Abstract
This paper presents the analysis of a renewal input multiple working vacations queue with balking, reneging and heterogeneous servers. Whenever the system becomes empty the second server leaves for a working vacation whereas the first server remains idle in the system. During a working vacation the second server provides service at a slower rate rather than completely stopping service. The steady-state probabilities of the model are obtained using supplementary variable and recursive techniques. Various performance measures of the model such as expected system length, expected balking rate, etc., have been discussed. Finally, some numerical results have been presented to show the effect of model parameters on the system performance measures.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ammar, S.I.: Transient analysis of a two-heterogeneous servers queue with impatient behavior. J. Egyptian Math. Soc. 22, 90–95 (2014)
Ammar, S.I., El-Sherbiny, A.A., El-Shehawy, S.A., Al-Seedy, R.O.: A matrix approach for the transient solution of an M/M/1/N queue with discouraged arrivals and reneging. Int. J. Comput. Math. 89(4), 482–491 (2012)
Al-Seedy, R.O., El-Sherbiny, A.A., El-Shehawy, S.A., Ammar, S.I.: Transient solution of the M/M/c queue with balking and reneging. Comput. Math. Appl. 57, 1280–1285 (2009)
Baba, Y.: Analysis of G I/M/1 queue with multiple working vacations. Oper. Res. Lett. 33, 201–209 (2005)
Banik, A., Gupta, U.C., Pathak, S.: On the G I/M/1/N queue with multiple working vacations - analytic analysis and computation. Appl. Math. Model 31, 1701–1710 (2007)
Chakravarthy, S.R.: Analysis of a multi-server queuing model with vacations and optional secondary services. Math. Appl. 41(2), 145–169 (2013)
Choudhry, A., Medhi, P.: Balking and reneging in multiserver Markovian queueing system. Int. J. Math. Oper. Res. 3(4), 377–394 (2011)
Goswami, V.: Analysis of discrete-time multi-server queue with balking. Int. J. Manage. Sci. Eng. Manage. 9(1), 21–32 (2014)
Hostad, P.: The G/M/m queue with finite waiting room. J. Appl. Prob. 12(4), 779–792 (1975)
Ke, J.C., Wu, C.H., Zhang, Z.G.: A note on a multi-server queue with vacations of multiple groups of servers. Qual. Tech. Quan. Manage. 10(4), 513–525 (2013)
Krishna Kumar, B., Madheswari, S.P.: An M/M/2 queueing system with heterogeneous servers and multiple vacations. Math. Comput. Model. 41, 1415–1429 (2005)
Krishnamoorthy, A., Sreenivasan, C.: An M/M/2 queueing system with heterogeneous servers including one with working vacation. Int. J. Stoch. Anal. 2012, 16 (2012). doi:10.1155/2012/145867
Servi, L.D., Finn, S.G.: M/M/1 queue with working vacations (M/M/1/W V). Perf. Eval. 50, 41–52 (2002)
Shawky, A.I.: On Poisson machine interference model: M/M/2/k/N with balking, reneging and heterogeneous repairmen. Commun. Fac. Sci. Univ. Ank. Series A1 53 (2), 7–12 (2004)
Vijaya Laxmi, P., Goswami, V., Jyothsna, K.: Analysis of finite buffer Markovian queue with balking, reneging and working vacations. Int. J. Strat. Dec. Sci 4(1), 11–24 (2013)
Yue, D., Yu, J., Yue, W.: A Markovian queue with two heterogeneous servers and multiple vacations. J. Indust. Manage. Opt. 5(3), 453–465 (2009)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Vijaya Laxmi, P., Jyothsna, K. Balking and Reneging Multiple Working Vacations Queue with Heterogeneous Servers. J Math Model Algor 14, 267–285 (2015). https://doi.org/10.1007/s10852-015-9271-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10852-015-9271-6