本文選題：排隊系統(tǒng) + 負顧客��； 參考：《燕山大學(xué)》2015年碩士論文

【摘要】：隨著信息技術(shù)的迅猛發(fā)展,各種各樣復(fù)雜的排隊系統(tǒng)也隨之不斷的涌現(xiàn),尤其是帶有負顧客和優(yōu)先權(quán)的排隊模型更具有實際的應(yīng)用價值。本文研究了等待空間有限的帶有負顧客、止步的、強占優(yōu)先權(quán)和成批到達的三個工作休假排隊模型,這些模型是已有文獻中相關(guān)模型的推廣。論文主要有以下三部分組成。首先考慮的是一個帶有負顧客和止步的有限容量M/M/1/N單重工作休假排隊系統(tǒng)。首先利用馬爾科夫過程理論建立了系統(tǒng)的穩(wěn)態(tài)概率所滿足的方程組,并利用分塊矩陣的方法求出了系統(tǒng)穩(wěn)態(tài)概率的矩陣解;其次在此基礎(chǔ)上得到了系統(tǒng)的平均等待隊長、平均隊長以及正顧客的損失率等性能指標;最后通過數(shù)值例子,分析了N=3時系統(tǒng)的參數(shù)vm和q對系統(tǒng)平均等待隊長、顧客的消失概率這兩個性能指標的影響。其次考慮的是一個帶有負顧客和止步的成批到達的有限容MX/M/1/N單重工作休假排隊系統(tǒng)。首先我們利用馬爾科夫過程理論建立了系統(tǒng)的穩(wěn)態(tài)概率所滿足的方程組,并利用分塊矩陣的方法求出了系統(tǒng)穩(wěn)態(tài)概率的矩陣解;其次在此基礎(chǔ)上得到了系統(tǒng)的平均等待隊長、平均隊長以及正顧客的損失率等性能指標;最后通過數(shù)值例子,分析了N=3時系統(tǒng)的參數(shù)vm和q,對系統(tǒng)的兩個重要性能指標平均隊長和顧客的消失概率的影響。最后在帶有負顧客和強占優(yōu)先權(quán)排隊系統(tǒng)的基礎(chǔ)上引入多重休假策略,考慮一個帶有負顧客和強占優(yōu)先權(quán)的有限容M/M/1/N多重休假排隊系統(tǒng)。首先我們利用馬爾科夫過程理論建立了系統(tǒng)穩(wěn)態(tài)概率所滿足的方程組,推導(dǎo)出系統(tǒng)穩(wěn)態(tài)概率向量的迭代計算公式;其次在此基礎(chǔ)上得到了系統(tǒng)的平均隊長、平均等待隊長以及顧客的平均損失率等性能指標;最后以N=3為例,對系統(tǒng)參數(shù)進行了敏感性分析。
[Abstract]:With the rapid development of information technology, a variety of complex queuing systems are emerging, especially the queuing model with negative customers and priority has more practical application value.In this paper, we study three working vacation queuing models with limited waiting space with negative customers, stop, preemptive priority and batch arrival. These models are generalizations of the related models in previous literatures.The paper is composed of three parts as follows.The first consideration is a finite capacity M/M/1/N single working vacation queuing system with negative customers and stop.In this paper, the equations of steady-state probability of the system are established by using Markov process theory, and the matrix solution of the steady-state probability of the system is obtained by using the method of block matrix, and then the average queue length of the system is obtained.Finally, the effects of the system parameters vm and Q on the average queue length and the customer vanishing probability are analyzed by numerical examples.Secondly, a finite capacity MX/M/1/N single working vacation queuing system with negative customers and stops is considered.First of all, we use Markov process theory to set up the equations satisfied by the steady-state probability of the system, and obtain the matrix solution of the steady-state probability of the system by using the method of block matrix, and then we obtain the average queue length of the system.Finally, through numerical examples, the effects of the parameters vm and qof the system with N = 3 on the average length and the customer disappearance probability of the two important performance indexes of the system are analyzed, such as the average queue length and the loss rate of the positive customer.Finally, a multiple vacation policy is introduced based on the queuing system with negative customers and preemptive priority, and a finite capacity M/M/1/N multiple vacation queueing system with negative customers and preemptive priority is considered.First of all, we establish the equations of steady-state probability of the system by using Markov process theory, and derive the iterative formula of the steady-state probability vector of the system, and then we obtain the average length of the system on the basis of which the average length of the system is obtained.The average waiting length and the average loss rate of the customer are analyzed. Finally, the sensitivity of the system parameters is analyzed by taking NN3 as an example.
【學(xué)位授予單位】：燕山大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：O226

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1 王玉;帶有負顧客和優(yōu)先權(quán)的排隊系統(tǒng)分析[D];燕山大學(xué);2012年

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本文編號：1766083