The Experts below are selected from a list of 324 Experts worldwide ranked by ideXlab platform
Djamil Aissani - One of the best experts on this subject based on the ideXlab platform.
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Bounds of the stationary distribution in M/G/1 retrial queue with two way communication and n types of outgoing calls ation and n type of outgoing call
Yugoslav Journal of Operations Research, 2019Co-Authors: Lala Alem Maghnia, Mohamed Boualem, Djamil AissaniAbstract:In this article we analyze the M/G/1 retrial queue with two way communication and n type of outgoing calls from a stochastic comparison viewpoint. The main idea is that given a complex Markov Chain which cannot be analyzed numerically, we propose to bound it by a new Markov Chain which is easier to solve by using a stochastic comparison approach. Particularly, we analyze the notion of monotonicity of the transition operator of the Embedded Markov Chain relative to the stochastic and convex orderings. Bounds are also obtained for the stationary distribution of the Embedded Markov Chain at departures epochs. Additionally, the performance measures of the system considered can be estimated by those of the M/M/1 retrial queue with two way communication when the service time distribution is NBUE (respectively, NWUE). Finally, we test numerically the accuracy of the proposed bounds.
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strong stability of the Embedded Markov Chain in an gi m 1 queue with negative customers
Applied Mathematical Modelling, 2010Co-Authors: Karim Abbas, Djamil AissaniAbstract:Abstract This paper is devoted to the investigation for sufficient conditions of the strong stability of the Embedded Markov Chain in GI/M/1 queueing system with negative customers. After perturbing the occurrence rate of the negative customers, we prove the strong stability of the considered Markov Chain with respect to a convenient weight variation norm. Furthermore, we estimate the deviation of its transition operators and provide an upper bound to the approximation error. This results allow us to understand how the negative customers will affect the system’s level of performance.
Xian Wang - One of the best experts on this subject based on the ideXlab platform.
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cost analysis of movement based location management in pcs networks an Embedded Markov Chain approach
IEEE Transactions on Vehicular Technology, 2014Co-Authors: Xian Wang, Rose Qingyang Hu, Shijinn HorngAbstract:In this paper, we develop an approach of Embedded Markov Chain to analyze the signaling cost of a movement-based location management (MBLM) scheme. This approach distinguishes itself from those developed in the literature in the following aspects. 1) It considers the location area (LA) architecture used by personal communication service (PCS) networks for location management. 2) It considers two different call handling models that determine after a call whether a location update should be performed. 3) It considers the effect of the call holding time on the call handling models. 4) It proposes to use a fluid flow model to describe the dependence between the cell and the LA residence time. We derive closed-form analytical formulas for the signaling cost, whose accuracy is manifested by a simulation. Based on the analytical formulas, we conduct a numerical study to evaluate the influence of various parameters on the signaling cost. The formulas can contribute to the implementation of the MBLM scheme in PCS networks including Fourth-Generation (4G) Long-Term Evolution. The modeling approach developed in this paper can be exploited to model other location management schemes.
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ICNC - Cost analysis of movement-based location update scheme using an approach of Embedded Markov Chain
2014 International Conference on Computing Networking and Communications (ICNC), 2014Co-Authors: Xian Wang, Rose Qingyang Hu, Geng WuAbstract:In this paper we develop an approach of Embedded Markov Chain to analyze the signaling cost of movement-based location update (MBLU) scheme implemented in a personal communication service (PCS) network with location area (LA) architecture. We propose to use a fluid flow model to characterize the dependency between cell residence time and LA residence time. We derive analytical formulas for the expected numbers of various types of location updates and for the expected paging area size. The accuracy of the analytical formulas is tested using a simulation. The analytical formulas can guide the implementation of the MBLU scheme in PCS networks. Moreover, the modeling approach can be explored to study other LU schemes.
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Cost analysis of movement-based location update scheme using an approach of Embedded Markov Chain
2014 International Conference on Computing Networking and Communications (ICNC), 2014Co-Authors: Xian Wang, Rose Qingyang Hu, Geng WuAbstract:In this paper we develop an approach of Embedded Markov Chain to analyze the signaling cost of movement-based location update (MBLU) scheme implemented in a personal communication service (PCS) network with location area (LA) architecture. We propose to use a fluid flow model to characterize the dependency between cell residence time and LA residence time. We derive analytical formulas for the expected numbers of various types of location updates and for the expected paging area size. The accuracy of the analytical formulas is tested using a simulation. The analytical formulas can guide the implementation of the MBLU scheme in PCS networks. Moreover, the modeling approach can be explored to study other LU schemes.
Kanjian Zhang - One of the best experts on this subject based on the ideXlab platform.
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potentials based optimization with Embedded Markov Chain for stochastic constrained system
Nonlinear Dynamics, 2012Co-Authors: Kang Cheng, Kanjian ZhangAbstract:In this paper, a RBF neural network based on-line optimization algorithm with performance potentials analysis method is presented for a class of stochastic constrained dynamic systems. The control signals of the considered systems are constrained to a range according to a subset of the whole state space. With the conception of an Embedded Markov Chain, an optimization approach on the basis of potentials is presented for a stochastic constrained system, where the optimization criterion is the long-time average performance. With this approach, the computation burden has been reduced because it only requires one to compute the control strategy on the states concerned, which are a subset of the whole state space. Furthermore, with the characteristic of approximation performance of RBF neural network, the potentials and the transition probability matrix are estimated conveniently by a sample path compared with the statistic approach or the method by solving the Poisson equation. The effectiveness of the optimization approach has been shown by the simulation results, finally.
Bjorn Bottcher - One of the best experts on this subject based on the ideXlab platform.
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Embedded Markov Chain approximations in Skorokhod topologies
Probability and Mathematical Statistics, 2019Co-Authors: Bjorn BottcherAbstract:We prove a J1-tightness condition for Embedded Markov Chains and discuss four Skorokhod topologies in a unified manner. To approximate a continuous time stochastic process by discrete time Markov Chains, one has several options to embed the Markov Chains into continuous time processes. On the one hand, there is a Markov embedding which uses exponential waiting times. On the other hand, each Skorokhod topology naturally suggests a certain embedding. These are the step function embedding for J1, the linear interpolation embedding forM1, the multistep embedding for J2 and a more general embedding for M2. We show that the convergence of the step function embedding in J1 implies the convergence of the other embeddings in the corresponding topologies. For the converse statement, a J1-tightness condition for Embedded time-homogeneous Markov Chains is given.Additionally, it is shown that J1 convergence is equivalent to the joint convergence in M1 and J2.
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Embedded Markov Chain approximations in skorokhod topologies
arXiv: Probability, 2014Co-Authors: Bjorn BottcherAbstract:In order to approximate a continuous time stochastic process by discrete time Markov Chains one has several options to embed the Markov Chains into continuous time processes. On the one hand there is the Markov embedding, which uses exponential waiting times. On the other hand each Skorokhod topology naturally suggests a certain embedding. These are the step function embedding for $J_1$, the linear interpolation embedding for $M_1$, the multi step embedding for $J_2$ and a more general embedding for $M_2$. We show that the convergence of the step function embedding in $J_1$ implies the convergence of the other embeddings in the corresponding topologies, respectively. For the converse statement a $J_1$-tightness condition for Embedded Markov Chains is given. The result relies on various representations of the Skorokhod topologies. Additionally it is shown that $J_1$ convergence is equivalent to the joint convergence in $M_1$ and $J_2$.
Lothar Breuer - One of the best experts on this subject based on the ideXlab platform.
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ON THE MAP/G/1 QUEUE WITH LEBESGUE-DOMINATED SERVICE TIME DISTRIBUTION AND LCFS PREEMPTIVE REPEAT SERVICE DISCIPLINE
Stochastic Models, 2020Co-Authors: Lothar BreuerAbstract:The present paper contains an analysis of the MAP/G/1 queue with last come first served (LCFS) preemptive repeat service discipline and Lebesgue-dominated service time distribution. The transient distribution is given in terms of a recursive formula. The stationary distribution as well as the stability condition are obtained by means of Markov renewal theory via a QBD representation of the Embedded Markov Chain at departures and arrivals.
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Transient and Stationary Distributions for the GI/G/k Queue with Lebesgue-Dominated Inter-Arrival Time Distribution
Queueing Systems, 2003Co-Authors: Lothar BreuerAbstract:In this paper, the multi-server queue with general service time distribution and Lebesgue-dominated iid inter-arival times is analyzed. This is done by introducing auxiliary variables for the remaining service times and then examining the Embedded Markov Chain at arrival instants. The concept of piecewise-deterministic Markov processes is applied to model the inter-arrival behaviour. It turns out that the transition probability kernel of the Embedded Markov Chain at arrival instants has the form of a lower Hessenberg matrix and hence admits an operator–geometric stationary distribution. Thus it is shown that matrix–analytical methods can be extended to provide a modeling tool even for the general multi-server queue.
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Transient and Stationary Distributions for the GI / G / k Queue with Lebesgue-Dominated Inter-Arrival Time Distribution
Queueing Systems, 2003Co-Authors: Lothar BreuerAbstract:In this paper, the multi-server queue with general service time distribution and Lebesgue-dominated iid inter-arival times is analyzed. This is done by introducing auxiliary variables for the remaining service times and then examining the Embedded Markov Chain at arrival instants. The concept of piecewise-deterministic Markov processes is applied to model the inter-arrival behaviour. It turns out that the transition probability kernel of the Embedded Markov Chain at arrival instants has the form of a lower Hessenberg matrix and hence admits an operator–geometric stationary distribution. Thus it is shown that matrix–analytical methods can be extended to provide a modeling tool even for the general multi-server queue.