Abstract
This paper studies a queueing system with a double queue of customers and permits fed by independent Markovian input processes. Customers can only be served when a permit for service is available. Their service times are governed by a PH-distribution. This system is isomorphic to a closed two-loop queueing network. We propose a computational approach to the stationary distribution of the queue length. The model was motivated by the sliding window flow-control mechanism widely used in communcation networks.
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
F. Baccelli, A.M. Makowski, A. Shwartz, Simple Computable Bounds and Approximations for the Fork-Join Queue in: T. Hasegawa, H. Takagi, Y. Takahashi (eds.), Computer Networking and Performance Evaluation North-Holland, Amsterdam- New York — Oxford 1986
U. N. Bhat, Finite Capacity Assembly-like Queues Queueing Systems 1 (1986), 85–101
J.L Carroll, A. van de Liefvoort, L. Lipsky, Solutions of M/G/1//N-type Loops with Extensions to M/G/1 and GI/M/1 Queues Oper. Res. 30 (1982), 490–514
S.D. Hohl, P.J. Kühn, Approximate Analysis of Row and Cycle Times in Queueing Networks in: L.F.M. de Moraes, E. de Souza e Silva, LF.G. Soares (eds.), Dafa Communications and their Performance, 471–485 North-Holland, Amsterdam- New York — Oxford 1988
U. Körner, H.G. Perros, S. Fdida, G. Shapiro, End to End Delays in a Catenet Environment in: L.F.M. de Moraes, E. de Souza e Silva, L.F.G. Soares (eds.), Data Communications and their Performance, 441–452 North-Holland, Amsterdam- New York — Oxford 1988
G. Latouche, Queues with Paired Customers J. Appl. Prob. 18 (1981), 684–696
G. Latouche, P.A. Jacobs, D.P. Gaver, Finite Markov Chain Models Skip-Free in One Direction Nav. Res. Log. Quart. 31 (1984), 571–588
M.F. Neuts, Matrix-Geometric Solutions in Stochastic Models Johns Hopkins University Press, Baltimore-London 1981
M. Reiser, Admission Delays on Virtual Routes with Window Flow Control in: G. Pujolle (ed.) Performance of Data Communication Systems and their Applications North-Holland, Amsterdam- New York — Oxford 1981
H.C. Tijms, Stochastic Modeling and Analysis J. Wiley, New York 1986
H. Zhenting, G. Quingfeng, Homogeneous Denumerable Markov Processes Springer, Berlin-Heidelberg and Science Press, Beijing 1988
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1989 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kramer, M. (1989). Assembly-Like Queues and Closed-Loop Systems with Admission Control. In: Stiege, G., Lie, J.S. (eds) Messung, Modellierung und Bewertung von Rechensystemen und Netzen. Informatik-Fachberichte, vol 218. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-75079-3_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-75079-3_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-51713-9
Online ISBN: 978-3-642-75079-3
eBook Packages: Springer Book Archive