Abstract
In this paper we present the analysis of BMAP/G/1 vacation models of non-M/G/1-type in a general framework. We provide new service discipline independent formulas for the vector generating function (GF) of the stationary number of customers and for its mean, both in terms of quantities at the start of vacation.
We present new results for vacation models with gated and G-limited disciplines. For both models discipline specific systems of equations are setup. Their numerical solution are used to compute the required quantities at the start of vacation.
This work is supported by the NAPA-WINE FP7-ICT (http://www.napa-wine.eu) and the OTKA K61709 projects.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Doshi, B.T.: Queueing systems with vacations - a survey. Queueing Systems 1, 29–66 (1986)
Takagi, H.: Queueing Analysis - A Foundation of Performance Evaluation, Vacation and Prority Systems, vol. 1. North-Holland, New York (1991)
Lucantoni, D.L.: New results on the single server queue with a batch Markovian arrival process. Stochastic Models 7, 1–46 (1991)
Neuts, M.F.: Structured stochastic matrices of M/G/1 type and their applications. Marcel Dekker, New York (1989)
Neuts, M.F.: Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach. The John Hopkins University Press, Baltimore (1981)
Lucantoni, D.L.: The BMAP/G/1 queue: A tutorial. In: Donatiello, L., Nelson, R. (eds.) Models and Techniques for Performance Evaluation of Computer and Communications Systems. Springer Verlag, Heidelberg (1993)
Chang, S.H., Takine, T.: Factorization and Stochastic Decomposition Properties in Bulk Queues with Generalized Vacations. Queueing Systems 50, 165–183 (2005)
Chang, S.H., Takine, T., Chae, K.C., Lee, H.W.: A unified queue length formula for BMAP/G/1 queue with generalized vacations. Stochastic Models 18, 369–386 (2002)
Ferrandiz, J.M.: The BMAP/G/1 queue with server set-up times and server vacations. Adv. Appl. Prob. 25, 235–254 (1993)
Shin, Y.W., Pearce, C.E.M.: The BMAP/G/1 vacation queue with queue-length dependent vacation schedule. J. Austral. Math. Soc. Ser. B 40, 207–221 (1998)
Banik, A.D., Gupta, U.C., Pathak, S.S.: BMAP/G/1/N queue with vacations and limited service discipline. Applied Mathematics and Computation 180, 707–721 (2006)
Fuhrmann, S.W., Cooper, R.B.: Stochastic Decompositions in the M/G/1 Queue with Generalized Vacations. Operations Research 33, 1117–1129 (1985)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Saffer, Z., Telek, M. (2008). Analysis of BMAP/G/1 Vacation Model of Non-M/G/1-Type. In: Thomas, N., Juiz, C. (eds) Computer Performance Engineering. EPEW 2008. Lecture Notes in Computer Science, vol 5261. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87412-6_16
Download citation
DOI: https://doi.org/10.1007/978-3-540-87412-6_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-87411-9
Online ISBN: 978-3-540-87412-6
eBook Packages: Computer ScienceComputer Science (R0)