The transient solution of time-dependent M/M/1 queues

The transient behavior of time-dependent M/M/1 queues is studied. The boundary probability function π₀(t), which is the probability that the queue is empty at time t, is shown with analyticity arguments to satisfy a Volterra-type integral equation. The boundary integral equation is derived, and a numerical algorithm is used to solve the integral equation and to find the expected queue size from π₀(t). The approach can be applied to many other types of time-dependent queues. Examples are given     

The M/G/1 queue with permanent customers

The authors examine an M/G/1 FCFS (first come, first served) queue with two types of customers: ordinary customers, who arrive according to a Poisson process, and permanent customers, who immediately return to the end of the queue after having received a service. The influence of the permanent customers on queue length and sojourn times of the Poisson customers is studied using results from queuing theory and from the theory of branching processes. In particular, it is shown that, when the service time distributions of the Poisson customers and all K permanent customers are negative exponential with identical means, the queue length and sojourn time distributions of the Poisson customers are the (K+1)-fold convolution of those for the case without permanent customers     

The M/G/1 Finite Capacity Queue with Delays

A steady-state analysis of theM/G/1finite capacity queue with delays is being made. In this model every busy period is followed by the execution of a noninterruptable task other than the servicing of ordinary customers; the duration of this task, called a delay, is a random variable with general distribution. Closed form expressions, easy to evaluate, are given for the distribution of the queue length and the first two moments of the queueing time distribution. A variant is also studied in which a busy period is followed by as many delays as possible, new delays being reinitiated as long as no customer has arrived.     

An M/G/1 vacation model of an FDDI station

The author defines and analyzes an M/G/1 vacation model that can be used to describe a single station in the fiber distributed data interface (FDDI). The M/G/1 model uses a service discipline called the exhaustive limited with limit variation discipline. According to this discipline, the server provides service until either the system is emptied or a randomly chosen limit of l frames has been served. The server then goes on a vacation before returning to service the queue again. The model can be used to gain insight into how the varying (timer-controlled) limit on the number of frames that can be transmitted during token visit at a station affects the mean waiting time in the timed-token protocol of FDDI. The analytical results of the M/G/1 vacation model are applied to an FDDI simulation example     

基于M/G/1模型的航班延误分析

飞机航班延误已成为困扰国内外航空运输业的一道世界性的难题.针对航空公司对航班延误分析的迫切需要,通过分析机场跑道的当前容量,应用排队论中的M/G/1模型,对机场起降飞机进行延误分析,提出一种评估机场跑道上航班延误的新方法,并用首都机场的实际数据进行验证.算例分析结果表明,此方法可为航空公司以及机场在航班安排方面提供有效的参考.     

混合服务方式下的M1+M2/G/1轮询系统的平均运行周期

本文给出了混合服务方式下的M1＋M2／G／1轮询系统平均运行周期的解析表达式。通过分析现有局域网协议模型的局限性，本文提出了更接近实际局域网协议的两类信息轮询系统模型，即M1＋M2／G／1系统；并且求解出该模型的平均运行周期的解析表达式以及不同稳定条件下的修正解析表达式；最后通过仿真验证了理论结果的正确性。     

Self-Similar Traffic in G/M/1 Queue Defined by the Weibull Distribution

The work considers a queuing system of the G/M/1 type that simulates service of self-similar traffic in a NodeB (e-NodeB) base station of a mobile operator. The feature of quality of service (QoS) characteristics estimation process for the self-similar traffic defined by the Weibull distribution is the solution based on the Laplace–Stieltjes transformation. The Laplace transformation for an infinite number of items under the Weibull distribution condition was found. It was shown that this series was equiconvergent to some convergence domain. The following QoS characteristics were obtained for the self-similar traffic: the average amount of time that a request spends in the system; the average number of requests waiting in the queue and the average queue length. The obtained results allowed to consider the real values of traffic serviced by a NodeB (e-NodeB) for their optimal deployment over a covered territory at the stage of frequency planning and operation of the 3G/UMTS and 4G/LTE networks.     

An Experimental Delay Analysis Based on M/G/1-Vacation Queues for Local Audio/Video Streams

The delay which is one of the quality of service parameters is considered to be a crucial factor for the effective usage of real-time audio and video streams in interactive multimedia collaborations. Among the various causes of the delay, we focus in this paper on the local delay concerned with the schemes which handle continuous inflow of encoded data from constant or variable bit-rate audio and video encoders. We introduce two kinds of implementation approaches, pull model and push model. While the pull model periodically pumps out the incoming data from the system buffer, the push model receives events from the device drivers. From our experiments based on Windows NT 3.51, it is shown that the push model outperforms the other for both constant and variable bit-rate streams in terms of the local delay, when the system suffers reasonable loads. We interpret this experimental data with M/G/1 multiple vacation queuing theories, and show that it is consistent with the queuing theoretic interpretations.     

Optimum alternatives of tandem G/G/K queues with disaster customers and retrial phenomenon: interactive voice response systems

In this paper, we study a tandem queue with retrials where the queue experiences disasters. The probability of system failure depends on the strength of equipment, which makes servers idle and causes the removal of all customers in queues and service areas at once. The customers in the queue are forced to orbit in a retrial queue during the system failure where they decide whether or not to come back to the system. Reducing the disaster arrival rate (the probability of system failure) by employing more servers and reducing the number of lost customers is very costly. Moreover, it is important to service the customers with no interruption and reduce the time in system. The developed scenarios are compared in five dimensions including time in system, cost of lost customer, operator cost, the number of uninterrupted service customers and cost of reducing disaster arrival rate (or empowering system cost). The scenarios are modeled by computer simulation. Then, the optimal scenario is chosen using data envelopment analysis. The optimal scenario maximizes system efficiency in terms of disaster arrival rate, cost of lost customers and the number of satisfied customers. In the main problem, the disasters arrive at the system according to Poisson process; the effect of changing the distribution function of disaster arrival has been investigated finally. We are among the first ones to study and optimize G/G/K tandem queuing systems with system failures and retrial phenomena in interactive voice response systems.     

On the M/G/1 queueing system with multiclass customers and fixed feedback

The M/G/1 queueing system with multiclass customer arrivals, fixed feedback, and first come first served policy is considered, where different classes of customers have different arrival rates, service-time distributions, and feedback numbers. The joint probabifity generation function of queue size of each class and the Laplace-Stieltjes transform of the total sojourn time of a customer in each class are presented, which extended the results obtained by Choi B D. The mean queue size of each class and mean total sojourn time of a customer in each class are obtained with this result. The results can be used in computer and communication networks for their performance analysis.     

Calculating time-dependent performance measures for the M/M/1 queue

Methods are discussed for computing transient performance measures for the M/M/1 queue. These performance measures are often expressed in terms of modified Bessel functions without any discussion about computation. In fact, a common expression for the probability transition function of the M/M/1 queue length process has an infinite sum of modified Bessel functions. For actually generating numbers, however, it is convenient to use numerical integration with associated integral representations, as was first pointed out by P.M. Morse (Oper. Res., vol.3, p.255-61, 1955)     

5G时代4G/5G共天馈面解决方案

4G建设时期,存在站点天面资源紧缺、无法新增抱杆、物业协调困难等问题,因此,5G时代在现有站点上新增抱杆的需求较难实现,如何实现4G/5G天线共天馈面及快速部署异常紧迫。探讨了4G/5G共天馈面的解决方案,提出一种适合中国电信单抱杆场景网络建设的天馈面解决方案,可以解决5G网络建设中无法新增抱杆、物业协调困难的问题。由于不增加天面资源,可减少铁塔租金,降低网络运营成本,同时可实现5G网络部署简化、便捷、高效。     

服务台可修的M／G／1排队系统—一些新的可靠性指标

本文进一步分析了服务台可修的Ｍ／Ｇ／１排队系统，获得忙期长度与此忙期中服务台失效次数的联合概率分布等一些新的可靠性指标，给出了计算时刻ｔ服务台失效的瞬时概率和（０，ｔ）中服务台的平均失效次数的近似表达式，最后用实例证明了其有效性。     

An M/G/1-type queueing system with non-perfect servers and no waiting capacity

A single server queue with Poisson arrivals and no waiting room is considered where two types of services are offered. An arriving customer has to undergo the first service but the second service is optional. The service times for both types of services are exponentially distributed. Transient and steady-state distributions have been obtained for the number in the system.     

Matrix-geometric solutions of M/G/1-type Markov chains: a unifyinggeneralized state-space approach

We present an algorithmic approach to find the stationary probability distribution of M/G/1-type Markov chains which arise frequently in performance analysis of computer and communication networks. The approach unifies finite- and infinite-level Markov chains of this type through a generalized state-space representation for the probability generating function of the stationary solution. When the underlying probability generating matrices are rational, the solution vector for level k, x_k, is shown to be in the matrix-geometric form x_k+1=gF^kH, k⩾0, for the infinite-level case, whereas it takes the modified form x_k+1=g₁F^k₁H₁+g ₂F^K-k-1₂H₂, 0⩽k⩽K, for the finite-level case. The matrix parameters in the above two expressions can be obtained by decomposing the generalized system into forward and backward subsystems, or, equivalently, by finding bases for certain generalized invariant subspaces of a regular pencil λE-A. We note that the computation of such bases can efficiently be carried out using advanced numerical linear algebra techniques including matrix-sign function iterations with quadratic convergence rates or ordered generalized Schur decomposition. The simplicity of the matrix-geometric form of the solution allows one to obtain various performance measures of interest easily, e.g., overflow probabilities and the moments of the level distribution, which is a significant advantage over conventional recursive methods     

4G移动回传解决方案

针对我国移动通信的现状,介绍了几款烽火通信为第4代移动通信提供的移动回传解决方案,例如BBU集中化的DWDM解决方案,PON承载Smal Cel 的热点、盲区解决方案,解决站址资源不足的小型化分组解决方案。     

Estimating changes in traffic intensity for M/M/1 queueing systems

In this paper, the principle of maximum likelihood is used to estimate change point of traffic intensity for the M/M/1 queueing model. The procedure is illustrated with a simulated example for each possible change in traffic intensity.     

Iterative Computation of the M/G/1 Queue Length Distribution via the Discrete Fourier Transform

An iterative method is presented by which the distribution of queue lengths in theM/G/1queue may be computed. The method applies to the nonsteady-state case and involves repeatedly performing convolutions. The steady-state solution may be obtained by performing the iterations until convergence occurs. A frequencydomain equivalent of the method is presented which gives much greater computational economy.     

Downtime of the service station in M/G/1 queueing system with repairable service station

In this paper the downtime of the service station in the M/G/1 queueing system with repairable service station is discussed. In the following, some new results are obtained: (a) the distribution and the mean value of the downtime during the generalized service time; (b) the distribution and the mean value of the downtime during the system busy period; (c) the mean value of the downtime per unit-time for infinite time span; (d) some asymptotic formulas for calculating the mean value of the downtime during the time interval (0, t]. These results would be of interest to reliability analysts.