SERIES EXPANSIONS FOR FINITE-STATE MARKOV CHAINS

Bernd Heidergott; Arie Hordijk; Miranda van Uitert

doi:10.1017/S0269964807000034

Abstract

This article provides series expansions of the stationary distribution of a finite Markov chain. This leads to an efficient numerical algorithm for computing the stationary distribution of a finite Markov chain. Numerical examples are given to illustrate the performance of the algorithm.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Heidergott, Bernd 2008. Perturbation analysis of Markov chains. p. 99.

Bouallouche-medjkoune, Louiza and Aissani, Djamil 2008. Quantitative Estimates in an M2/G2/1 Priority Queue with Non-Preemptive Priority: The Method of Strong Stability. Stochastic Models, Vol. 24, Issue. 4, p. 626.

Boukir, L. Bouallouche-Medjkoune, L. and Aïssani, D. 2009. Strong Stability of the Batch Arrival Queueing Systems. Stochastic Analysis and Applications, Vol. 28, Issue. 1, p. 8.

Abbas, Karim and Aïssani, Djamil 2010. Strong stability of the embedded Markov chain in an GI/M/1 queue with negative customers. Applied Mathematical Modelling, Vol. 34, Issue. 10, p. 2806.

Heidergott, Bernd Hordijk, Arie and Leder, Nicole 2010. Series Expansions for Continuous-Time Markov Processes. Operations Research, Vol. 58, Issue. 3, p. 756.

Leder, Nicole Heidergott, Bernd and Hordijk, Arie 2010. An Approximation Approach for the Deviation Matrix of Continuous-Time Markov Processes with Application to Markov Decision Theory. Operations Research, Vol. 58, Issue. 4-part-1, p. 918.

Benouaret, Zina and Aïssani, Djamil 2010. Strong stability in a two-dimensional classical risk model with independent claims. Scandinavian Actuarial Journal, Vol. 2010, Issue. 2, p. 83.

Abbas, Karim Heidergott, Bernd and Aissani, Djamil 2010. A Taylor series approach to the numerical analysis of the M/D/1/N queue. Procedia Computer Science, Vol. 1, Issue. 1, p. 1553.

Abbas, Karim and Aïssani, Djamil 2010. Structural Perturbation Analysis of a Single Server Queue with Breakdowns. Stochastic Models, Vol. 26, Issue. 1, p. 78.

Mouhoubi, Zahir and Aïssani, Djamil 2010. New perturbation bounds for denumerable Markov chains. Linear Algebra and its Applications, Vol. 432, Issue. 7, p. 1627.

Rahmoune, Fazia and Aïssani, Djamil 2011. Rapid Modelling and Quick Response. p. 17.

Hamadouche, Naima and Aïssani, Djamil 2011. Approximation in the M 2/G 2/1 Queue with Preemptive Priority. Methodology and Computing in Applied Probability, Vol. 13, Issue. 3, p. 563.

Abbas, Karim and Aïssani, Djamil 2011. Rapid Modelling and Quick Response. p. 3.

Lekadir, Ouiza and Aïssani, Djamil 2011. Error bounds on practical approximation for two tandem queue with blocking and non-preemptive priority. Computers & Mathematics with Applications, Vol. 61, Issue. 7, p. 1810.

Bareche, Aïcha and Aïssani, Djamil 2011. Statistical techniques for a numerical evaluation of the proximity of G/G/1 and G/M/1 queueing systems. Computers & Mathematics with Applications, Vol. 61, Issue. 5, p. 1296.

Adel-Aissanou, Karima Abbas, Karim Aïssani, Djamil and Hong, Wei-Chiang 2012. Strong Truncation Approximation in Tandem Queues with Blocking. Mathematical Problems in Engineering, Vol. 2012, Issue. 1,

Berdjoudj, Louiza Benaouicha, Mustapha and Aïssani, Djamil 2012. Measure of performances of the strong stability method. Mathematical and Computer Modelling, Vol. 56, Issue. 11-12, p. 241.

Ouazine, Sofiane and Abbas, Karim 2014. A Numerical Analysis of the M/G/1/N Queue with Vacations. IFAC Proceedings Volumes, Vol. 47, Issue. 2, p. 504.

Gouberman, Alexander and Siegle, Markus 2014. Stochastic Model Checking. Rigorous Dependability Analysis Using Model Checking Techniques for Stochastic Systems. Vol. 8453, Issue. , p. 156.

Berkhout, Joost and Heidergott, Bernd 2014. A Series Expansion Approach to Risk Analysis of an Inventory System with Sourcing. IFAC Proceedings Volumes, Vol. 47, Issue. 2, p. 510.

Download full list

Article contents

SERIES EXPANSIONS FOR FINITE-STATE MARKOV CHAINS

Abstract

Access options

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Article contents

SERIES EXPANSIONS FOR FINITE-STATE MARKOV CHAINS

Abstract

Access options

Save article to Kindle

Save article to Dropbox

Save article to Google Drive

Reply to: Submit a response

Your details

You have entered the maximum number of contributors

Conflicting interests