A Two-Server Bulk Service Queuing Model with a Permanent Server and a Temporary Server on Hold

Authors

  • Kuntal Bakuli Department of Statistics, Banwarilal Bhalotia College, Asansol, West Bengal, India
  • Manisha Pal Department of Statistics, University of Calcutta, Kolkata, West Bengal, India

Keywords:

Bulk service queue, two servers, permanent serve, temporary server

Abstract

In this paper, we consider a bulk service queuing model with a fixed bulk size and a single permanent server. An additional server is kept on hold and is allowed to serve when the queue length exceeds certain threshold value. The model is analyzed using embedded Markov chain. A comparison of the performance of the model with the following models have also been made – (i) two-server bulk service model, (ii) bulk service model with two independent queues corresponding to two servers and (iii) a single server bulk service model with double service capacity of the server.

References

Abolnikov L, Dshalalow JH. On a multilevel controlled bulk queueing system Mx /G(r, R)/1. J Appl Math Stoch Anal. 1992; 5: 237-260.

Arora KL. Two-server bulk-service queuing process. Oper Res. 1964; 12(2): 286-294.

Bailey NTJ. A continuous treatment of a simple queue using generating functions. J Roy Stat.1954; B16: 288-291.

Banerjee A, Gupta U, Chakravarthy S. Analysis of a finite-buffer bulk-service queue under Markovian arrival process with batch-size-dependent service. Comput Oper Res. 2015; 60: 138-149.

Banerjee A, Gupta U, Goswami V. Analysis of finite-buffer discrete-time batch-service queue with batch-size-dependent service. Comput Ind Eng. 2014; 75: 121-128.

Bakuli K, Pal M. Bulk service queuing system with impatient customers: a computational approach. Thail Stat. 2017; 15(1): 1-10.

Chaudhry M, Templeton J. The queuing system M/Gb /l and its ramifications. Eur J Oper Res.1981; 6: 56-60.

Chaudhry ML, Gupta UC. Modelling and analysis of M/G(a, b)/1/N queue-a simple alternative approach. Queueing Syst.1999; 31: 95-100.

Chaudhry ML, Chang SH. Analysis of the discrete-time bulk-service queue Geo/GY /1/N + B, Oper Res Lett. 2004; 32: 355-363.

Downton, F. Waiting time in bulk service queues. J Roy Stat.1955; 17: 256-261.

Ghare P. Multichannel queuing system with bulk service. Oper Res. 1968; 16: 189-192.

Ghimre S, Ghimre R, Thapa G, Farnandes S. Multi-server batch service queuing model with variable service rates. IJAMSS. 2017; 6(4): 43-54.

Gold H, Tran-Gia P. Performance analysis of a batch service queue arising out of manufacturing system modeling. Queueing Syst. 1993; 14: 413-426.

Gupta U, Laxmi PV. Analysis of the MAP/G(a, b)/1/N queue. Queueing Syst.2001; 38: 109-124.

Gupta UC, Goswami V. Performance analysis of finite buffer discrete-time queue with bulk service. Comput Oper Res. 2002; 29:1331-1341.

Hoel PG, Port SC, Stone CJ. Introduction to stochastic process. Prospect Heights: Waveland Press; 1987.

Holman D, Chaudhry M, Ghosal A. Some results for the general bulk service queueing system. Bull Aus Math Soc. 1981; 23: 161-179.

Jaiswal N. Bulk-service queuing problem. Oper Res. 1960; 8: 139-143.

Krishnamoorthy A. and Ushakumari P. A queueing system with single arrival bulk service and single departure. Math Comput Model. 2000; 31: 99-108.

Medhi J. Waiting time distribution in a Poisson queue with a general bulk service rule. Manage Sci. 1975; 21: 777-782.

Neuts MF. A general class of bulk queues with Poisson input. Ann Math Stat. 1967; 38(3): 759-770.

Pakes AG. Some conditions for ergodicity and recurrence of Markov chains. Oper Res. 1969; 17(6): 1058-1061.

Seneta E. Finite approximations to infinite non-negative matrices, II: refinements and applications. Mathematical Proceedings of the Cambridge Philosophical Society, 1968; 64(2): 465-470.

Wolf D. Approximation of the invariant probability measure of an infinite stochastic matrix. Adv Appl Prob. 1980; 12(3): 710-726.

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Published

2023-03-29

How to Cite

Bakuli, K. ., & Pal, M. . (2023). A Two-Server Bulk Service Queuing Model with a Permanent Server and a Temporary Server on Hold. Thailand Statistician, 21(2), 351–369. Retrieved from https://ph02.tci-thaijo.org/index.php/thaistat/article/view/249006

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