Batch Arrival Queueing Model with Unreliable Server
-
2018-10-02 https://doi.org/10.14419/ijet.v7i4.10.20910 -
Busy State, Idle state, Matrix Geometric Method, Repair State, Stationary distribution, , Server breakdown. -
Abstract
The unreliable server with provision of temporary server in the context of application has been investigated. A temporary server is installed when the primary server is over loaded i.e., a ï¬xed queue length of K-policy customers including the customer with the primary server has been build up. The primary server may breakdown while rendering service to the customers; it is sent for the repair. This type of queuing system has been investigated using Matrix Geometric Method to obtain the probabilities of the system steady state.
AMS subject classiï¬cation number— 60K25, 60K30 and 90B22.
Â
Â
-
References
[1] Aissani A, Unreliable queueing with repeated orders. Microelectron and Reliability, 33:2093-2106, 1993.
[2] Bhargava C. and M. Jain, Unreliable multi-server queuing system with modiï¬ed vacation policy, OPSEARCH, doi:http://dx.doi.org/10.1007/s12597-013-0138-1, 2013.
[3] Chakaravarthy S.R., A multi-server synchronous vacation model with thresholds and a probabilistic decision rule, Ero. J. oper. Res., Vol.182, pp. 305-320, 2007.
[4] Eager D. L., Lazowska E. D. and J. Zahorjan, A comparison of receiver-initiated and sender-initiated adaptive load sharing, perf.Eval., Vol.6, pp.53-68, 1986.
[5] Gharbi, N. and M. Ioualalen, Numerical investigation of ï¬nite – source multi server system with different vacation policies, J. Comp. Appl. Math., Vol. 234, pp 625-635, 2010.
[6] Haridass M, and R. Arumuganathan , studied analysis of a bulk queue with unreliable server and single vacation, Int. J. Open Problems Compt. Math., Vol. 1, No. 2, 2008
[7] Indra and Vijay Rajan, Studied queueing analysis of markovian queue having two heterogeneous server with catastrophes using matrix
[8] geometric technique, international Journal of statistics and systems, vol.12, pp.205-212, 2017.
[9] Jain M. and A. Jain, Working vacations queuing models with mul tiple types of server breakdowns, Appl. Math. model.vol.34,pp.1-13, 2010.
[10] Kalayanraman R. and M. Seenivasan, The stationary analysis of M/M/4/4+1 queueing model, Annamalai university Science Journal 46:103-110,2010.
[11] Kalayanraman R. and M. Seenivasan, The stationary analysis of M/M/5/5+1 queueing model with linear retrial rate, proceeding of the international Conference on Mathematical Science ( ICMS-2014) published by Elsevier, pp.749-753, 2014.
[12] Ke, j.C, Wu C.H. and Z.G Zhang, A Note on a multi server Queue with Vacations of Multiple Groups of Servers, Quant. Tech.Quant.Mgmt., Vol. 10, pp.513-525, 2013.
[13] Krishna Kumar B. and S.P Madheswari, An M/M/2 queuing sys tem with heterogeneous servers and multiple vacations, Math. Comput. Model., Vol. 41, pp. 1415- 1429, 2005.
[14] Kushner H. J, Heavy traffic analysis of controlled Queuing and Communication Networks Springer-Verlag, New York, 2001.
[15] Leite S.C. and M.D. Fragoso, Heavy traffic analysis of state- dependent parallel queues with trigger and an application to web search systems Perf.Eval.,Vol.67, pp.913-928, 2010.
[16] Neuts M.F, Markov chains with applications queueing theory, which have a matrix geometric invariant probability vector, Adv. Appl. Prob., Vol.10, pp.185-212, 1978.
[17] Neuts M.F, Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach. The Johns Hopkins University Press, Balti more, 1981.
[18] Neuts M.F and D. M. Lucantoni, A Markovian queue with N servers subject to breakdowns and repairs, Management Science, 25, 849-861 1979.
[19] Parthasarathy P.R. and R. Sudhesh, Transient solution of a multi server Poisson queue with N-policy, Comput.Math.Appl, Vol.55,pp.550-562, 2008.
[20] Renisagaya Raj. M and B. Chandrasekar,, Matrix – Geometric Method for queueing model with subject to breakdown and N-Policy vacations, Mathematica Aeterna, Vol. 5, pp.917-926, 2015.
[21] Renisagaya Raj. M and B. Chandrasekar, Matrix – Geometric Method for queueing model with state-Dependent arrival of an unreli able server and PH service, Mathematica Aeterna, Vol. 6, no.1 pp.107-1166, 2016.
[22] Vinod. B, Unreliable queueing system, Comp.oper. Res. 12, 323- 340(1985).
-
Downloads
-
How to Cite
Seenivasan, M., & S.Subasri, K. (2018). Batch Arrival Queueing Model with Unreliable Server. International Journal of Engineering & Technology, 7(4.10), 269-273. https://doi.org/10.14419/ijet.v7i4.10.20910Received date: 2018-10-04
Accepted date: 2018-10-04
Published date: 2018-10-02