Complutense University Library

A state-dependent Markov-modulated mechanism for generating events and stochastic models


Artalejo, Jesús R. and Gómez-Corral, Antonio (2010) A state-dependent Markov-modulated mechanism for generating events and stochastic models. Mathematical Methods in the Applied Sciences, 33 (11). pp. 1342-1349. ISSN 0170-4214

Official URL:;jsessionid=A5D4725A115991536540A53A7772D452.d01t04


In this paper, we introduce a versatile block-structured state-dependent event (BSDE) approach that provides a methodological tool to construct non-homogeneous Markov-modulated stochastic models. Alternatively, the BSDE approach can be used to construct even a part (e.g. the arrival process) of the model. To illustrate the usefulness of the BSDE approach, several arrival patterns as well as queueing and epidemic models are considered. In particular, we deal with a state-dependent quasi-birth-and-death process that gives a constructive generalization of the scalar birth-and-death process and the homogeneous quasi-birth-and-death process.

Item Type:Article
Uncontrolled Keywords:Stochastic models;Queueing; Epidemics
Subjects:Sciences > Mathematics > Stochastic processes
ID Code:15033

Neuts MF. Matrix-geometric Solutions in Stochastic Models: An Algorithmic Approach. The Johns Hopkins University Press: Baltimore, MD, 1981.

Neuts MF. Structured Stochastic Matrices of M/G/1 Type and their Applications. Marcel Dekker: New York, 1989.

Tijms HC. A First Course in Stochastic Models. Wiley: Chichester, 2003.

Dshalalow JH. Queueing systems with state dependent parameters. In Frontiers in Queueing: Models and Applications in Science and Engineering, Dshalalow JH (ed.). CRC Press: Boca Raton, 1997; 61–116.

Artalejo JR, Li QL. Performance analysis of a block-structured discrete-time retrial queue with state-dependent arrivals. Discrete Event Dynamic Systems 2009; DOI: 10.1007/s10626-009-0075-6 (available online).

Chakka R, Do TV. The $MM\sum_{k=1}^{K}CPP_{k}/GE/c/L$MM∑Kk=1CPPk/GE/c/L $G$G-queue with heterogeneous servers: steady state solution and an application to performance evaluation. Performance Evaluation 2007; 64:191–209.

Lucantoni DM. New results on the single server queue with a batch Markovian arrival process. Stochastic Models 1991; 7:1–46.

He Q-M, Neuts MF. Markov chains with marked transitions. Stochastic Processes and their Applications 1998; 74:37–52. Allen LJS. An Introduction to Stochastic Processes with Applications to Biology. Prentice-Hall: New Jersey, 2003.

Daley DJ, Gani J. Epidemic Modelling: An Introduction. Cambridge Studies in Mathematical Biology, vol. 15. Cambridge University Press: Cambridge, 1999.

Kitaev MYu, Rykov W. Controlled Queueing Systems. CRC Press: Boca Raton, 1995.

Artalejo JR, Economou A. Markovian controllable queueing systems with hysteretic policies: busy period and waiting time analysis. Methodology and Computing in Applied Probability 2005; 7:353–378.

Darroch JN, Seneta E. On quasi-stationary distributions in absorbing continuous-time finite Markov chains. Journal of Applied Probability 1967; 4:192–196.

Chao X, Miyazawa M, Pinedo M. Queueing Networks: Customers, Signals and Product Form Solutions. Wiley: Chichester, 1999.

Deposited On:26 Apr 2012 08:11
Last Modified:08 Mar 2016 14:49

Repository Staff Only: item control page