Abstract
An energy-saving model based on the M/G/1/N-type finite-buffer queue with independent and generally distributed repeated vacations is considered. Using the formula of total probability and the idea of embedded Markov chain, a system of integral equations for conditional transient queue-size distributions is found. A closed-form representation for the solution of the corresponding system built for Laplace transforms is obtained. Numerical example is attached as well.
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
Similar content being viewed by others
References
J. Abate, G.L. Choudhury, W. Whitt, An introduction to numerical transform inversion and its application to probability models, in Computational Probability, ed. by W. Grassmann (Kluwer Academic, Boston, 2000), pp. 257–323
J.W. Cohen, The Single Server Queue (North-Holland, Amsterdam, 1982)
N.T. Dinh, A power efficiency based delay constraint mechanism for mobile WiMAX systems, in Computers, Networks, Systems & Industrial Engineering, ed. by R. Lee. SCI, vol. 265 (2011), pp. 181–191
F.-C. Jiang, D.-C. Huang, Ch.-T. Yang, F.-Y. Leu, Lifetime elongation for wireless sensor network using queue-based approaches. J. Supercomput. 59, 1312–1335 (2012)
W.M. Kempa, The transient analysis of the queue-length distribution in the batch arrival system with N-policy, multiple vacations and setup times. AIP Conf. Proc. 1293, 235–242 (2010)
W.M. Kempa, Analysis of departure process in batch arrival queue with multiple vacations and exhaustive service. Commun. Stat., Theory Methods 40(16), 2856–2865 (2011)
W.M. Kempa, Departure process in finite-buffer queue with batch arrivals. Lect. Notes Comput. Sci. 6751, 1–13 (2011)
W.M. Kempa, The virtual waiting time in a finite-buffer queue with a single vacation policy. Lect. Notes Comput. Sci. 7314, 47–60 (2012)
W.M. Kempa, Transient analysis of the output process in the GI/M/1-type queue with finite buffer. AIP Conf. Proc. 1487, 193–200 (2012)
V.S. Korolyuk, Boundary-Value Problems for Compound Poisson Processes (Naukova Dumka, Kiev, 1975) (in Russian)
V. Mancuso, S. Alouf, Analysis of power saving with continuous connectivity. Comput. Netw. 56, 2481–2493 (2012)
http://standards.ieee.org/getieee802/download/802.16e-2005.pdf
Acknowledgement
The project was financed with subsidies from the National Science Centre in Poland, granted by virtue of the decision number DEC-2012/07/B/ST6/01201.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Kempa, W.M. (2015). Queue-Size Distribution in Energy-Saving Model Based on Multiple Vacation Policy. In: Mityushev, V., Ruzhansky, M. (eds) Current Trends in Analysis and Its Applications. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-12577-0_80
Download citation
DOI: https://doi.org/10.1007/978-3-319-12577-0_80
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-12576-3
Online ISBN: 978-3-319-12577-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)