Performance Analysis of a Batch Arrival Queueing System Under Fuzzy Environment

Abstract

In this paper, we investigate the steady-state performance analysis of a batch arrival queueing system  under fuzzy environment. In practice, operational parameters such as arrival and service rates are rarely known with precision. Randomness-Fuzziness consistency principle is used to define a normal law of fuzziness established by two distinct laws of randomness for the system’s uncertain parameters. Two different models are constructed and analysed; the  model, which feature fuzzy batch arrivals paired with service as a crisp value and  model, where batches arrive at a crisp value but undergo service governed by a Triangular Fuzzy Number. This approach yields the membership functions for essential steady state system performance measures. Numerical example is solved to demonstrate the practical application and validity of the theoretical models.