在非抢占优先站点轮询系统中顾客等待时间

为了解决银行顾客排队现象,本文提出解决这种排队现象的服务策略,根据服务原则建立模型--具有非抢占优先站点轮询系统,讨论系统在平稳条件下,对于具有一个非抢占的优先权站点且采用穷尽服务方式下的轮询系统进行理论分析,利用排队理论,给出每个站点的队长的概率母函数及顾客的等待时间的拉普拉斯*斯蒂尔切斯变换,实现了该服务方案的定性分析.     

具有非抢占优先站点的轮询系统顾客队长

本文讨论轮询系统在系统平稳条件下,对于具有一个非抢占的优先权站点且采用穷尽服务方式下的轮询系统进行理论分析,给出服务员轮询到每个站点时该站点的队长及数学期望。     

GI／G／1排队系统的队长和等待时间的瞬时分布

本是[1，2]的继续,在本中利用马氏骨架过程给出了GI／G／1排队系统的队长的瞬时分布的另一新的计算方法和等待时间的计算方法。     

带启动时间的N-策略Geo/G/1排队系统的队长分布及容量的优化设计

考虑带启动时间的N-策略离散时间Geo/G/1排队系统,使用全概率分解技术,从任意初始状态出发,研究了队长的瞬态和稳态性质,推导出了在任意时刻n瞬态队长分布的z -变换的递推表达式、稳态队长分布的递推表达式和附加队长分布的表达式,并获得稳态队长的随机分解结果.最后,通过数值实例,讨论了稳态队长分布对系统参数的敏感性,并阐述了获得便于计算的稳态队长分布的表达式在系统容量的优化设计中的重要应用价值.     

假期中顾客以概率θ进人的Geo/G/1(E,SV)排队系统的队长分布

考虑单重休假的Geo/G/1离散时间排队系统,其中在服务员休假期间到达的顾客以概率θ(0<θ≤1)进入系统.通过引入"服务员忙期"和使用全概率分解技术,从任意初始状态出发,研究了队长的瞬态和稳态性质,导出了在任意时刻n瞬态队长分布的z-变换的递推表达式和稳态队长分布的递推表达式,以及稳态队长的随机分解.最后,通过数值实例,讨论了稳态队长分布对系统参数的敏感性,并阐述了获得便于计算的稳态队长分布的表达式在系统容量设计中有重要的价值.     

成批到达的有特殊服务时间的多重休假排队系统分析

本文利用嵌入马尔可夫链方法研究了多重休假M^X／Gn／1排队系统。首先，利用概率分析法得到了排队系统的嵌入马尔可夫链的一步转移概率矩阵，以此为依据得到系统的稳态队长和同批第一个接受服务顾客的稳态等待时间。     

Queue Length Distribution in a FIFO Single-Server Queue with Multiple Arrival Streams Having Different Service Time Distributions

This paper considers the queue length distribution in a class of FIFO single-server queues with (possibly correlated) multiple arrival streams, where the service time distribution of customers may be different for different streams. It is widely recognized that the queue length distribution in a FIFO queue with multiple non-Poissonian arrival streams having different service time distributions is very hard to analyze, since we have to keep track of the complete order of customers in the queue to describe the queue length dynamics. In this paper, we provide an alternative way to solve the problem for a class of such queues, where arrival streams are governed by a finite-state Markov chain. We characterize the joint probability generating function of the stationary queue length distribution, by considering the joint distribution of the number of customers arriving from each stream during the stationary attained waiting time. Further we provide recursion formulas to compute the stationary joint queue length distribution and the stationary distribution representing from which stream each customer in the queue arrived.     

Polling systems with multiple coupled servers

We consider polling systems with multiple coupled servers. We explore the class of systems that allow an exact analysis. For these systems we present distributional results for the waiting time, the marginal queue length, and the joint queue length at polling epochs. The class in question includes several single-queue systems with a varying number of servers, two-queue two-server systems with exhaustive service and exponential service times, as well as infinite-server systems with an arbitrary number of queues, exhaustive or gated service, and deterministic service times.     

排队系统平稳等待时间的性质

讨论了M/G/1排队系统平稳等待时间的随机序关系及利用Mathematica 4.0软件探讨了爱尔朗排队系统Er/M/1（r≤6）的平稳等待时间的分布。     

The Virtual Waiting Time for the Batch Arrival Queueing Systems

Abstract

In the article the G ^η I/G/1-type batch arrival system with infinite waiting-room is considered. The explicit formulae for the distribution of the virtual waiting time at any fixed moment t and as t → ∞ are obtained. The study is based on generalization of Korolyuk's method for semi-markov random walks.     

部分服务台休假的M/M/c排队的等待时间

我们证明了Erlang分布的若干有趣性质，使用这些性质，给出部分服务台休假的排队系统中等待时间分布的一个简洁而直观的表达式．     

具有等待者的Kornai-Weibul排队模型的修正与分析

这篇文章首先明确地指出，具有等待的买者的Ｋｏｒｎａｉ－Ｗｅｉｂｕｌ排队模型与没有等待者的Ｋｏｒｎａｉ－Ｗｅｉｂｕｌ排队模型具有相同的纰漏．其次，本文在较自然的条件下严格地证明了修正后的模型存在“正常状态”．研究Ｋｏｒｎａｉ－Ｗｅｉｂｕｌ排队模型理论能够深刻地揭示计划经济的弊端．     

Analytical Distribution of Waiting Time in the M/{iD}/1 Queue

We give an analytical formula for the steady-state distribution of queue-wait in the M/G/1 queue, where the service time for each customer is a positive integer multiple of a constant D > 0. We call this an M/{iD}/1 queue. We give numerical algorithms to calculate the distribution. In addition, in the case that the service distribution is sparse, we give revised algorithms that can compute the distribution more quickly.AMS subject classification: 60K25, 90B22