The Experts below are selected from a list of 13005 Experts worldwide ranked by ideXlab platform
Herwig Bruneel - One of the best experts on this subject based on the ideXlab platform.
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delay in a discrete time queueing model with batch arrivals and batch services
International Conference on Information Technology: New Generations, 2008Co-Authors: Dieter Claeys, Koenraad Laevens, Joris Walraevens, Herwig BruneelAbstract:During the past decades batch-service queueing models have been studied extensively, especially with regard to the system content. Some researchers have studied the distribution of the customer delay, but not in the case of batch arrivals, which is a non-trivial extension. In this paper, we compute the Probability Generating Function of the delay in a discrete-time batch-service queueing model with batch arrivals and single-slot service times. We make extensive use of residue theory. It is further shown that moments of the delay can be derived from the obtained Probability Generating Function.
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a discrete time queueing model with a batch server operating under the minimum batch size rule
Next Generation Teletraffic and Wired Wireless Advanced Networking, 2007Co-Authors: Dieter Claeys, Koenraad Laevens, Joris Walraevens, Herwig BruneelAbstract:In telecommunications networks, usually an aggregation of information units (a batch) is transmitted instead of individual information units. In order to obtain performance measures for such networks, we analyze a discrete-time queueing model with a batch server operating under the minimum batch size (MBS) service policy. Specifically, we calculate the steady-state Probability Generating Function (PGF) of the system contents at the beginning of an arbitrary slot. This PGF enables us to derive some important performance measures. Furthermore, we investigate, through some numerical examples, the influence of some parameters on the optimal choice of the MBS. In this paper, we focus on the influence of the load and the distribution of the service times.
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delay characteristics in discrete time gi g 1 queues with non preemptive priority queueing discipline
Performance Evaluation, 2002Co-Authors: Joris Walraevens, Bart Steyaert, Herwig BruneelAbstract:Priority scheduling for packets is becoming a hot topic, as attempts are being made to integrate voice services in existing data networks. In this paper, we consider a discrete-time queueing system with head-of-line (HOL) non-preemptive priority scheduling. Two classes of traffic will be considered, i.e., high-priority and low-priority traffic, which both generate variable-length packets. We will derive expressions for the Probability Generating Function of the packet delay of the high-priority traffic and the low-priority traffic. From these, some performance measures (such as the mean value) will be derived. These will be used to illustrate the significance of priority scheduling and will be applied to an output queueing switch.
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delay analysis for discrete time queueing systems with multiple randomly interrupted servers
European Journal of Operational Research, 1995Co-Authors: Koenraad Laevens, Herwig BruneelAbstract:This paper analyzes the performance of discrete-time multiserver queues, subjected to random server interruptions. The arrival process is general independent. The numbers of available servers from slot to slot are modelled as a set of random variables. These are assumed to be i.i.d. Under these assumptions, an expression for the Probability Generating Function of the delay is derived. From this Function the first two moments of the delay are obtained. The result is shown to agree with Little's theorem. In addition, an analytic approximation for the tail probabilities of both delay and system contents is presented. A numerical example is included to illustrate the analysis.
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a general relationship between buffer occupancy and delay in discrete time multiserver queueing models applicable in atm networks
International Conference on Computer Communications, 1993Co-Authors: Bart Steyaert, Herwig Bruneel, Yijun XiongAbstract:A multiserver discrete-time buffer system is studied. Packets arrive in the system according to a general correlated process, which is not further specified. The service times of the packets are of constant length. Explicit expressions are derived for the distribution, the Probability Generating Function, and the mean and variance of the packet delay, in terms of the distribution, the Probability Generating Function, and the mean and variance of the buffer contents. It is observed that knowledge of the exact nature of the arrival process is not required to be able to derive these relationships between the statistics of the delay and the occupancy. >
Koenraad Laevens - One of the best experts on this subject based on the ideXlab platform.
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delay in a discrete time queueing model with batch arrivals and batch services
International Conference on Information Technology: New Generations, 2008Co-Authors: Dieter Claeys, Koenraad Laevens, Joris Walraevens, Herwig BruneelAbstract:During the past decades batch-service queueing models have been studied extensively, especially with regard to the system content. Some researchers have studied the distribution of the customer delay, but not in the case of batch arrivals, which is a non-trivial extension. In this paper, we compute the Probability Generating Function of the delay in a discrete-time batch-service queueing model with batch arrivals and single-slot service times. We make extensive use of residue theory. It is further shown that moments of the delay can be derived from the obtained Probability Generating Function.
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a discrete time queueing model with a batch server operating under the minimum batch size rule
Next Generation Teletraffic and Wired Wireless Advanced Networking, 2007Co-Authors: Dieter Claeys, Koenraad Laevens, Joris Walraevens, Herwig BruneelAbstract:In telecommunications networks, usually an aggregation of information units (a batch) is transmitted instead of individual information units. In order to obtain performance measures for such networks, we analyze a discrete-time queueing model with a batch server operating under the minimum batch size (MBS) service policy. Specifically, we calculate the steady-state Probability Generating Function (PGF) of the system contents at the beginning of an arbitrary slot. This PGF enables us to derive some important performance measures. Furthermore, we investigate, through some numerical examples, the influence of some parameters on the optimal choice of the MBS. In this paper, we focus on the influence of the load and the distribution of the service times.
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delay analysis for discrete time queueing systems with multiple randomly interrupted servers
European Journal of Operational Research, 1995Co-Authors: Koenraad Laevens, Herwig BruneelAbstract:This paper analyzes the performance of discrete-time multiserver queues, subjected to random server interruptions. The arrival process is general independent. The numbers of available servers from slot to slot are modelled as a set of random variables. These are assumed to be i.i.d. Under these assumptions, an expression for the Probability Generating Function of the delay is derived. From this Function the first two moments of the delay are obtained. The result is shown to agree with Little's theorem. In addition, an analytic approximation for the tail probabilities of both delay and system contents is presented. A numerical example is included to illustrate the analysis.
S Pradhan - One of the best experts on this subject based on the ideXlab platform.
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queue length distribution of a batch service queue with random capacity and batch size dependent service m g r y 1 m g y _ r 1
Opsearch, 2016Co-Authors: S Pradhan, U.c. Gupta, S. K. SamantaAbstract:Abstract This paper considers a single-server batch-service queue with random service capacity of the server and service time depends on the size of the batch. Customers arrive according to Poisson process and service times of the batches are generally distributed. We obtain explicit closed-form expression for the steady-state queue-length distribution at departure epoch of a batch based on roots of the associated characteristic equation of the Probability Generating Function. Moreover, we also discuss the case when the characteristic equation has non-zero multiple roots. The queue-length distribution at random epoch is obtained using the classical principle based on ‘rate in = rate out’ approach. Finally, variety of numerical results are presented for a number of service time distributions including gamma distribution.
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analyzing an infinite buffer batch arrival and batch service queue under batch size dependent service policy
Journal of The Korean Statistical Society, 2016Co-Authors: S Pradhan, U.c. Gupta, S. K. SamantaAbstract:Abstract In this paper, we investigate an infinite-buffer queue with batch-arrival and batch-service wherein a single server operates under random serving capacity rule with service time dependent on the size of the batch under the service. First, we derive the Probability Generating Function of state probabilities at service completion epoch, from which an entire spectrum regarding queue-length at various epochs is extracted. Using the departure epoch probabilities, we establish a stable relationship between departure and random epochs probabilities based on ‘rate in = rate out’ approach. Further, random epoch probabilities are used to obtain pre-arrival epoch probabilities. Finally, we illustrate our analytical results by means of numerical computation which includes the case of multiple roots.
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queue length and server content distribution in an infinite buffer batch service queue with batch size dependent service
Advances in Operations Research, 2015Co-Authors: U.c. Gupta, S PradhanAbstract:We analyze an infinite-buffer batch-size-dependent batch-service queue with Poisson arrival and arbitrarily distributed service time. Using supplementary variable technique, we derive a bivariate Probability Generating Function from which the joint distribution of queue and server content at departure epoch of a batch is extracted and presented in terms of roots of the characteristic equation. We also obtain the joint distribution of queue and server content at arbitrary epoch. Finally, the utility of analytical results is demonstrated by the inclusion of some numerical examples which also includes the investigation of multiple zeros.
Andrew Luong - One of the best experts on this subject based on the ideXlab platform.
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generalized method of moments and generalized estimating Functions based on Probability Generating Function for count models
Open Journal of Statistics, 2020Co-Authors: Andrew LuongAbstract:Generalized method of moments based on Probability Generating Function is considered. Estimation and model testing are unified using this approach which also leads to distribution free chi-square tests. The estimation methods developed are also related to estimation methods based on generalized estimating equations but with the advantage of having statistics for model testing. The methods proposed overcome numerical problems often encountered when the Probability mass Functions have no closed forms which prevent the use of maximum likelihood (ML) procedures and in general, ML procedures do not lead to distribution free model testing statistics.
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some simple method of estimation for the parameters of the discrete stable distribution with the Probability Generating Function
Communications in Statistics - Simulation and Computation, 2009Co-Authors: Louis G Doray, Shu Mei Jiang, Andrew LuongAbstract:In this article, we develop a method to estimate the two parameters of the discrete stable distribution. By minimizing the quadratic distance between transforms of the empirical and theoretical Probability Generating Functions, we obtain estimators simple to calculate, asymptotically unbiased, and normally distributed. We also derive the expression for their variance–covariance matrix. We simulate several samples of discrete stable distributed datasets with different parameters, to analyze the effect of tuncation on the right tail of the distribution.
S. K. Samanta - One of the best experts on this subject based on the ideXlab platform.
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queue length distribution of a batch service queue with random capacity and batch size dependent service m g r y 1 m g y _ r 1
Opsearch, 2016Co-Authors: S Pradhan, U.c. Gupta, S. K. SamantaAbstract:Abstract This paper considers a single-server batch-service queue with random service capacity of the server and service time depends on the size of the batch. Customers arrive according to Poisson process and service times of the batches are generally distributed. We obtain explicit closed-form expression for the steady-state queue-length distribution at departure epoch of a batch based on roots of the associated characteristic equation of the Probability Generating Function. Moreover, we also discuss the case when the characteristic equation has non-zero multiple roots. The queue-length distribution at random epoch is obtained using the classical principle based on ‘rate in = rate out’ approach. Finally, variety of numerical results are presented for a number of service time distributions including gamma distribution.
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analyzing an infinite buffer batch arrival and batch service queue under batch size dependent service policy
Journal of The Korean Statistical Society, 2016Co-Authors: S Pradhan, U.c. Gupta, S. K. SamantaAbstract:Abstract In this paper, we investigate an infinite-buffer queue with batch-arrival and batch-service wherein a single server operates under random serving capacity rule with service time dependent on the size of the batch under the service. First, we derive the Probability Generating Function of state probabilities at service completion epoch, from which an entire spectrum regarding queue-length at various epochs is extracted. Using the departure epoch probabilities, we establish a stable relationship between departure and random epochs probabilities based on ‘rate in = rate out’ approach. Further, random epoch probabilities are used to obtain pre-arrival epoch probabilities. Finally, we illustrate our analytical results by means of numerical computation which includes the case of multiple roots.
