The Experts below are selected from a list of 186 Experts worldwide ranked by ideXlab platform
Francois Baccelli - One of the best experts on this subject based on the ideXlab platform.
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expansions for joint laplace transform of stationary waiting times in max linear systems with Poisson Input
Queueing Systems, 2001Co-Authors: Hayriye Ayhan, Francois BaccelliAbstract:We give a Taylor series expansion for the joint Laplace transform of stationary waiting times in open (max,+)-linear stochastic systems with Poisson Input. Probabilistic expressions are derived for coefficients of all orders. Even though the computation of these coefficients can be hard for certain systems, it is sufficient to compute only a few coefficients to obtain good approximations (especially under the assumption of light traffic). Combining this new result with the earlier expansion formula for the mean stationary waiting times, we also provide a Taylor series expansion for the covariance of stationary waiting times in such systems. It is well known that (max,+)-linear systems can be used to represent stochastic Petri nets belonging to the class of event graphs. This class contains various instances of queueing networks like acyclic or cyclic fork-and-join queueing networks, finite or infinite capacity tandem queueing networks with various types of blocking, synchronized queueing networks and so on. It also contains some basic manufacturing models such as kanban networks, assembly systems and so forth. The applicability of this expansion technique is discussed for several systems of this type.
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transient and stationary waiting times in max linear systems with Poisson Input
Queueing Systems, 1997Co-Authors: Francois Baccelli, Sven Hasenfuss, Volker SchmidtAbstract:We consider a certain class of vectorial evolution equations, which are linear in the (max,+) semi-field. They can be used to model several types of discrete event systems, in particular queueing networks where we assume that the arrival process of customers (tokens, jobs, etc.) is Poisson. Under natural Cramer type conditions on certain variables, we show that the expected waiting time which the nth customer has to spend in a given subarea of such a system can be expanded analytically in an infinite power series with respect to the arrival intensity \lambda. Furthermore, we state an algorithm for computing all coefficients of this series expansion and derive an explicit finite representation formula for the remainder term. We also give an explicit finite expansion for expected stationary waiting times in (max,+)-linear systems with deterministic queueing services.
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martingale relations for the m gi 1 queue with markov modulated Poisson Input
Stochastic Processes and their Applications, 1991Co-Authors: Francois Baccelli, Armand M. MakowskiAbstract:This paper is concerned with single server queueing systems with renewal service process and Poisson arrivals modulated by a finite-state Markov chain. Exponential martingales are associated with a chain embedded at service completion epochs in the stochastic process describing the joint evolution of the number of customers in the queue and the state of the environment. The analysis of these martingales leads to a new and unified treatment of various known results concerning the stability condition and the steady state statistics, as well as to several new properties. Noteworthy among them are a conservation law that relates the duration of the busy period to the state of the environment at the end of the busy period, and some absolute continuity properties with respect to other queues of the same type.
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Martingale relations for the M⧸GI⧸1 queue with Markov modulated Poisson Input
Stochastic Processes and their Applications, 1991Co-Authors: Francois Baccelli, Armand M. MakowskiAbstract:This paper is concerned with single server queueing systems with renewal service process and Poisson arrivals modulated by a finite-state Markov chain. Exponential martingales are associated with a chain embedded at service completion epochs in the stochastic process describing the joint evolution of the number of customers in the queue and the state of the environment. The analysis of these martingales leads to a new and unified treatment of various known results concerning the stability condition and the steady state statistics, as well as to several new properties. Noteworthy among them are a conservation law that relates the duration of the busy period to the state of the environment at the end of the busy period, and some absolute continuity properties with respect to other queues of the same type.
David Koops - One of the best experts on this subject based on the ideXlab platform.
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Nonparametric Estimation of Service Time Characteristics in Infinite-Server Queues with Nonstationary Poisson Input
Stochastic Systems, 2019Co-Authors: Alexander Goldenshluger, David KoopsAbstract:This paper provides a mathematical framework for estimation of the service time distribution and expected service time of an infinite-server queueing system with a nonhomogeneous Poisson arrival pr...
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Nonparametric estimation of service time characteristics in infinite-server queues with nonstationary Poisson Input
arXiv: Statistics Theory, 2018Co-Authors: Alexander Goldenshluger, David KoopsAbstract:This paper provides a mathematical framework for estimation of the service time distribution and the expected service time of an infinite-server queueing system with a nonhomogeneous Poisson arrival process, in the case of partial information, where only the number of busy servers are observed over time. The problem is reduced to a statistical deconvolution problem, which is solved by using Laplace transform techniques and kernels for regularization. Upper bounds on the mean squared error of the proposed estimators are derived. Some concrete simulation experiments are performed to illustrate how the method can be applied and to provide some insight in the practical performance.
Xiangqun Yang - One of the best experts on this subject based on the ideXlab platform.
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the non linear properties of spike rate perceptron with sub Poisson Input
International Conference on Natural Computation, 2010Co-Authors: Xuyan Xiang, Yingchun Deng, Xiangqun YangAbstract:We present more specific non-linear properties of Spike-Rate Perceptron with sub-Poisson Inputs based on the diffusion approximation of renewal process, which employs both first and second statistical representation, i.e. the means, variances and correlations of the synaptic Input. It shows that such perceptron is also able to perform various complex non-linear tasks, and to successfully solve the XOR problem. Here such perceptron offers the same advantage that includes both the mean and the variance of the Input signal as Spike-Rate Perceptron.
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ICNC - The non-linear properties of Spike-Rate Perceptron with sub-Poisson Input
2010 Sixth International Conference on Natural Computation, 2010Co-Authors: Xuyan Xiang, Yingchun Deng, Xiangqun YangAbstract:We present more specific non-linear properties of Spike-Rate Perceptron with sub-Poisson Inputs based on the diffusion approximation of renewal process, which employs both first and second statistical representation, i.e. the means, variances and correlations of the synaptic Input. It shows that such perceptron is also able to perform various complex non-linear tasks, and to successfully solve the XOR problem. Here such perceptron offers the same advantage that includes both the mean and the variance of the Input signal as Spike-Rate Perceptron.
Jewgeni H Dshalalow - One of the best experts on this subject based on the ideXlab platform.
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ergodicity conditions and invariant probability measure for an embedded markov chain in a controlled bulk queueing system with a bilevel service delay discipline part ii
Applied Mathematics Letters, 1992Co-Authors: Lev Abolnikov, Jewgeni H DshalalowAbstract:Abstract The authors introduce and study a class of bulk queueing systems with a compound Poisson Input modulated by a semi-Markov process, a general multilevel control service and a queue length dependent service delay discipline. A necessary and sufficient condition for the ergodicity of an embedded Markov chain describing the evolution of the queue is established and its stationary distribution is obtained.
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Ergodicity conditions and invariant probability measure for an embedded Markov chain in a controlled bulk queueing system with a bilevel service delay discipline part II
Applied Mathematics Letters, 1992Co-Authors: Lev Abolnikov, Jewgeni H DshalalowAbstract:AbstractThe authors continue to study a class of bulk queueing systems with a compound Poisson Input modulated by a semi-Markov process, service control and a queue length dependent service delay discipline. A necessary and sufficient criterion of ergodicity of an embedded process is established and its stationary distribution is derived
Wojciech Burakowski - One of the best experts on this subject based on the ideXlab platform.
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Evaluation of mean waiting time in the system with vacations
2012Co-Authors: M. Sosnowski, Wojciech BurakowskiAbstract:The paper analyses the system with vacations with deterministic busy and vacation periods, constant service times and Poisson Input stream. For this system, we derive approximate formula describing mean waiting time as a function of mean waiting time of the equivalent system without vacations, lengths of busy/vacation periods and service time. The accuracy of the formula is checked by comparing with the simulation.
