Analysis of Waiting Times in M/M/1 Queue Model Using Fuzzy Control Chart

Abstract

This paper proposes a technique to construct fuzzy control chart (graphical technique) for the waiting time in the queue model FM/FM/1 where the inter-arrival and service time are Fuzzified. Fuzzy queue is more realistic than the conventional crisp queue models. The basic idea of this paper is based upon Zadeh extension principle .The objective is transform fuzzy control chart of FM/FM/1 model to a family of crisp model by α-cut approach.  Parametric (NLP) Non- linear program approach is followed to derive the membership function of upper and lower bounds for control chart parameters   Trapezoidal fuzzy numbers are used to determine the validity of the proposed method, numerical example is illustrated.