Stationary Characteristics of the Single-Server Queue System with Losses and Immediate Service Quality Control

Semi-Markovian model of operation of a single-server queue system with losses and immediate service quality control has been built. In case of unsatisfactory request service quality, its re-servicing is carried out. Re-servicing is executed till it is regarded satisfactory. Time between request income, and request service time are assumed to be random values with distribution functions of general kind. An explicit form of the system stationary characteristics has been defined.

A Maintenance Service Improvement Approach Based on Queue Networks: Application

The quest to increase the performance of production systems that have become complex leads to the transfer to the maintenance function of the responsibility of guaranteeing the availability of such systems. Also, we will never stop saying that maintenance must integrate into all of the company’s initiatives, to affirm its role, which is to ensure greater availability and sustainability of the means of production. The objective of this paper is to evaluate the reliability and availability of a system without knowing the distribution law of the operating times. Among the methods for evaluating dependability criteria (Fault Trees, Petri Nets, etc.), we are interested in queues that have the advantage of taking into account functional dependencies, thus allowing a quantified optimization of maintenance. Indeed, queues make it possible to model parallel or sequential processes, implementing operations taking place at the same time or one after the other, meeting the needs of modeling production systems. The main result of this paper is the study of the influence of availability on the reliability of a multi-state production system.

A NEW AND DIRECT METHOD OF ANALYSIS THE DEPARTURE PROCESSES OF SINGLE SERVER QUEUEING SYSTEMS

In this paper, using the stochastic decomposition and renewal theory we provide the direct method for analysis the departure process of single sever M/G/1 queueing system, and further discuss the departure process of GI/G/1 queueing system. The method provided in this paper is new and concise, which make us see dearly the structure of the departure process of a single server queueing system.

M/G/1 Vacation Queueing Systems with Server Timeout

We consider a single-server vacation queueing system that operates in the following manner. When the server returns from a vacation, it observes the following rule. If there is at least one customer in the system, the server commences service and serves exhaustively before taking another vacation. If the server finds the system empty, it waits a fixed time c. At the expiration of this time, the server commences another vacation if no customer has arrived;otherwise, it serves exhaustively before commencing another vacation. Analytical results are derived for the mean waiting time in the system. The timeout scheme is shown to be a generalized scheme of which both the single vacation and multiple vacations schemes are special cases, with c=∞and c=0, respectively. The model is extended to the N-policy vacation queueing system.

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.

SUBGEOMETRIC RATES OF CONVERGENCE OF THE GI/G/1 QUEUEING SYSTEM

The article deals with the waiting time process of the GI/G/1 queueing system.We shall give that the rate of convergence to the stationary distribution and the decay of the stationary tail only depend on the tail of the service distribution,but not on the interarrival distribution.We shall also give explicit criteria for the rate of convergence and decay of stationary tail for three specific types of subgeometric cases（Case 1：the rate function r（n）=exp（sn1/1＋α）,α〉0,s〉0;Case 2：polynomial rate function r（n）=nα,α〉0;Case 3：logarithmic rate function r（n）=logαn,α〉0）.

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.

Optimal policy for controlling two-server queueing systems with jockeying

This paper studies the optimal policy for joint control of admission, routing, service, and jockeying in a queueing system consisting of two exponential servers in parallel.Jobs arrive according to a Poisson process.Upon each arrival, an admission/routing decision is made, and the accepted job is routed to one of the two servers with each being associated with a queue.After each service completion, the servers have an option of serving a job from its own queue, serving a jockeying job from another queue, or staying idle.The system performance is inclusive of the revenues from accepted jobs, the costs of holding jobs in queues, the service costs and the job jockeying costs.To maximize the total expected discounted return, we formulate a Markov decision process(MDP) model for this system.The value iteration method is employed to characterize the optimal policy as a hedging point policy.Numerical studies verify the structure of the hedging point policy which is convenient for implementing control actions in practice.

Development and Investigation of the Program Model of Multichannel Queueing System with Unreliable Recoverable Servers in Matlab Environment

In real life, in different industries, we often deal with systems designed for multiple use for performing single-type tasks. Processes taking place at this time are called service of requirements, and the systems themselves—Queueing Systems. This article is dedicated to computer software modelling of processes taking place in the systems in question, Markov processes in particular. In this article, by means of Matlab environment, software realization of one of the typical models of queueing service theory-multichannel QS with unreliable recoverable servers and limited number of requirements in the system, is fulfilled. The results of this research are important because it gives the possibility to use received results to determine optimality degree of some real queueing systems that possess Markov property.

An Algorithm for Estimating the Expected Number of Customers for a Class of Markovian Queueing Systems

An algorithm is presented for estimating the expected number of customers for a class of Markovian queueing systems. The class is characterized by those systems whose transition matrix for the underlying customer arrival and departure process is finite, irreducible, and aperiodic. The algorithm does not depend on a closed-form solution for the limiting behavior of the queue. The expected number of customers is frequently used as a measure of effectiveness to describe the behavior of the system or to optimize its design or control. To calculate such a quantity one must usually obtain a closed-form expression for the steady-state probabilities. Unfortunately, of the myriad of Markovian queueing systems, only a few have known closed-form expressions for their steady-state probabilities. The most well-known, using Kendall’s notation, are the M/M/1 and the M/M/c system. The algorithm described below estimates the expected number in the system under steady-state without a need for closed form steady-state probabilities. All that is needed is the transition matrix for the underlying Markov chain.

Electronic System Using Artificial Intelligence for Queue Management

The Covid-19 pandemic has brought changes in behaviour in public places. Indeed, the health and political authorities, in order to fight against the virus in a preventive manner, require the respect of barrier gestures: social distance, mask, vaccine, gel. Still in terms of public health, long waits in a place for a service have a negative impact on the health of fragile categories such as the disabled, pregnant women and the elderly. The technical devices used for queue management must now take into account the health context, identity, particularity and behaviour of people. This paper presents an electronic system developed with artificial intelligence for queue management in public facilities. This design personalises the user’s ticket by automatically integrating the name, facial image, age and possible disability status. At the counters, a system of name calling, sound and screen display, allows users to follow the queue without having a ticket printed on thermal paper with a high carbon footprint. This solution also makes illiterate users autonomous in the queue, allowing them to maintain their dignity and to respect the safety distance between people. The device allows the establishment’s manager, depending on the context, to activate positive discrimination of the disabled or the elderly, to control the Covid-19 mark or the health pass by QR Code. This queue manager performs biometric authentication by facial recognition before the user is registered in the queue register, which prevents fraud by people who do not want to respect the order of arrival of users. This work has led to the improvement of the technical management of queues by introducing more equity, inclusion, solidarity, health and ecology.

THE QUEUEING SYSTEM M^(x)/M/c→/PH^(r)/1/K

The two-stage tandem queueing system M(z)/M/c→/PH(r)/1/K is studied in this paper. Customers arrive at stage-Ⅰ system in batches according to a Poisson process, and the size of the batch, x , is a r. v. within a range of a finite number of positive integers. The stage- Ⅱ ststem has finite capacity, where customers are served in batches with a PH-distribution and the size of the batch is a positive integer r. Only after served in stage- Ⅰ system, and then served in stage- Ⅱ system, can the customers depart from the whole system. Several definitions such as the stage- Ⅰ service blocked time, the first-class and the second-class batch waiting times, and the batch sojourn time are introduced, and their distributions are obtained respectively.

A Fully Adaptive Active Queue Management Method for Congestion Prevention at the Router Buffer

Active queue management(AQM)methods manage the queued packets at the router buffer,prevent buffer congestion,and stabilize the network performance.The bursty nature of the traffic passing by the network routers and the slake behavior of the existing AQM methods leads to unnecessary packet dropping.This paper proposes a fully adaptive active queue management(AAQM)method to maintain stable network performance,avoid congestion and packet loss,and eliminate unnecessary packet dropping.The proposed AAQM method is based on load and queue length indicators and uses an adaptive mechanism to adjust the dropping probability based on the buffer status.The proposed AAQM method adapts to single and multiclass traffic models.Extensive simulation results over two types of traffic showed that the proposed method achieved the best results compared to the existing methods,including Random Early Detection(RED),BLUE,Effective RED(ERED),Fuzzy RED(FRED),Fuzzy Gentle RED(FGRED),and Fuzzy BLUE(FBLUE).The proposed and compared methods achieved similar results with low or moderate traffic load.However,under high traffic load,the proposed AAQM method achieved the best rate of zero loss,similar to BLUE,compared to 0.01 for RED,0.27 for ERED,0.04 for FRED,0.12 for FGRED,and 0.44 for FBLUE.For throughput,the proposed AAQM method achieved the highest rate of 0.54,surpassing the BLUE method’s throughput of 0.43.For delay,the proposed AAQM method achieved the second-best delay of 28.51,while the BLUE method achieved the best delay of 13.18;however,the BLUE results are insufficient because of the low throughput.Consequently,the proposed AAQM method outperformed the compared methods with its superior throughput and acceptable delay.

A Spectrum Occupancy Model for Primary Users in Cognitive Radio Systems

There are abundant research results related to cognitive radio systems (CR systems), but using queueing models to portray CR systems is a new research trend. In this paper, a single-server retrial cognitive radio system with a linear retrial rate has been considered. The system has two types of users: primary users and secondary users. Secondary users have no effect on primary users because primary users have preemptive precedence. As a result, our purpose is to examine some performance indicators such as the expected queue length for primary users, the probability of the system being idle or occupied by a secondary user, and the probability of the system being busy. This paper begins by deriving the expressions for the generating functions based on the balance equations, so that we can calculate our goal conveniently.

带有负顾客和启动时间的排队系统最优策略分析

本文考虑带有负顾客和启动时间的排队系统的均衡策略和社会最优问题.负顾客到达时,会使得服务台故障,并且迫使正在接受服务的顾客离开系统.当系统中最后一名顾客的服务完成后,服务台立即关闭.当有新顾客到达时,服务台经历一段随机的启动时间,进而服务顾客.基于线性“收益-成本”结构,本文得到了顾客在几乎不可视和完全不可视两种情形下顾客的均衡进入概率.利用遗传算法得到顾客的最优进入概率.最后,通过数值例子展现了最优进入概率和最优社会福利关于系统参数的敏感性变化,并比较了两种信息水平下的最优社会福利.

LabVIEW中Queue技术在发电机监测系统中的应用

介绍了基于虚拟仪器的在线监测系统的基本组成,其采用PCI总线仪器和LabVIEW可视化的虚拟仪器系统开发平台,把传统仪器的所有功能模块集成在一台计算机中,用户可以通过修改虚拟仪器的软件改变其功能与规模。该系统有效地利用了LabVIEW提供的同步控制Queue技术实现了发电机在现场运行环境下运行状态的监测显示,体现出了其一定的优势。

M/M/1排队系统输出过程的转移概率与瞬时分布

本文对M/M/1排队系统,求出其输出过程在顾客到达时刻的转移概率及在任意时刻的分布.

基于Message Queue技术的医疗信息交换与共享集成平台研究

对目前医院信息系统集成方式进行了分析,简单介绍了IBM Message Queue的技术特点,通过介绍重症监护系统(ICU系统)和HIS系统之间的集成方案,阐述了基于消息机制构建医疗信息交换与共享集成平台的思路和方法。

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。

基于运动目标检测的候车排队时间预测方法研究与实践——以虹桥机场T2航站楼出租车上客区为例

上海虹桥国际机场是虹桥枢纽以及虹桥商务区的重要组成部分,周围陆侧交通设施多样且便捷,配套有轨交、机场巴士、出租车、私家车等陆侧交通方式,具有强大的区域辐射力。其中,出租车由于具备方便快捷等优势正成为许多旅客尤其是夜间航班到港旅客的首选离港交通工具,并造成离港出租车上客区频繁发生排队客流淤积拥挤的现象。文章对现有的运动目标检测技术进行横向对比,以虹桥机场T2航站楼出租车上客区作为研究对象,首先分析了该区域监控视频数据特点,采用改进的结合三帧差分和混合高斯模型的检测算法对运动目标进行提取;接着对运动目标进行分类与跟踪,并测算排队乘客实时上车速度,提出一种基于运动目标检测的候车排队时间预测方法;最后,设计虹桥机场出租车管理信息发布系统,实现对候车客流排队时间预测与关键交通信息的可视化展示。