Parametric nonlinear programming for fuzzified queuing systems with catastrophe

Abstract

The concept of catastrophe, happening at random and leading to force to abandon all present customers, data, machines immediately and the instantly inoperative of the service facilities until a new arrival of the customer is not uncommon in many practical problems of the computer and communication systems. In this research article, we present a process to frame the membership function of queuing system' characteristics of the classical single server M/M/1 fuzzy queuing model having fuzzified exponentially distributed inter-arrival time and service time with fuzzy catastrophe. We employ the α-cut approach to transform fuzzy queues into a family of the conventional crisp intervals for the queuing characteristics which are computed with a set of the parametric nonlinear program using their membership functions. We employ basic fuzzy arithmetic fundamental, Zadeh's extension principle, Yager's ranking index to establish fuzzy relation among different rates and to compute corresponding defuzzify values.