Development and Analysis of Generalized Queuing Model
DOI:
https://doi.org/10.26438/ijcse/v6i11.1532Keywords:
Queue length, Average waiting time, Poisson Law, Moment generating function, ProbabilityAbstract
In the present work a generalized queuing model has been developed to investigate the various queuing characteristics in steady state. The model consists of two global servers having three servers each which are connected in tricum biserial way. The comprehensive governing equations has been given in mathematical formulation which has been used to find the various output parameters i.e., queue lengths, variances, joint probabilities, traffic intensities, average waiting time for customers. The present model is named a generalized queuing model because several models available in the literature can be developed as the special cases
References
[1] R.R.P. Jackson, “Queuing systems with phase-type service”, Operational Research Quarterly, 5, pp. 109-120, 1954.
[2] P.L. Maggu, “Phase type service queues with two servers in biseries”, Journal of Operational Research Society of Japan, Vol. 13, No.1, pp. 6-16, 1970.
[3] K. L. Arya, “System of two servers in biseries with a serial service channel and phase type service” Zeitschrift fur Operations Research, Vol. 16 B, pp. 115-122, 1972.
[4] M. Singh, “Steady state behaviour of serial queuing processes with impatient customers”, Math, Operations forsch. U. statist. Ser., Vol. 15, No.2, pp. 289-298, 1984.
[5] R. Hassin, M. Haviv, “To Queue or Not to Queue: Equilibrium
Behavior in Queueing Systems”, International Series in Operations Research & Management Science, Vol. 59, pp. 109-122, 2003.
[6] D. Gupta, T.P. Singh, R. Kumar, “Analysis of a network queue model comprised of biserial and parallel channel linked with a common server” Ultra Science, Vol. 19, No. 2 M, 407-418, 2007.
[7] T.P. Singh, V. Kumar, R. Kumar, “On transient behaviour of a queuing network with parallel biserial queues”, JMASS, Vol.1, No.2, pp.68-75, 2005.
[8] V. Kumar, T.P. Singh, R. Kumar, “Steady state behaviour of a queue model comprised of two subsystems with biserial linked with common channel”, Reflection des ERA., Vol.1, No.2, pp.135-152, 2007.
[9] M.S. El-Paoumy, “On Poisson Bulk Arrival Queue: M X /M / 2 / N with Balking, Reneging and Heterogeneous servers”, Applied Mathematical Sciences, Vol. 2, No. 24, 1169 – 1175, 2008.
[10] S.K. Agrawal, B.K. Singh, “Computation of various queue characteristics using tri-cum biserial queuing model connected with a common server”, International Journal of Mathematics Trends and Technology (IJMTT), Vol. 56, No. 1, pp. 81-90, 2008. doi: 10.14445/22315373/IJMTT-V56P510.
[11] S.K. Agrawal, B.K. Singh, “A Comprehensive study of Various Queue Characteristics using Tri-Cum Biserial Queuing Model”, International Journal of Scientific Research in Mathematical and Statistical Sciences (IJSRMSS), Vol. 5, Issue 2, pp. 46-56, 2008. doi: 10.26438/ijsrmss/v5i2.4656.
[12] S.K. Agrawal, B.K. Singh, “An Investigation of Tri-Cum Biserial Queuing Model Connected with Three Servers”, International Journal of Emerging Technologies and Innovative Research
(JETIR), Vol. 5, issue 9, pp. 493-509, 2018. Doi: 10.1729/Journal.18346.
[13] S.K. Agrawal and B.K. Singh, “Influence of Reneging and Jockeying on Various Queuing Characteristics of Tri-Cum Biserial
Based Queue Model”, International Journal of Mechanical Engineering and Technology (IJMET), Vol. 9, Issue 10, pp.
(1062)-(1073), 2018
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