Gómez-Corral, Antonio
(2004)
*Sojourn times in a two-stage queueing network with blocking.*
Naval Research Logistics (NRL), 51
(8).
pp. 1068-1089.
ISSN 0894-069X

PDF
Restringido a Repository staff only hasta 2020. 189kB |

Official URL: http://onlinelibrary.wiley.com/doi/10.1002/nav.20044/pdf

## Abstract

The model considered in this paper involves a tandem queue consisting of a sequence of two waiting lines. The main feature of our model is blocking, i.e., as soon as the second waiting line reaches a certain upper limit, the first line is blocked. The input of units to the tandem queue is the MAP (Markovian arrival process), and service requirements are of phase type. Our objective is to study the sojourn time distribution under the first-come-first-serve discipline by analyzing the sojourn time through times until absorption in appropriately defined quasi-birth-and-death processes and continuous-time Markov chains.

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

Uncontrolled Keywords: | Blocking; Markovian arrival process; phase type distribution; quasi-birth-anddeath process; tandem queue |

Subjects: | Sciences > Mathematics > Operations research |

ID Code: | 15625 |

References: | J. Abate and W. Whitt, Numerical inversion of Laplace transforms of probability distributions, ORSA J Comput 7 (1995), 36–43. B. Avi-Itzhak and S. Halfin, Servers in tandem with communication and manufacturing blocking,J Appl Probab 30 (1993), 429–437. B. Avi-Itzhak and M. Yadin, A sequence of two servers with no intermediate queue, Management Sci 11 (1965), 553–564. S. Balsamo, V. de Nitto Persone´, and R. Onvural, Analysis of queueing networks with blocking,Kluwer Academic, Boston, 2001. L. Bright and P.G. Taylor, Calculating the equilibrium distribution in level dependent quasi-birthand-death processes, Stoch Models 11 (1995), 497–525. A. Gómez-Corral, A tandem queue with blocking and Markovian arrival process, Queueing Syst Theory Appl 41 (2002), 343–370. A. Gómez-Corral, A matrix-geometric approximation for tandem queues with blocking and repeated attempts, Oper Res Lett 30 (2002), 360–374. A. Gómez-Corral, On a tandem G-network with blocking, Adv Appl Probab 34 (2002), 626–661. W.K. Grassmann and S. Drekic, An analytical solution for a tandem queue with blocking, Queueing Syst Theory Appl 36 (2000), 221–235. N.G. Hall and C. Sriskandarajah, A survey of machine scheduling problems with blocking and no-wait in process, Oper Res 44 (1996), 510–525. B.R. Haverkort, A.P.A. van Moorsel, and A. Dijkstra, “MGMtool: A performance analysis tool based on matrix geometric methods,” Modelling techniques and tools, R. Pooley and J. Hillston (Editors),Edinburgh University Press, Edinburgh, 1993, pp. 312–316. G.C. Hunt, Sequential arrays of waiting lines, Oper Res 4 (1956), 674–683. J.J. Hunter, Mathematical techniques of applied probability. Volume 1. Discrete time models: Basic theory, Academic Press, New York, 1983. A. Klemm, C. Lindemann, and M. Lohmann, Modeling IP traffic using the batch Markovian arrival process, Performance Eval 54 (2003), 149–173. |

Deposited On: | 14 Jun 2012 09:31 |

Last Modified: | 08 Mar 2016 15:59 |

Repository Staff Only: item control page