Analysis of Various Queueing Models Using Fuzzy Logic

Abstract

Queueing models are widely used to study waiting-line systems in service, transportation, production, communication, and industrial environments. Classical queueing theory usually assumes that arrival rates, service rates, and batch sizes are known exactly. In many real-life situations, however, these parameters are uncertain and are better represented through linguistic or fuzzy values. This paper analyzes bulk-arrival multi-server queueing models under triangular and trapezoidal fuzzy environments. The ????-cut method and the DSW algorithm are used to obtain fuzzy performance measures, including the expected number of customers in the queue, expected number of customers in the system, mean waiting time in the queue, and mean waiting time in the system. A numerical example based on a toll-tax system is used, where vehicles arrive in bulk and are served through three toll counters. The results show that triangular fuzzy numbers provide narrower performance intervals, while trapezoidal fuzzy numbers produce wider uncertainty ranges. The comparison helps identify how different fuzzy representations affect queueing performance under uncertain arrival and service conditions.