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.     

Exact analysis of a class of GI/G/1-type performability models

We present an exact decomposition algorithm for the analysis of Markov chains with a GI/G/1-type repetitive structure. Such processes exhibit both M/G/1-type & GI/M/1-type patterns, and cannot be solved using existing techniques. Markov chains with a GI/G/1 pattern result when modeling open systems which accept jobs from multiple exogenous sources, and are subject to failures & repairs; a single failure can empty the system of jobs, while a single batch arrival can add many jobs to the system. Our method provides exact computation of the stationary probabilities, which can then be used to obtain performance measures such as the average queue length or any of its higher moments, as well as the probability of the system being in various failure states, thus performability measures. We formulate the conditions under which our approach is applicable, and illustrate it via the performability analysis of a parallel computer system.     

Hybrid approach to speech recognition using hidden Markov modelsand Markov chains

The paper presents a hybrid of a hidden Markov model and a Markov chain model for speech recognition. In this hybrid, the hidden Markov model is concerned with the time-varying property of spectral features, while the Markov chain accounts for the interdependence of spectral features. The log-likelihood scores of the two models, with respect to a given utterance, are combined by a postprocessor to yield a combined log-likelihood score for word classification. Experiments on speaker-independent and multispeaker isolated English alphabet recognition show that the hybrid outperformed both the hidden Markov model and the Markov chain model in terms of recognition     

Solution for M/G/1 queues

M/G/1 type queueing systems are frequently found in the performance evaluation of communication systems. The authors develop a new solution method for these queues: their results are an alternative to both standard forms of exact analysis, and to diffusion approximations, while offering comparable computational complexity to the latter     

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.     

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.     

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     

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。     

Steady-state tracking analysis of the RLS algorithm for time-varying channels: a general state-space approach

We present a general technique for analyzing the steady-state tracking performance of the recursive least squares (RLS) algorithm for estimating Rayleigh fading channels in terms of the mean squared identification error (MSIE) or mean squared deviation (MSD). The technique may be used with a general-order vector-autoregressive (VAR) model. Numerical results obtained using the technique agree closely with experimental results.     

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.     

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.     

Stiffness-tolerant methods for transient analysis of stiff Markov chains

Three methods for numerical transient analysis of Markov chains, the modified Jensen's method (Jensen's method with steady-state detection of the underlying DTMC and computation of Poisson probabilities using the method of Fox and Glynn [1]), a third-order L-stable implicit Runge-Kutta method, and a second-order L-stable method, TR-BDF2, are compared. These methods are evaluated on the basis of their performance (accuracy of the solution and computational cost) on stiff Markov chains. Steady-state detection in Jensen's method results in large savings of computation time for Markov chains when mission time extends beyond the steady-state point. For stiff models, computation of Poisson probabilities using traditional methods runs into underflow problems. Fox and Glynn's method for computing Poisson probabilities avoids underflow problems for all practical problems and yields highly accurate solutions. We conclude that for mildly stiff Markov chains, the modified Jensen's method is the method of choice. For stiff Markov chains, we recommend the use of the L-stable ODE methods. If low accuracy (upto eight decimal places) is acceptable, then TR-BDF2 method should be used. If higher accuracy is desired, then we recommend third-order implicit Runge-Kutta method.     

Modeling a shared-load k-out-of-n:G system

A Markov model for analyzing the reliability and availability of an n-unit shared-load repairable k-out-of-n:G system with imperfect switching is presented. The equations for both time-dependent and steady-state system availability are given. An inverse Laplace transform is used to solve the simultaneous differential equations for the nonrepairable case. A generalized analytic function for system reliability is obtained. Examples are provided to demonstrate the model and the impact of a load-sharing strategy on the reliability. The load-sharing strategy can improve system reliability and availability, if the controller and switching parameters are adequate. The proposed approach and solution are helpful to system engineers and reliability analysts     

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。     

Low-order approximations of Markov chains in a decision theoretic context (Corresp.)

The idea of finding a low-order approximation to a Markov chain is considered. The approximating process is characterized by a smaller number of parameters than the original one. As a criterion for approximation the lower order process is required to be the most difficult to discriminate from the original one in a decision theoretical context, i.e., achieving maximal Bayes error probability. It is shown that the Hellinger distance metric is closely related to the discrimination performance and provides robust approximation. It is then used to derive the best memoryless approximation, with a possibly reduced number of states, to a first-order Markov chain.     

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.     

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.     

On a method of the analysis of the M/G/1-EPS queueing system and moments of the sojourn time

A method of the analysis of a queueing system with the processor-sharing discipline is briefly described. In addition, recurrent formulas applied to calculate the moments of the distribution of the random variable describing a call’s sojourn time of length u.