随机环境中的M/MY/1排队系统

文献［４］讨论了随机环境中的Ｍ／Ｍ／１排队模型，本文提出和讨论随机环境中的Ｍ／Ｍｙ／１排队模型，在统计平衡条件下给出了队长和等待队长的平稳分布以及平均队长和平均等待队长，得到了等待时间和逗留时间分布以及平均等待时间和平均逗留时间。     

部分服务台同步多重休假的GI/M/c稳态队长

在经典GI/M/c排队中引入部分服务台同步多重休假策略,利用拟单生过程和矩阵几何解的方法,求解系统的稳态队长分布及其条件随机分解。     

A queueing process with varying degree of service

This article describes and presents some results of the analysis of a queueing process where the degree of service given to a customer is subject to control by the management. The control doctrine used is based on the queue length and also on the recent history of the system.     

On multipopulation queuing systems with first-come first-served discipline

Steady-state probabilities for a multipopulation single channel multiserver queuing system with first-come first-served queue discipline are established. Special cases lead to simplified formulas which sometimes can be evaluated using existing statistical and/or queuing tables. Optimization aspects are considered involving control of service rates. Several applications are presented.     

Performance analysis of queue length monitoring of M/G/1 systems

This study investigates the statistical process control application for monitoring queue length data in M/G/1 systems. Specifically, we studied the average run length (ARL) characteristics of two different control charts for detecting changes in system utilization. First, the nL chart monitors the sums of successive queue length samples by subgrouping individual observations with sample size n. Next is the individual chart with a warning zone whose control scheme is specified by two pairs of parameters, (upper control limit, d_u) and (lower control limit, d_l), as proposed by Bhat and Rao (Oper Res 20 (1972) 955–966). We will present approaches to calculate ARL for the two types of control charts using the Markov chain formulation and also investigate the effects of parameters of the control charts to provide useful design guidelines for better performance. Extensive numerical results are included for illustration. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

An M/M/1 queue with delayed feedback

We present some results for M/M/1 queues with finite capacities with delayed feedback. The delay in the feedback to an M/M/1 queue is modelled as another M-server queue with a finite capacity. The steady state probabilities for the two dimensional Markov process {N(t), M(t)} are solved when N(t) = queue length at server 1 at t and M(t) = queue length at server 2 at t. It is shown that a matrix operation can be performed to obtain the steady state probabilities. The eigenvalues of the operator and its eigenvectors are found. The problem is solved by fitting boundary conditions to the general solution and by normalizing. A sample problem is run to show that the solution methods can be programmed and meaningful results obtained numerically.     

On queues with dependent interarrival and service times

AnM/G/1 queueing system is studied in which the service time required by a customer is dependent on the interarrival time between his arrival and that of his predecessor Assuming the two variables are “associated,” we prove that the expected delay in this system is less than or equal to than of a conventional M/G/1 queue This conclusion has been verified via simulation by Mitchell and Paulson [9] for a special class of dependent M/M/1 queue. Their model is a special case of the one we consider here. We also study another modified GI/G/1 queue. where the arrival process and/or the service process are individually “associated”.     

混合排队规则的战术装备维修保障系统分析

首先将战术装备维修保障过程描述为M/M/c/k混合规则的排队过程,其损坏装备到达服从相互独立的泊松分布,维修时间服从相互独立的指数分布。同时考虑系统的到达率和维修率随系统中装备数量的变化,重要战损装备等待维修时的不耐烦性以及重要装备对一般装备的强占性优先权情况,结合战术装备维修保障系统的结构和规模,建立战术装备维修保障M/M/3/12排队模型。列出模型的平衡方程,采用矩阵的分析方法得到重要装备和一般装备的稳态分布表达式,并以队长为指标进行了系统性能的计算。     

基于复杂排队系统的TOC服务模型与性能分析

三值光学计算机的运算请求处理过程缺乏合理、系统的性能评价标准与体系。基于M/M/1、M/M/n、MX/M/1和M/MB/1构成的复杂排队系统,构建了三值光学计算机的四阶段服务模型,同时建立了立即调度和结束时调度两种不同策略与算法。基于不同排队系统讨论了运算请求的接收时间、预处理时间、运算时间和发送时间的计算方法,进而得到最终响应时间。最后,通过仿真实验对两种策略的模型进行验证,结果表明结束时调度策略明显优于立即调度策略。     

The queue G/M/m/N: Busy period and cycle,waiting time under reverse and random order service

The busy period, busy cycle, and the numbers of customers served and lost therein, of the G/M/m queue with balking is studied via the embedded Markov chain approach. It is shown that the expectations of the two discrete variables give the loss probability. For the special case G/M/1/N a closed expression in terms of contour integrals is obtained for the Laplace transform of these four variables. This yields as a byproduct the LIFO waiting time distribution for the G/M/m/N queue. The waiting time under random order service for this queue is also studied.     

有限服务能力的损失制排队系统M/M/1分析

提出了随机服务系统的服务能力问题,给出有限服务能力的损失制M／M／1模型的描述和其稳态解,并求出了评价系统运行的几个主要数量指标。     

State-dependent gap acceptance

This paper considers a traffic problem in which vehicles queue up according to a Poisson process on a single-lane entrance ramp prior to merging into a major stream of vehicular traffic. In order to then prevent the ramp queue from becoming too large, a model is proposed which considers a lowering of the critical gap as the ramp queue size increases. With the critical gap assumed to be a nonincreasing function of the number of vehicles on the ramp at instances that correspond to departure times of lead vehicles from the ramp queue, the resultant model is an M/G/1 queue with state-dependent service times. Some general results are obtained for this model and a specific case discussed in moderate detail.     

基于Stateflow的排队系统仿真方法

论述了排队系统与Stateflow相关概念，利用有限状态机理论与面向对象编程思想，提出了建立基于Stateflow排队系统模型的分析步骤，阐述了应用Stateflow对排队系统进行建模与仿真的方法，使用Stateflow对M／M／1／∞／∞／FIFO类型排队系统进行了具体的建模与仿真。仿真结果表明，基于Stateflow的模型与仿真能够有效地描述排队系统的统计特性，并具有可视化、流程化和层次化的特点。     

Stochastic analysis of a single server retrial queue with general retrial times

Retrial queueing systems are widely used in teletraffic theory and computer and communication networks. Although there has been a rapid growth in the literature on retrial queueing systems, the research on retrial queues with nonexponential retrial times is very limited. This paper is concerned with the analytical treatment of an M/G/1 retrial queue with general retrial times. Our queueing model is different from most single server retrial queueing models in several respectives. First, customers who find the server busy are queued in the orbit in accordance with an FCFS (first‐come‐first‐served) discipline and only the customer at the head of the queue is allowed for access to the server. Besides, a retrial time begins (if applicable) only when the server completes a service rather upon a service attempt failure. We carry out an extensive analysis of the queue, including a necessary and sufficient condition for the system to be stable, the steady state distribution of the server state and the orbit length, the waiting time distribution, the busy period, and other related quantities. Finally, we study the joint distribution of the server state and the orbit length in non‐stationary regime. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 561–581, 1999     

On queueing systems with variable service capacities

In some queueing systems the total service capacity utilized at any given time is a variable under the control of a decision maker. Management doctrines are examined which prescribe the actual service capacity as a function of the queue length and the recent history of the system. Steady state probabilities, expected queue lengths and frequencies of change in capacity are evaluated for a wide class of possible control schemes. Optimization procedures are outlined.     

Queues with stochastic service rates

The purpose of this paper is to explore an extension of the output discipline for the Poisson input, general output, single channel, first-come, first-served queueing system. The service time parameter, μ, is instead considered a random variable, M. In other words, the service time random variable, T, is to be conditioned by a parameter random variable, M. Therefore, if the distribution function of M is denoted by F_M(μ) and the known conditional service time distribution as B(t |_μ), then the unconditional service distribution is given by B(t) = Pr {T ≤ t}. = ∫_-∞^∞ B(t |_μ) dF_M(μ). Results are obtained that characterize queue size and waiting time using the imbedded Markov chain approach. Expressions are derived for the expected queue length and Laplace-Stieltjes transforms of the steady-state waiting time when conditional service times are exponential. More specific results are found for three special distributions of M: (1) uniform on [1.2]; (2) two-point; and (3) gamma.     

基于排队论的防空导弹群作战效能研究

结合防空导弹群防空战斗的特点,利用可列状态生灭过程的排队论方法,研究了防空导弹群作战效能,建立了数学模型,分析了导弹群防空武器系统对目标平均击毁概率的计算方法,并通过引入拦截适宜性因子对理想条件下的排队模型进行了修正,为类似问题的研究提供了一种参考。     

The effect of prior assumptions on the expected cost of m/m/1 queueing systems with unknown arrival rate

In this study we deal with the determination of optimal service rate in an M/M/1 queue. The arrival rate is unknown and assumed to be a random variable with a known distribution function. Holding and operating costs are considered and service rate is determined to minimize total expected discounted costs for infinite horizon. The effects of the arrival rate's distribution properties on the characteristics of the system are examined.     

一个具有相互独立、不同分布服务时间序列的排队模型

讨论的排队模型 ,放宽了GI/G/1系统中“服务时间独立同分布”的限制 ,只要求各服务时间相互独立 ,因而较GI/G/1排队模型能更合理地拟合实际问题 .在此较宽的条件下 ,利用补充变量的方法 ,求得了该排队系统队长的瞬时分布     

Sensitivity of queueing models to the assumption of exponentiality

This study deals with determining the effects on queuing models of assuming that interarrival and service times are exponentially distributed. Steady-state expected value measures of congestion are compared for a variety of GI/G models when assuming an M/M model as an approximation. The majority of this effort involves single-channel queues; however, some multichannel situations are also considered. In addition, effects of the exponential approximation are observed in certain cost-optimization models.