Gómez Corral, Antonio
(2005)
*On a finite-buffer bulk-service queue with disasters.*
Mathematical Methods of Operations Research, 61
(1).
pp. 57-84.
ISSN 1432-2994

PDF
Restricted to Repository staff only until 2020. 409kB |

Official URL: http://www.springerlink.com/content/th2mh8al9tl0x511/fulltext.pdf

## Abstract

We deal with a finite-buffer bulk-service queue with disasters. The arrival streams of units and disasters are Markovian arrival processes (MAPs). We study the stationary distribution of the embedded Markov chain at post-departure epochs. The block structure allows us to derive a general approach amenable to numerical calculation following results of the theory for censored Markov chains and level-dependent quasi-birth-and-death processes. We give tractable analytical formulas for the departure process and the stationary distributions of the system state at arbitrary and pre-arrival epochs. The effect of the disaster stream on certain probabilistic descriptors is graphically illustrated.

Item Type: | Article |
---|---|

Uncontrolled Keywords: | Bulk-service, Censored Markov chain, Clearing, Disasters, Finite-buffer queue, Markovian arrival process (MAP), Quasi-birth-and-death process (QBD |

Subjects: | Sciences > Mathematics > Operations research |

ID Code: | 15622 |

References: | Artalejo JR and Gómez-Corral A (1998) Analysis of a stochastic clearing system with repeated attempts. Stochastic Models 14:623–645 Artalejo JR and Gómez-Corral A (1999) On a single server queue with negative arrivals and request repeated. Journal of Applied Probability 36:907–918 Artalejo JR (2000) G-networks: A versatile approach for work removal in queueing networks. European Journal of Operational Research 126:233–249 Bailey NTJ (1954) A continuous time treatment of a simple queue using generating functions. Journal of the Royal Statistical Society B 16:288–291 Bini DA, Meini B and Ramaswami V (2000) Analyzing M=G=1 paradigms through QBDs: the role of the block structure in computing the matrix G. In: Latouche G and Taylor P (eds.) Advances in Algorithmic Methods for Stochastic Models. Notable Publications. New Jersey, pp. 73–86 Boxma OJ, Perry D and Stadje W (2001) Clearing models for M=G=1 queues. Queueing Systems 38:287–306 Chakravarthy S (1993) Analysis of a finite MAP=G=1 queue with group services. Queueing Systems 13:385–407 Chao X, Miyazawa M and Pinedo M (1999) Queueing Networks: Customers, Signals and Product Form Solutions. Wiley. Chichester Chaudhry ML and Templeton JGC (1983) A First Course in Bulk Queues. Wiley. New York Chaudhry ML and Gupta UC (1999) Modelling and analysis of M=G½a;b=1=N queue-A simple alternative approach. Queueing Systems 31:95–100 Çinlar E (1975) Introduction to Stochastic Processes. Prentice Hall. Englewood Cliffs Dudin AN and Nishimura S (1999) A BMAP=SM=1 queueing system with Markovian arrival input and disasters. Journal of Applied Probability 36:868–915 Gelenbe E (1991) Product-form queueing networks with negative and positive customers.Journal of Applied Probability 28:656–663 Gómez-Corral A (2002) On a tandem G-network with blocking. Advances in Applied Probability 34:626–661 GrassmannWK and Stanford DA (2002) Matrix analytic methods. In: GrassmannWK (ed.)Computational Probability. Kluwer Academic Publishers. Boston, pp. 153–203 Gupta UC and Vijaya Laxmi P (2001) Analysis of the MAP=Ga;b=1=N queue. Queueing Systems 38:109–124 Harrison PG and Pitel E (1996) The M=G=1 queue with negative customers. Advances in Applied Probability 28:540–566 Hunter JJ (1983) Mathematical Techniques of Applied Probability. Volume 1, Discrete Time Models: Basic Theory. Academic Press. New York Jain G and Sigman K (1996) A Pollaczek-Khintchine formula for M=G=1 queues with disasters. Journal of Applied Probability 33:1191–1200 Latouche G and Ramaswami V (1999) Introduction to Matrix Analytic Methods in Stochastic Modeling. ASA-SIAM. Philadelphia Lucantoni DM, Meier-Hellstern KS and Neuts MF (1990) A single-server queue with server vacations and a class of non-renewal arrival processes. Advances in Applied Probability 22:676–705 Lucantoni DM (1991) New results on the single server queue with a batch Markovian arrival process. Stochastic Models 7:1–46 Neuts MF (1979) A versatile Markovian arrival process. Journal of Applied Probability 16:764–779 Neuts MF (1981) Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach. The Johns Hopkins University Press. Baltimore Neuts MF (1989) Structured Stochastic Matrices of M/G/1 Type and Their Applications.Marcel Dekker. New York Ramaswami V (1998) The generality of quasi-birth-and-death processes. In: Alfa AS and Chakravarthy SR (eds.) Advances in Matrix Analytic Methods for Stochastic Models.Notable Publications. New Jersey, pp. 93–113 |

Deposited On: | 14 Jun 2012 09:38 |

Last Modified: | 06 Feb 2014 10:28 |

Repository Staff Only: item control page