Efficient Calculation of Rare Event Probabilities in Markovian Queueing Networks

Mikeev, Linar; Sandmann, Werner; Wolf, Verena

doi:10.4108/icst.valuetools.2011.245597

Cited by 7 publications

(4 citation statements)

References 25 publications

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“…Our method exploits the population structure of the model, which is present in many important application fields of MJPs. Based on experience with other work based on truncation, the approach can be expected to scale up to at least a few million states [33]. Compared to previous work, our method neither relies on approximations of unknown accuracy nor additional information such as a suitable change of measure in the case of importance sampling.…”

Section: Resultsmentioning

confidence: 99%

Analysis of Markov Jump Processes under Terminal Constraints

Backenköhler

Bortolussi

Großmann

et al. 2021

Tools and Algorithms for the Construction and Analysis of Systems

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Many probabilistic inference problems such as stochastic filtering or the computation of rare event probabilities require model analysis under initial and terminal constraints. We propose a solution to this bridging problem for the widely used class of population-structured Markov jump processes. The method is based on a state-space lumping scheme that aggregates states in a grid structure. The resulting approximate bridging distribution is used to iteratively refine relevant and truncate irrelevant parts of the state-space. This way, the algorithm learns a well-justified finite-state projection yielding guaranteed lower bounds for the system behavior under endpoint constraints. We demonstrate the method’s applicability to a wide range of problems such as Bayesian inference and the analysis of rare events.

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Section: Resultsmentioning

confidence: 99%

Analysis of Markov Jump Processes under Terminal Constraints

Backenköhler

Bortolussi

Großmann

et al. 2021

Tools and Algorithms for the Construction and Analysis of Systems

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“…The direct numerical simulation that we consider is based on the dynamic state space truncation developed for uniformization methods [Mateescu et al 2010b] and for integration schemes such as Runge Kutta methods [Andreychenko et al 2012;Mikeev et al 2011]. The main idea is to exploit the inflow-outflow form of (2) for the construction of the dynamic state space.…”

Section: Direct Numerical Simulationmentioning

confidence: 99%

Model Reconstruction for Moment-Based Stochastic Chemical Kinetics

Andreychenko

Mikeev

Wolf

2015

ACM Trans. Model. Comput. Simul.

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Based on the theory of stochastic chemical kinetics, the inherent randomness of biochemical reaction networks can be described by discrete-state continuous-time Markov chains. However, the analysis of such processes is computationally expensive and sophisticated numerical methods are required. Here, we propose an analysis framework in which we integrate a number of moments of the process instead of the state probabilities. This results in a very efficient simulation of the time evolution of the process. To regain the state probabilities from the moment representation, we combine the fast moment-based simulation with a maximum entropy approach for the reconstruction of the underlying probability distribution. We investigate the usefulness of this combined approach in the setting of stochastic chemical kinetics and present numerical results for three reaction networks showing its efficiency and accuracy. Besides a simple dimerization system, we study a bistable switch system and a multiattractor network with complex dynamics. ACM Reference Format:Alexander Andreychenko, Linar Mikeev, and Verena Wolf. 2015. Model reconstruction for moment-based stochastic chemical kinetics. ACM Trans. Model.

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“…Two node queuing networks are considered and event of buffer overflow at the second node is studied [15]. The ideas from importance sampling simulation into a non simulative numerical method is used for the computation of rare event probabilities in Markovian queuing networks [16].In this paper we consider a single M/M/1 queue and a two M/M/1 queues in tandem Jackson network for analyzing and estimating the buffer overflow probability in a telecommunication networks. The arrival and service rates in a Jackson networks are modulated by finite state Markov process.…”

Section: Introductionmentioning

confidence: 99%

Analysis and estimation of overflow probability in Jackson queueing networks

Panda

Reza

2013

2013 International Conference on Emerging Trends in Communication, Control, Signal Processing and Computing Applications (C2SPC

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In this paper we consider a single M/M/1 queue and two M/M/1 queue in tandem Jackson networks for analyzing and estimating the overflow probability in a telecommunication networks. The arrival and service rates in a Jackson networks are modulated by finite state Markov process. First we estimated the buffer overflow in a single M/M/1 queueing network then we estimated the buffer overflow in two queues in tandem queueing network. Numerical and experimental results of buffer overflow on a single M/M/1 queue and a two queue in tandem are discussed.

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Efficient Calculation of Rare Event Probabilities in Markovian Queueing Networks

Cited by 7 publications

References 25 publications

Analysis of Markov Jump Processes under Terminal Constraints

Analysis of Markov Jump Processes under Terminal Constraints

Model Reconstruction for Moment-Based Stochastic Chemical Kinetics

Analysis and estimation of overflow probability in Jackson queueing networks

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