Abstract
In this paper we introduce the new M/M/1 retrial queue with working vacations which is motivated by the performance analysis of a Media Access Control function in wireless systems. We give a condition for the stability of the model, which has an important impact on setting the retrial rate for such systems. We derive the closed form solution in equilibrium for the retrial M/M/1 queue with working vacations, and we also show that the conditional stochastic decomposition holds for this model as well.
Similar content being viewed by others
References
Adams C., Gelenbe E., Vicard J.: An experimentally validated model of the paging drum. Acta Informatica 11, 103–117 (1979)
Arora A., Jin F., Sahin G., Mahmoud H., Choi H.A.: Throughput analysis in wireless networks with multiple users and multiple channels. Acta Informatica 43(3), 147–164 (2006)
Artalejo J.R., Economou A., Gómez-Corral A.: Applications of maximum queue lengths to call center management. Comput. OR 34(4), 983–996 (2007)
Artalejo J.R., Economou A., Gómez-Corral A.: Algorithmic analysis of the Geo/Geo/c. Europ. J. Oper. Res. 189(3), 1042–1056 (2008)
Artalejo J.R., Gómez-Corral A.: Retrial Queueing Systems. Springer, Berlin (2008)
Chakka R., Harrison P.G.: A Markov modulated multi-server queue with negative customers—the MM CPP/GE/c/L G-queue. Acta Informatica 37, 881–919 (2001)
Doshi B.T.: Queueing systems with vacations—a survey. Queueing Syst. Theory Appl 1(1), 29–66 (1986)
Gelenbe E., Iasnogorodski R.: A queue with server of walking type. Ann. Inst. Henry Poincaré, Sér B (Probab. Stat.) XVI(1), 63–73 (1980)
Gelenbe, E., Mitrani, I.: Analysis and synthesis of computer systems. Academic Press (London and New York), 1980. Japanese translation: Ohm-Sha Publishing Co., Tokyo 1988. Expanded 2nd edn: World Scentific, Singapore (2009)
IEEE 802.11 Working Group (2007-06-12). IEEE 802.11-2007: Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications. ISBN 0-7381-5656-9.
Kumar B., Raja J.: On multiserver feedback retrial queues with balking and control retrial rate. Ann. Oper. Res. 141(22), 211–232 (2006)
Liu W., Xu X., Tian N.: Stochastic decompositions in the M/M/1 queue with working vacations. Oper. Res. Lett. 35, 595–600 (2007)
Lopez-Herrero M.: A maximum entropy approach for the busy period of the M/G/1 retrial queue. Ann. Oper. Res. 141(11), 271–281 (2006)
Mitrani I., Chakka R.: Spectral expansion solution for a class of Markov models: application and comparison with the matrix-geometric method. Perform. Eval. 23, 241–260 (1995)
Mushko V., Jacob M., Ramakrishnan K., Krishnamoorthy A., Dudin A.: Multiserver queue with addressed retrials. Ann. Oper. Res. 141(19), 283–301 (2006)
Servi L.D., Finn S.G.: M/M/1 queues with working vacations (M/M/1/WV). Perform. Eval 50(1–4), 41–52 (2002)
Tian N., Zhang Z.G.: Stationary Distributions of GI/M/c Queue with PH Type Vacations. Queueing Syst. Theory Appl. 44(2), 183–202 (2003)
Wüchner P., Sztrik J., de Meer H.: Finite-source M/M/S retrial queue with search for balking and impatient customers from the orbit. Comput. Netw. 53(8), 1264–1273 (2009)
Zhang Z.G., Tian N.: Analysis on queueing systems with synchronous vacations of partial servers. Perform. Eval. 52(4), 269–282 (2003)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Do, T.V. M/M/1 retrial queue with working vacations. Acta Informatica 47, 67–75 (2010). https://doi.org/10.1007/s00236-009-0110-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00236-009-0110-y