STUDY OF QUEUING BEHAVIOUR UNDER THE ENVIRONMENT OF FUZZY LOGICS

Abstract

Queuing Behaviour systems are analyzed in banks, hospitals, restaurants, transport systems, service counters, computer systems, and other industrial systems using queueing theory. Most classical queueing models start with the assumption that request/response characteristics are known precisely. In actual applications, however, the above parameters may not be well known, may be ambiguous, or may be expressed in natural language. The uncertainty can be represented by fuzzy numbers and fuzzy function in fuzzy logic representation. This paper studies the behaviour of M/M/1and M/M/2queueing models under a fuzzy environment. The arrival rate and service rate are represented as triangular fuzzy numbers. The fuzzy performance measures obtained are traffic intensity, number of customers in queue, number of customers (Q) in system, waiting time (w) in queue and waiting time (W) in system using the α-cut method and the DSW algorithm. Finally, a numerical example is used for comparison of fuzzy M/M/1 and fuzzy M/M/2 models. As the number of servers is increased, the size of the queues decreases as does the waiting time, as indicated by the results. So fuzzy queueing models are a more valid technique for analysing systems with an uncertain behaviour of arrival and service conditions.