部分服务台同步多重休假的GI/M/c稳态等待时间

在前期研究的基础上,利用概率计算的方法,研究了在经典GI/M/c排队系统中引入部分服务台同步多重休假策略后的稳态等待时间及其随机分解.     

基于排队论的机要保障装备系统建模与优化

运用排队论的理论和方法对由机要保障装备构成的随机服务系统进行建模和优化.首先通过建模分析得出该系统符合M/G/c/c/(模型,进而从不用的应用角度建立系统效能模型和愿望模型来实现系统的优化设计,最后通过对实验数据的分析得到一些有用的结论并给出效能模型中参数的参考取值范围.     

Bernoulli抵消策略的负顾客的M/G/1排队系统

负顾客的排队模型是排队论近年来的新兴分支。文中引入了带有B ernou lli抵消策略的负顾客的M/G/1排队模型,即到达的负顾客以概率p抵消队首正在接受服务的正顾客,以1-p的概率抵消队尾的正顾客,利用补充变量法,状态转移法和L变换,最后得到系统稳态队长的概率母函数。     

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。     

基于N-策略的多级适应性休假的M/G/1排队系统

N-策略的休假排队模型有着广泛的应用背景。在文献[2-3]的基础上,研究了N-策略多级适应性休假M/G/1排队系统。通过使用全概率分析方法、拉普拉斯变换和拉普拉斯-斯蒂阶变换理论,得到各阶段队长的瞬态分布、队长的母函数以及平均队长的递推表达式。为预测某时刻顾客数量的概率大小、获得利益最大化的阈值N提供了理论依据。     

"M/M/1"在单火力单元射击多目标火力分配中的应用

在单服务台排队系统理论的基础上,建立了单火力单元对多个目标射击的系统仿真模型,对此模型进行了分析,给出了模型的适用范围,并通过在计算机上仿真运行实例,验证了该仿真模型的正确性.该方法是一种有益的尝试与探索,对局部作战指挥决策有一定的参考价值.     

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。     

多UAV/MALD协同下战机生存力评估模型

对战机在多架无人机(Unmanned Aerial Vehicle,UAV)或小型空射诱饵弹(Miniature Air Launched Decoy,MALD)协同下执行突防任务的飞机生存模型进行了研究,建立了飞机生存力分析的等效时间模型;建立了基于M/M/1/N排队论的战机在地面防空系统的威胁下,由多架UAV/MALD协同下的生存力评估模型,并通过计算实例,比较了地面防空单元作战通道、UAV和MALD投放速率、战机使用对抗措施等因素对战机生存力的影响.结果表明,通过投放UAV/MALD会降低战机被地面防空系统"服务"的概率,但是也会因为增加了防空系统对战机的平均"服务"时间而降低战机生存力,在使用UAV/MALD时需要合理设置投放参数,才能达到提高被掩护战机生存力的目的.     

排队论在后勤保障中的应用

应用标准的M/M/n模型,证明在一定条件下,n个服务台集中在一起服务,优于各自独立的n个只有一个服务台的服务机构,从而证明在后勤工作中统一使用保障力量、相对集中配置保障力量原则的正确性。     

基于复杂排队系统的三值光学计算机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、M~X/M/1和M/M~B/1构成的复杂排队系统,构建三值光学计算机的四阶段服务模型,同时建立立即调度和结束时调度两种策略和算法。基于不同排队系统讨论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。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。     

A queueing system with vacations after N services

This article is devoted to the study of an M/G/1 queue with a particular vacation discipline. The server is due to take a vacation as soon as it has served exactly N customers since the end of the previous vacation. N may be either a constant or a random variable. If the system becomes empty before the server has served N customers, then it stays idle until the next customer arrival. Such a vacation discipline arises, for example, in production systems and in order picking in warehouses. We determine the joint transform of the length of a visit period and the number of customers in the system at the end of that period. We also derive the generating function of the number of customers at a random instant, and the Laplace–Stieltjes transform of the delay of a customer. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 646–658, 2015     

Waiting times for M/G/1 queues with service-time or delay-dependent server vacations

This article shows how to determine the stationary distribution of the virtual wait in M/G/1 queues with either one-at-a-time or exhaustive server vacations, depending on either service times or accrued workload. For the first type of dependence, each vacation time is a function of the immediately preceding service time or of whether the server finds the system empty after returning from vacation. In this way, it is possible to model situations such as long service times followed by short vacations, and vice versa. For the second type of dependence, the vacation time assigned to an arrival to follow its service is a function of the level of virtual wait reached. By this device, we can model situations in which vacations may be shortened whenever virtual delays have gotten excessive. The method of analysis employs level-crossing theory, and examples are given for various cases of service and vacation-time distributions. A closing discussion relates the new model class to standard M/G/1 queues where the service time is a sum of variables having complex dependencies. © 1992 John Wiley & Sons, Inc.     

Distribution of the workload in multiclass queueing systems with server vacations

The steady-state workload at an arbitrary time is considered for several single-server queueing systems with nonpreemptive services for multiple classes of customers (arriving according to Poisson processes) and server vacation (switchover) times. The distribution of the workload at an arbitrary point during the vacation period is obtained for systems with setup times, and for polling systems with exhaustive, gated, or globally gated service disciplines. From the stochastic decomposition property, this workload is added to the workload in the corresponding M/G/1 system without vacations to give the workload at an arbitrary time in vacation systems. Dependence of the workload distribution on the vacation parameters is studied.     

A note on sojourn times in M/G/1 queues with instantaneous,bernoulli feedback

Queueing systems which include the possibility for a customer to return to the same server for additional service are called queueing systems with feedback. Such systems occur in computer networks for example. In these systems a chosen customer will wait in the queue, be serviced and then, with probability p, return to wait again, be serviced again and continue this process until, with probability (1 – p) = q, it departs the system never to return. The time of waiting plus service time, the nth time the customer goes through, we will call his nth sojourn time. The (random) sum of these sojourn times we will call the total sojourn time (abbreviated, sojourn time when there is no confusion which sojourn time we are talking about). In this paper we study the total sojourn time in a queueing system with feedback. We give the details for M/G/1 queues in which the decision to feedback or not is a Bernoulli process. While the details of the computations can be more difficult, the structure of the sojourn time process is unchanged for the M/G/1 queue with a more general decision process as will be shown. We assume the reader is familiar with Disney, McNickle and Simon [1].     

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     

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.     

Probabilistic priorities in the M/G/1 queue

A simple method is presented for deriving the mean and variance of the queueing time distribution in an M/G/1 queue when the priorities assigned to customers have an assignment probability distribution. Several examples illustrate the results. The mean and variance of the queueing time distribution for the longest service time discipline are derived, and its disadvantages are discussed.     

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”.