Paper Info
Title
Effective algorithm for computation of the stationary distribution of multi-dimensional level-dependent Markov chains with upper block-Hessenberg structure of the generator.
Abstract
Multi-dimensional level-dependent Markov chains with the upper block-Hessenberg structure of the generator have found extensive applications in applied probability for solving the problems of queueing, reliability, inventory, etc. However, the problem of computing the stationary distribution of such chains is not completely solved. There is a known algorithm for multi-dimensional Asymptotically Quasi-Toeplitz Markov Chains, but, it is required a large amount of computer resources and time-consuming. In this paper, we propose a new effective algorithm that is much less time- and memory-consuming. The new algorithm can be used for analyzing any multi-dimensional Markov chain with the considered structure of the generator. To numerically demonstrate the advantages of this algorithm over the known one, we use it for analysis of a novel single-server retrial queueing system with the batch Markovian arrival process (BMAP), a finite buffer, non-persistent customers and an unreliable server. We derive a transparent ergodicity condition for this queueing system. Then, assuming that this condition is fulfilled, we apply the new algorithm and demonstrate its advantages over the known one.
Year
DOI
Venue
2020
10.1016/j.cam.2019.112425
Journal of Computational and Applied Mathematics
Keywords
Field
DocType
Level-dependent multi-dimensional Markov chains,Effective algorithm,Batch Markovian arrival process,Unreliable service,Retrial queue
Multi dimensional,Ergodicity,Applied probability,Markov chain,Algorithm,Queueing theory,Markovian arrival process,Stationary distribution,Mathematics,Computation
Journal
Volume
ISSN
Citations 
366
0377-0427
0
PageRank 
References 
Authors
0.34
0
4
Name
Order
Citations
PageRank
Sergei A. Dudin100.68
Alexander N. Dudin223140.78
Olga Kostyukova3124.47
O. S. Dudina4598.80