Construction of Fuzzy Queues

Abstract

近幾年，等候系統開始被廣泛的應用於分析工作上可能產生的延遲。\r\n平均花費在系統中和等候線上的時間成為描述等候系統行為兩個最基本的數量。除了工作的延遲外，我們考慮顧客在等候線上的延遲也會受到滿意度的影響。由於顧客滿意度會影響顧客的到達率，因此系統到達率和系統服務率變成模糊集合。我們建構一個模糊的等候系統並且提出一個去模糊化的方法。這篇論文研究的目的在於呈現一個分析系統的方法，利用此方法解決模糊的系統中最佳化的問題。\r\n\r\n關鍵字: 模糊等候，最佳化。

Queueing models for analyzing the possible delay of tasks have\r\nbeen studied for past several decades. Since then, the average\r\ntime spent in the system and the average time spent in queue have become two of the most fundamental quantities describing a\r\nqueueing system`s behavior. In additional to the delay of tasks,\r\nwe consider the satisfaction of customers affected by several\r\nfactors in system. Since the satisfaction reflects the arrival rate and service rate, the arrival rate and the service rate seem more close to the fuzzy sets. We construct a fuzzy queueing model and introduce an optimization problem of a fuzzy queue. The objective of this optimization problem is to present an approach that analyzes the model and decide the optimal number of servers while minimizing the total cost which is a fuzzy set. As a result, we provide a solution procedure to compute the required performance measure in a service-oriented environment.\r\n\r\nKeywords: Fuzzy Queue, Optimization

Contents\r\nAbstract . . . . . . . . . . . . . . . . . . . . . . . . . i\r\n中文摘要 . . . . . . . . . . . . . . . . . . . . . . . . . ii\r\n1 Introduction 1\r\n2 Fuzzy Matrices 4\r\n2.1 Research Background . . . . . . . . . . . . . . . . 4\r\n2.2 Convergence of Fuzzy Matrices . . . . . . . . . . . 7\r\n3 A Fuzzy Queueing System 12\r\n3.1 Fuzzy Sets of Service Rates . . . .. . . . . . . . . 12\r\n3.2 Fuzzy Sets of Arrival Rates . . . . . . . . . . . . 13\r\n3.3 Transition Matrix . . . . . . . . . . . . . . . . . 14\r\n4 An Optimization Model 17\r\n4.1 Model Description . . . . . . . . . . . . . . . . . 17\r\n4.2 Defuzzy Methods . . . . . . . . . . . .. . . . . . . 19\r\n4.3 Illustrative Examples . . . . . . . . . . . . . . . 21\r\n4.4 Comparison in Different Defuzzy Methods . . . . . . 27\r\n5 Conclusions 42\r\nReferences 45\r\nAppendix 1 47\r\nAppendix 2 49\r\nAppendix 3 53