the optimal number of customers in system to deactivate the second server (Q). The decision model provides knowledge to construct rules used in a fuzzy inference system. The MATLAB Fuzzy Inference Toolbox is used to construct a fuzzy system to aid management in determining when to initiate the second server and when to turn it off, according to specific parameters.