【摘要】：排隊(duì)論或稱隊(duì)論,是研究各種排隊(duì)性質(zhì)的理論,是為了研究如何設(shè)計(jì)、使用一個服務(wù)系統(tǒng),且使這個服務(wù)系統(tǒng)既能滿足實(shí)際問題解決的需要,同時使整個過程花費(fèi)最少的一門學(xué)科。如果用數(shù)學(xué)思想來解釋,可以把它歸結(jié)為運(yùn)籌學(xué)。排隊(duì)問題,現(xiàn)實(shí)生活中無處不在。而排隊(duì)問題的解決的關(guān)鍵是如何優(yōu)化排隊(duì)系統(tǒng)中主要性能指標(biāo),如負(fù)荷配置、顧客平均等待隊(duì)長、顧客平均等待時間、緩沖區(qū)占有量及某種穩(wěn)定狀態(tài)出現(xiàn)的概率等。然而諸如這些優(yōu)化問題的目標(biāo)函數(shù)均是非線性的,通常的優(yōu)化算法難以得到滿意的結(jié)果。本文主要是研究如何將排隊(duì)問題中某些性能指標(biāo)的非線性優(yōu)化問題轉(zhuǎn)化成運(yùn)籌學(xué)中的凸優(yōu)化問題,并用目前凸優(yōu)化理論中較完備且成熟的內(nèi)點(diǎn)法,作為計(jì)算工具。全文主要對排隊(duì)問題中顧客平均等待隊(duì)長這一性能指標(biāo)的優(yōu)化問題進(jìn)行研究分析,首先將原問題近似等價為幾何規(guī)劃問題,然后通過變量替換,轉(zhuǎn)換成凸優(yōu)化問題,最后利用凸優(yōu)化內(nèi)點(diǎn)法進(jìn)行具體的算法設(shè)計(jì)和收斂性分析。結(jié)果證明,將凸優(yōu)化內(nèi)點(diǎn)法引入排隊(duì)系統(tǒng)這一性能指標(biāo)的優(yōu)化問題中,能夠充分展示了內(nèi)點(diǎn)算法的優(yōu)點(diǎn),整個算法迭代次數(shù)少,收斂速度快,收斂結(jié)果滿足排隊(duì)系統(tǒng)實(shí)際需求,且在具體提高整個排隊(duì)系統(tǒng)服務(wù)效率和服務(wù)質(zhì)量頗有成效。
[Abstract]:Queuing theory, or queue theory, is a theory that studies the nature of queuing. It is to study how to design and use a service system, and to make the service system meet the needs of practical problem solving. A discipline that simultaneously minimizes the cost of the whole process. If it is explained by mathematical thought, it can be reduced to operational research. The problem of queuing is ubiquitous in real life. The key to solve the queuing problem is how to optimize the main performance indicators in the queuing system, such as load allocation, customer average waiting length, customer average waiting time, buffer possession and probability of occurrence of some stable state. However, the objective functions of these optimization problems are nonlinear, and the usual optimization algorithms are difficult to obtain satisfactory results. In this paper, we mainly study how to transform the nonlinear optimization problem of some performance indexes in queueing problem into convex optimization problem in operational research, and use the more complete and mature interior point method in convex optimization theory as a calculation tool. In this paper, the optimization problem of customer average waiting length in queuing problem is studied and analyzed. Firstly, the original problem is equivalent to geometric programming problem, and then the optimization problem is transformed into convex optimization problem by variable substitution. Finally, the convex optimization interior point method is used to design the algorithm and analyze the convergence. The results show that the convex optimization interior point method can fully demonstrate the advantages of the interior point algorithm when it is introduced into the optimization problem of queueing system. The whole algorithm has fewer iterations, faster convergence speed, and the convergence results can meet the actual needs of queueing system. Moreover, it is effective to improve the service efficiency and service quality of the whole queuing system.
【學(xué)位授予單位】：南京大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O226
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本文編號：2310181