A Non-Preemptive Priority Queueing System with a Single Server Serving Two Queues M/G/1 and M/D/1 with Optional Server Vacations Based on Exhaustive Service of the Priority Units

We study a vacation queueing system with a single server simultaneously dealing with an M/G/1 and an M/D/1 queue. Two classes of units, priority and non-priority, arrive at the system in two independent Poisson streams. Under a non-preemptive priority rule, the server provides a general service to the priority units and a deterministic service to the non-priority units. We further assume that the server may take a vacation of random length just after serving the last priority unit present in the system. We obtain steady state queue size distribution at a random epoch. Corresponding results for some special cases, including the known results of the M/G/1 and the M/D/1 queues, have been derived.

On One Model of Multichannel Queuing System with Unreliable Repairable Servers and Input Memory

The work deals with the development of analytical model of multichannel technical queuing system with unreliable servers and input memory where server failure flows and incoming request flows comply with Poissonian laws, while the flows of failed facilities repairs and flows of incoming requests comply with exponential laws of probability distribution. Random process of system change-over is a Markovian process with continuous time and discrete states. Relations binding basic parameters and output characteristics of the system indicated are obtained as probabilities of system staying in the given moment in one of the possible states. The proposed model is the most generalized compared to some models known in literature which could be considered as special cases of the considered model.

Customer Joining Behavior and Regulation Strategy in Visible Multi-Server Queues with Synchronous Vacations of Partial Servers

This paper studies customer joining behavior and system regulation strategy in nonexhaustive visible M/M/m queues with synchronous vacations of a part of the servers.Once this part of the servers are idle,they take multiple vacations simultaneously(vacation period).Until there are customers waiting in the queue,they are reactivated and all servers are busy or idle(busy period).The authors call this part of the servers as“partial servers”.In view of the fully visible queue and the almost visible queue,the authors obtain customers’equilibrium joining threshold strategies and their socially optimal joining threshold strategies,respectively,and observe that customer joining behavior in equilibrium generally makes the system overcrowded,which makes the equilibrium social welfare lower than the optimal social welfare.After regulation,interestingly,for optimizing social welfare,the system manager hopes not only customers arriving in vacation period pay attention to the number of partial servers,but also customers arriving in busy period should care about it rather than ignore.Moreover,arranging more servers for vacation does not necessarily lead to the decrease of social welfare on condition that the number of partial servers is close to m.As for the information advantage of the fully visible case,it is not obvious for increasing social welfare and even unfavorable to servers’profit unless the number of partial servers is big enough.Furthermore,given the different composition of social welfare,there exists the optimal number of partial servers and the optimal arrival rate of customers for maximizing social welfare.

Effects of Reneging, Server Breakdowns and Vacation on a Batch Arrival Single Server Queueing System with Three Fluctuating Modes of Service

This article examines the effects of reneging, server breakdown and server vacation on the various states of the batch arrivals queueing system with single server providing service to customers in three fluctuating modes. In this queueing system, any batch arrival joins the queue if the server is busy or on vacation or under repair. However, if the server is free, one customer from the arriving batch joins the service immediately while others join the queue. In case of server breakdown, the customer whose service is interrupted returns back to the head of the queue. As soon as the server has is repaired, the server attends to the customer in mode 1. For this queueing system, customers that are impatient due to breakdown and server vacation may renege (leave the queue without getting service). Due to fluctuating modes of service delivery, the system may provide service with complete or reduced efficiency. Consequently, we construct the mathematical model and derive the probability generating functions of the steady state probabilities of several states of the system including the steady state queue size distribution. Further, we discuss some particular cases of the proposed queueing model. We present numerical examples in order to demonstrate the effects of server vacation and reneging on the various states of the system. The study revealed that an increase in reneging and a decrease in server vacation results in a decrease in server utilization and an increase in server’s idle time provided rates of server breakdown and repair completion are constant. In addition, the probability of server vacation, the probability of system is under repair and the probabilities that the server provides service in three fluctuating modes decreases due to an increase in reneging and a decrease in vacation completion rates.

一种基于区块链的MQTT协议优化算法

通信协议的设计已然成为实现设备与互联网通信的重要支撑,其覆盖了整个物联网系统的各个环节。针对传统物联网协议中关键数据被伪造或篡改的安全问题,文章设计了一种在数据传输过程中使用区块链技术来保证传输数据安全的改进消息队列遥测传输(message queue telemetry transmission,MQTT)协议,进而保证了存储在broker的数据不被恶意篡改。通过仿真实验证明,该方法具有高效、轻量以及易实现等多方面的特点,在保护物联网的数据安全方面效果十分显著。

部分服务台同步多重休假的排队库存系统

本文研究了(s,S)库存策略的多服务台排队库存系统,其中库存为空时有部分服务台同步多重休假,休假时间服从指数分布。顾客到达为泊松过程,每个服务台的服务时间和补货时间均服从指数分布。利用拟生灭过程和矩阵几何解法,计算了系统稳态概率和一些性能指标,并给出了系统单位时间的平均费用函数。最后,通过数值算例分析了参数对费用函数的影响,并得到最优库存策略和最优平均费用。

具有耐烦服务员和N-策略的M/G/1可中断休假排队系统

考虑具有耐烦服务员和N-策略的M/G/1休假排队系统,其中服务员的假期可中断.运用全概率分解技术、更新理论和拉普拉斯变换工具,分析了系统的瞬态队长分布和稳态队长分布,获得了瞬态队长分布的拉普拉斯变换表达式和稳态队长分布的递推表达式,并进一步证明了稳态队长的随机分解性质.最后,通过建立费用结构模型,结合数值实例,讨论了使系统在长期单位时间内的期望费用最小的最优控制策略N*.

Python Server Page Performance Analysis and Modeling

Today, in the field of computer networks, new services have been developed on the Internet or intranets, including the mail server, database management, sounds, videos and the web server itself Apache. The number of solutions for this server is therefore growing continuously, these services are becoming more and more complex and expensive, without being able to fulfill the needs of the users. The absence of benchmarks for websites with dynamic content is the major obstacle to research in this area. These users place high demands on the speed of access to information on the Internet. This is why the performance of the web server is critically important. Several factors influence performance, such as server execution speed, network saturation on the internet or intranet, increased response time, and throughputs. By measuring these factors, we propose a performance evaluation strategy for servers that allows us to determine the actual performance of different servers in terms of user satisfaction. Furthermore, we identified performance characteristics such as throughput, resource utilization, and response time of a system through measurement and modeling by simulation. Finally, we present a simple queue model of an Apache web server, which reasonably represents the behavior of a saturated web server using the Simulink model in Matlab (Matrix Laboratory) and also incorporates sporadic incoming traffic. We obtain server performance metrics such as average response time and throughput through simulations. Compared to other models, our model is conceptually straightforward. The model has been validated through measurements and simulations during the tests that we conducted.

THE QUEUE-LENGTH DISTRIBUTION FOR M^x/G/1 QUEUE WITH SINGLE SERVER VACATION

This paper studies the bulk-arrival M-x/G/1 queue with single server vacation. By introducing the server busy period and using the Laplace transform, the recursion expression of the Laplace transform of the transient queue-length distribution is derived. Furthermore, the distribution and stochastic decomposition result of the queue length at a random point in equilibrium are obtained. Especially some results for the single-arrival M/G/1 queue with single server vacation and bulk-arrival M-x/G/1 queue but with no server vacation can be derived directly by the results obtained in this paper.

AN M/G/1 RETRIAL QUEUE WITH SECOND MULTI-OPTIONAL SERVICE,FEEDBACK AND UNRELIABLE SERVER

An M/G/1 retrial queue with two-phase service and feedback is studied in this paper, where the server is subject to starting failures and breakdowns during service. Primary customers get in the system according to a Poisson process, and they will receive service immediately if the server is available upon arrival. Otherwise, they will enter a retrial orbit and are queued in the orbit in accordance with a first-come-first-served （FCFS） discipline. Customers are allowed to balk and renege at particular times. All customers demand the first “essential” service, whereas only some of them demand the second “multi-optional” service. It is assumed that the retrial time, service time and repair time of the server are all arbitrarily distributed. The necessary and sufficient condition for the system stability is derived. Using a supplementary variable method, the steady-state solutions for some queueing and reliability measures of the system are obtained.

THE TRANSIENT SOLUTION FOR M/G/1 QUEUEWITH SERVER VACATIONS

In this paper, the transient solutions for M/G/1 queues with single server vacation and multiple server vacations are firstly studied, and the recursion expressions of their Laplace transform are given. Further the distribution and stochastic decomposition result of the queue length at a random point in equilibrium are directly obtained from the transient solution. As will be seen this paper provides a intuitive and elegant method for studying transient solutions for M/G/1 queues with single server.

Analysis of the WWW System Performance

A simple, high-level, open queueing network model is presented from which several general performance results for WWW server on the Internet are derived. Multiple-Server systems are also analyzed.A theoretical upper bound on the serving capacity of WWW server is defined. The effects of file size,server speed, and network bandwidth on response time are also investigated. In addition, the relative merits of several methods of improving server performance are evaluated.

On One Analytical Model of a Probability Estimation of Quality and Efficiency of Functioning of Complex Technical Queuing Systems

The work is dedicated to the development of analytical model of probability estimation of reliability, productivity, quality and efficiency of functioning of the complex technical queuing system consisting of the arbitrary number of marked groups of the service devises (channels, facilities, servers) differing with reliable characteristics (parameters of refusals and restorations) of forming their composition (also of arbitrary number) marked, identical, unreliable and restorable serving channels in which for serving come in requirements with intensities depending on marking of channels. In the considered system it is supposed that the currents of refusals of serving devices and currents of coming requirements are subdued to Poisson, and the currents of restorations of refused devices and the currents of services of coming requirements—exponential laws of distribution of probabilities. A stochastic process of transfers of a system by that is Markovian process with continuous time and discrete states. Correlations linking the basic parameters and exit characteristics of the systems of the pointed out type are obtained in a view of probabilities of the system location in the given moment of time in one of the possible states.

A Single Server Queue with Coxian-2 Service and One-Phase Vacation (M/C-2/M/1 Queue)

In this paper, we study a single server queueing system with Coxian-2 service. In Particular, we study M/C-2/M/1 queue with Coxian-2 service and exponential vacation. We assume that units (customers) arrive at the system one by one in a Poisson process and the server provides one-by-one service based on first in first out (FIFO) rule. We obtained the steady state queue size distributions in terms of the probability generating functions, the average number of customers and their average waiting time in the system as well as in the queue.

同步多重休假M/M/c不可视排队系统中的顾客行为及定价策略研究

本文研究同步多重休假M/M/c排队系统中顾客的止步行为和定价策略。当系统为空时,c个服务员同时进入休假状态,一次休假结束后,若系统仍为空,所有服务员继续进行下一次休假,否则同步返回工作状态。基于系统信息几乎不可视和完全不可视两种情形,首先推导出系统的队长稳态分布和顾客的平均逗留时间等性能指标,接着分别从个人最优和系统整体最优的角度出发建立个人剩余效用函数和单位时间社会收益函数,得到两种情形下顾客的均衡止步策略与社会最优止步策略,然后依此为系统制定定价策略,以实现社会收益的最大化。最后,通过数值实验,分别对两种情形下顾客的均衡到达率,社会最优到达率,最优社会收益与系统定价策略关于服务员数量进行灵敏度分析,观察其变化规律及相互关系,以及信息量对顾客行为的影响。

基于BiLSTM神经网络的多服务器门限服务系统性能分析

为了满足运行速度快、时延低、性能好、公平性好等特点,提出了多服务器门限服务系统,并利用BiLSTM(Bi-direc-tional Long Short-Term Memory)神经网络对其进行预测分析,使用多服务器接入方式来降低网络时延,改善系统性能。多个服务器调度时,可以采用同步和异步两种方式。首先,研究多服务器门限服务的系统模型。其次,在单服务器的基础上,利用嵌入马尔可夫链和概率母函数的分析方法对多服务器门限服务的平均排队队长、平均循环周期和平均时延进行求解;同时,利用Matlab进行仿真实验,分别将单服务器系统与多服务器系统的理论值与仿真值进行系统分析,对比多服务器同步和异步两种方式。最后,构建BiLSTM神经网络来预测多服务器系统的性能。实验结果表明,该多服务器系统异步方式优于同步和单服务器系统,多服务器异步系统的性能更好,时延更低,效率更高。综合对比多服务器的3种基本服务系统,在保证公平性的情况下,门限服务系统更加稳定。并且使用BiLSTM神经网络预测算法能够准确预测系统的性能,提高计算效率,对轮询系统的性能评价具有指导意义。

面对有限理性顾客的体验式服务系统最优定价与服务速度研究

在体验式服务系统中,服务时间越长,顾客越满意,但是同时增大了顾客接受服务所需的等待时间,因此企业通常面临着服务速度和服务质量的两难选择。本文采用logit模型刻画有限理性顾客的选择行为,考虑服务台不可靠的体验式服务系统。基于排队博弈理论,分别在垄断和竞争结构下分析管理者的最优定价和服务率决策,并对两种结构进行比较,最后探讨有限理性对顾客效用的影响。研究结果表明:(i)竞争的引入降低了企业的市场份额,但是同类服务的总市场份额增大;(ii)竞争的引入导致企业降低服务速率来提高服务质量,但是服务价格可能同时提高;(iii)竞争的引入可以带来更高的社会福利;(iv)当市场规模较大时,管理者在追求其自身收益最大化时,会导致有限理性顾客进入服务系统所获得的效用为负;但是当市场规模较小时,管理者的最优决策可以保证顾客的效用为正。

有限容量多服务员排队系统全忙期分布函数的一种直观计算途径

排队系统忙期长度是衡量系统运行效率的重要性能指标,它在与排队系统相关的优化问题建模中有着广泛而重要的应用。受数学方法的制约,一段时间以来多服务员有限缓冲空间排队系统的忙期概率分布函数未得到充分的重视与研究。依托马氏多服务员有限缓冲空间排队系统的子全忙期分布及与其相关联的有限缓冲空间排队系统全忙期分布之间的重要关系,给出了寻求马氏多服务员有限容量排队系统服务员全忙期分布函数Laplace-Stieltjes变换的一个迭代计算公式。同时,为了计算该全忙期分布函数在任意给定时刻处的函数值,利用有理函数部分分式分解方法和极点处的留数计算规则对上述Laplace-Stieltjes变换进行了从s域到时间域的反演,并给出了基于变换特征根的半解析化全忙期分布函数反演公式。使用Mathematica软件编程,在数值算例中通过与现有文献结果的对比,证实了所提出分析方法的可行性与简洁性。这为实际工程应用提供了一种较为直观且操作性较强的多服务台有限缓冲空间排队系统全忙期分布函数的计算方法。