467 research outputs found

    Bayesian inference and prediction for the GI/M/1 queueing system

    Get PDF
    This article undertake Bayesian inference and prediction for GI/M/1 queueing systems. A semiparametric model based on mixtures of Erlang distributions is considered to model the general interarrival time distribution. Given arrival and service data, a Bayesian procedure based on birth-death Markov Chain Monte Carlo methods is proposed. An estimation of the system parameters and predictive distributions of measures such as the stationary system size and waiting time is give

    ANALYSIS OF BULK ARRIVALS IN QUEUEING MODELS

    Get PDF
           Present paper surveys the literature on bulk queueing models. The concept of bulk arrivals and bulk services has gained a tremendous significance in present situations. Due to congestion problem everywhere (banks, metro stations, bus stops, railway reservation, traffic … etc.) researchers have to focus their attention to develop models and mechanism to deal with the same. A number of models have been developed in the area of queueing theory incorporating bulk queueing models. These bulk queueing models can be applied to resolve the congestion problems. Through this survey, an attempt has been made to review the work done on bulk queues, modeling various phenomenons. The goal is to provide sufficient information to analysts, managers and industry people who are interested in using queueing theory to model congestion problems and want to locate the details of relevant models

    Queueing models for token and slotted ring networks

    Get PDF
    Currently the end-to-end delay characteristics of very high speed local area networks are not well understood. The transmission speed of computer networks is increasing, and local area networks especially are finding increasing use in real time systems. Ring networks operation is generally well understood for both token rings and slotted rings. There is, however, a severe lack of queueing models for high layer operation. There are several factors which contribute to the processing delay of a packet, as opposed to the transmission delay, e.g., packet priority, its length, the user load, the processor load, the use of priority preemption, the use of preemption at packet reception, the number of processors, the number of protocol processing layers, the speed of each processor, and queue length limitations. Currently existing medium access queueing models are extended by adding modeling techniques which will handle exhaustive limited service both with and without priority traffic, and modeling capabilities are extended into the upper layers of the OSI model. Some of the model are parameterized solution methods, since it is shown that certain models do not exist as parameterized solutions, but rather as solution methods

    BAYESIAN CONTROL OF THE NUMBER OF SERVERS IN A GI/M/C QUEUING SYSTEM

    Get PDF
    In this paper we consider the problem of designing a GI/M/c queueing system. Given arrival and service data, our objective is to choose the optimal number of servers so as to minimize an expected cost function which depends on quantities, such as the number of customers in the queue. A semiparametric approach based on Erlang mixture distributions is used to model the general interarrival time distribution. Given the sample data, Bayesian Markov chain Monte Carlo methods are used to estimate the system parameters and the predictive distributions of the usual performance measures. We can then use these estimates to minimize the steady-state expected total cost rate as a function of the control parameter c. We provide a numerical example based on real data obtained from a bank in Madrid.

    TRANSIENT BAYESIAN INFERENCE FOR SHORT AND LONG-TAILED GI/G/1 QUEUEING SYSTEMS

    Get PDF
    In this paper, we describe how to make Bayesian inference for the transient behaviour and busy period in a single server system with general and unknown distribution for the service and interarrival time. The dense family of Coxian distributions is used for the service and arrival process to the system. This distribution model is reparametrized such that it is possible to define a non-informative prior which allows for the approximation of heavytailed distributions. Reversible jump Markov chain Monte Carlo methods are used to estimate the predictive distribution of the interarrival and service time. Our procedure for estimating the system measures is based in recent results for known parameters which are frequently implemented by using symbolical packages. Alternatively, we propose a simple numerical technique that can be performed for every MCMC iteration so that we can estimate interesting measures, such as the transient queue length distribution. We illustrate our approach with simulated and real queues.

    Transient bayesian inference for short and long-tailed GI/G/1 queueing systems

    Get PDF
    In this paper, we describe how to make Bayesian inference for the transient behaviour and busy period in a single server system with general and unknown distribution for the service and interarrival time. The dense family of Coxian distributions is used for the service and arrival process to the system. This distribution model is reparametrized such that it is possible to define a non-informative prior which allows for the approximation of heavytailed distributions. Reversible jump Markov chain Monte Carlo methods are used to estimate the predictive distribution of the interarrival and service time. Our procedure for estimating the system measures is based in recent results for known parameters which are frequently implemented by using symbolical packages. Alternatively, we propose a simple numerical technique that can be performed for every MCMC iteration so that we can estimate interesting measures, such as the transient queue length distribution. We illustrate our approach with simulated and real queues

    Performance analysis of time-dependent queueing systems: survey and classification

    Full text link
    Many queueing systems are subject to time-dependent changes in system parameters, such as the arrival rate or number of servers. Examples include time-dependent call volumes and agents at inbound call centers, time-varying air traffic at airports, time-dependent truck arrival rates at seaports, and cyclic message volumes in computer systems.There are several approaches for the performance analysis of queueing systems with deterministic parameter changes over time. In this survey, we develop a classification scheme that groups these approaches according to their underlying key ideas into (i) numerical and analytical solutions,(ii)approaches based on models with piecewise constant parameters, and (iii) approaches based on mod-ified system characteristics. Additionally, we identify links between the different approaches and provide a survey of applications that are categorized into service, road and air traffic, and IT systems

    Markovian bulk-arrival and bulk-service queues with general state-dependent control

    Get PDF
    We study a modified Markovian bulk-arrival and bulk-service queue incorporating general state-dependent control. The stopped bulk-arrival and bulk-service queue is first investigated, and the relationship between this stopped queue and the full queueing model is examined and exploited. Using this relationship, the equilibrium behaviour for the full queueing process is studied and the probability generating function of the equilibrium distribution is obtained. Queue length behaviour is also examined, and the Laplace transform of the queue length distribution is presented. The important questions regarding hitting times and busy period distributions are answered in detail, and the Laplace transforms of these distributions are presented. Further properties regarding the busy period distributions including expectation and conditional expectation of busy periods are also explored
    • …
    corecore