Publication: A matrix-geometric approximation for tandem queues with blocking and repeated attempts
Loading...
Full text at PDC
Publication Date
2002
Authors
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
Citations
Exportar
Abstract
Our interest is in the study of the MAP/PH/1/1 --> (.)/PH/1/K + 1 queue with blocking and repeated attempts. The main feature of its infinitesimal generator is the spatial heterogeneity caused by the transitions due to successful repeated attempts. We develop an algorithmic solution by making a simplifying approximation which yields an infinitesimal generator which is spatially homogeneous and has a modified matrix-geometric stationary vector. The essential tool in our analysis is the general theory on quasi-birth-and-death processes.
Description
UCM subjects
Unesco subjects
Keywords
Citation
J.R. Artalejo, A. G)omez-Corral, Steady state solution of a single-server queue with linear repeated requests, J. Appl. Probab. 34 (1997) 223–233.
J.R. Artalejo, A. G)omez-Corral, M.F. Neuts, Numerical analysis of multiserver retrial queues operating under a full access policy, in: G. Latouche, P. Taylor (Eds.), Advances in Algorithmic Methods for Stochastic Models, Notable Publications, Chennai, 2000,pp. 1–19.
J.R. Artalejo, A. G)omez-Corral, M.F. Neuts, Analysis of multiserver queues with constant retrial rate, European J. Oper. Res. 135 (2001) 123–135.
B. Avi-Itzhak, S. Hal2n, Servers in tandem with communication and manufacturing blocking, J. Appl. Probab. 30 (1993) 429–437.
B. Avi-Itzhak, M. Yadin, A sequence of two servers with no intermediate queue, Management Sci. 11 (1965) 553–564.
L. Bright, P.G. Taylor, Calculating the equilibrium distribution in level dependent quasi-birth-and-death processes, Stochastic Models 11 (1995) 497–525.
B.D. Choi, Y. Chang, MAP1; MAP2=M=c retrial queue with the retrial group of 2nite capacity and geometric loss, Math. Comput. Modelling 30 (1999) 99–113.
A.E. Conway, J. Keilson, Analysis of a two-stage 2nite buPer =ow controlled queueing model by a compensation Method, Oper. Res. Lett. 18 (1995) 65–74.
J.E. Diamond, A.S. Alfa, The MAP=PH=1 retrial queue, Stochastic Models 14 (1998) 1151–1177.
G.I. Falin, J.G.C. Templeton, Retrial Queues, Chapman & Hall, London, 1997.
G.I. Falin, A. G)omez-Corral, On a bivariate Markov process arising in the theory of single-server retrial queues, Statist. Neerlandica 54 (2000) 67–78.
W.K. Grassman, S. Drekic, An analytical solution for a tandem queue with blocking, Queueing Systems 36 (2000) 221–235.
N.G. Hall, C. Sriskandarajah, A survey of machine scheduling problems with blocking and no-wait in process, Oper. Res. 44 (1996) 510–525.
C. Langaris, The waiting-time process of a queueing system with gamma-type input and blocking, J. Appl. Probab. 23 (1986) 166–174.
G. Latouche, V. Ramaswami, A logarithmic reduction algorithm for quasi-birth-death processes, J. Appl. Probab. 30 (1993) 650–674.
G. Latouche, V. Ramaswami, Introduction to MatrixAnalytic Methods in Stochastic Modeling, ASA-SIAM, Philadelphia, 1999.
D.M. Lucantoni, K.S. Meier-Hellstern, M.F. Neuts, A single-server queue with server vacations and a class of non-renewal arrival processes, Adv. Appl. Probab. 22 (1990) 676–705.
E. Moutzoukis, C. Langaris, Two queues in tandem with retrial customers, Probab. Eng. Inform. Sci. 15 (2001) 311–325.
M.F. Neuts, Two queues in series with a 2nite, intermediate waiting room, J. Appl. Probab. 5 (1968) 123–142.
M.F. Neuts, Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach, The Johns Hopkins University Press, Baltimore, 1981.
M.F. Neuts, B.M. Rao, Numerical investigation of a multiserver retrial model, Queueing Systems 7 (1990) 169–190.
H.G. Perros, A bibliography of papers on queueing networks with 2nite capacity queues, Performance Evaluation 10 (1989) 255–260.
H.G. Perros, Queueing Networks with Blocking, Oxford University Press, New York, 1994.
N.U. Prabhu, Transient behaviour of a tandem queue, Management Sci. 13 (1967) 631–639.