A Fuzzy-Based Control System for Customers’ Admission in a Two-Station Queue Network

Abstract

The study proposes a fuzzy-based control of admission of customers in a queue network with two stations in tandem. Each of the stations has individual arrival streams which may either be accepted or rejected. Class i arrivals occur in a Poisson stream with constant rate λi, i = 1, 2. Successive services in each station j are independent and exponentially distributed, with mean 1/µj in station j, j =1, 2, irrespective of the customer’s class. The objective of the study is to decide an optimal admission policy based on the state of the queue such that profit is maximized. The state of the system is described by (z1, z2), where zi is the number of customers in station i, and i = 1, 2. The tool adopted is a fuzzy process which determines this policy using the fuzzy input values, s and λ giving a corresponding decision, dec. which is either a ‘1’ or ‘0’ representing ‘Admit’ or ‘Reject’ respectively. The membership functions of arrivals were defined and implemented using fuzzy rules to derive a fuzzy output of decision which either ‘Admit’ or ‘Reject’ an arrival. Numerical results show a considerable improvement in the control of customers’ admission and it was concluded that the proposed method is efficient in the control of customers’ admission in queue network.