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Fuzzy control of two-station queueing networks with two types of customers

Yannis Phillis, Runtong Zhang

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Summary

This paper considers tandem two-station queueing networks with two types of customers. Firstly, we examine a model where type 1 customers visit station 1 only while type 2 customers visit both stations in sequence. Each station has a single server and unlimited buffer capacity. The service rate in station 1 is variable. The cost depends on the queue length and selected rate. The objective is to dynamically route customers of both types to station 1 and choose the service rate, based on the state of the system, so as to minimize the average cost over an infinite horizon. Secondly, we examine a system in which station 1 has one server, station 2 two servers, and the buffers have infinite capacity. Two types of customers are first served at station 1 and subsequently proceed to the buffer of a given server according to type in station 2. A reward is earned whenever station 1 accepts a customer and a holding cost is incurred by a customer in buffer at station 2. The objective is to dynamically select the type of customer to be next served at station 1 so as to maximize the average benefit. Customer routing, service rate selection, and flow control are considered simultaneously. We use fuzzy control to solve these complex problems. Simulation shows that the approach is efficient.

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