ON DEVIATION MATRICES FOR BIRTH–DEATH PROCESSES

G. M. Koole; F. M. Spieksma

doi:10.1017/S0269964801152071

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We study deviation matrices of birth–death processes. This is relevant to the control of multidimensional queueing systems. We give an algorithm for computing deviation matrices for birth–death processes. As an application, we compute them explicitly for the M/M/s/N and M/M/s/∞ queues.

Crossref Citations

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

Heidergott, Bernd and Hordijk, Arie 2003. Taylor series expansions for stationary Markov chains. Advances in Applied Probability, Vol. 35, Issue. 4, p. 1046.

Bhulai, Sandjai and Koole, Ger 2003. On the structure of value functions for threshold policies in queueing models. Journal of Applied Probability, Vol. 40, Issue. 03, p. 613.

Bhulai, Sandjai and Koole, Ger 2003. On the structure of value functions for threshold policies in queueing models. Journal of Applied Probability, Vol. 40, Issue. 3, p. 613.

Mathirajan, M. and Sivakumar, A.I. 2006. A literature review, classification and simple meta-analysis on scheduling of batch processors in semiconductor. The International Journal of Advanced Manufacturing Technology, Vol. 29, Issue. 9-10, p. 990.

De Turck, Koen De Clercq, Sofian Wittevrongel, Sabine Bruneel, Herwig and Fiems, Dieter 2012. Analytical and Stochastic Modeling Techniques and Applications. Vol. 7314, Issue. , p. 227.

Katehakis, Michael N. and Smit, Laurens C. 2012. A SUCCESSIVE LUMPING PROCEDURE FOR A CLASS OF MARKOV CHAINS. Probability in the Engineering and Informational Sciences, Vol. 26, Issue. 4, p. 483.

Hamoudi, Zina Aïssani, Djamil and Heidergott, Bernd 2014. Non-Parametric Sensitivity Analysis of the Finite M/M/1 Queue. IFAC Proceedings Volumes, Vol. 47, Issue. 2, p. 498.

Kim, Jaehee Kim, Chang Ouk and Kwak, Choonjong 2015. Analysis of timeout mechanism in a testing-repair model. International Journal of Production Research, Vol. 53, Issue. 7, p. 1996.

Hautphenne, Sophie Kerner, Yoav Nazarathy, Yoni and Taylor, Peter 2015. The intercept term of the asymptotic variance curve for some queueing output processes. European Journal of Operational Research, Vol. 242, Issue. 2, p. 455.

Katehakis, Michael N. Smit, Laurens C. and Spieksma, Floske M. 2015. DES AND RES PROCESSES AND THEIR EXPLICIT SOLUTIONS. Probability in the Engineering and Informational Sciences, Vol. 29, Issue. 2, p. 191.

Braunsteins, Peter Hautphenne, Sophie and Taylor, Peter G. 2016. The roles of coupling and the deviation matrix in determining the value of capacity in M/M/1/C queues. Queueing Systems, Vol. 83, Issue. 1-2, p. 157.

Hautphenne, Sophie and Haviv, Moshe 2016. THE BIAS OPTIMAL K IN THE M/M/1/K QUEUE: AN APPLICATION OF THE DEVIATION MATRIX. Probability in the Engineering and Informational Sciences, Vol. 30, Issue. 1, p. 61.

Takhedmit, Baya and Abbas, Karim 2017. A parametric uncertainty analysis method for queues with vacations. Journal of Computational and Applied Mathematics, Vol. 312, Issue. , p. 143.

Berkhout, Joost and Heidergott, Bernd F. 2019. Analysis of Markov Influence Graphs. Operations Research, Vol. 67, Issue. 3, p. 892.

Bachi, Katia Abbas, Karim and Heidergott, Bernd 2021. Statistical Taylor series expansion: An approach for epistemic uncertainty propagation in Markov reliability models. RAIRO - Operations Research, Vol. 55, Issue. , p. S593.

Article contents

ON DEVIATION MATRICES FOR BIRTH–DEATH PROCESSES

Abstract

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