Computation of Various Queue Characteristics using Tri-Cum Biserial Queuing Model Connected with a Common Server

Sachin Kumar Agrawal; B. K. Singh

doi:https://doi.org/10.14445/22315373/IJMTT-V56P510

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 56 | Number 1 | Year 2018 | Article Id. IJMTT-V56P510 | DOI : https://doi.org/10.14445/22315373/IJMTT-V56P510

Computation of Various Queue Characteristics using Tri-Cum Biserial Queuing Model Connected with a Common Server

Sachin Kumar Agrawal, B. K. Singh

Citation :

Sachin Kumar 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, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V56P510

Abstract

The present paper deals with the investigation of various characteristics of a developed queuing model in which three servers are connected in parallel in tri-cum biserial way with a common server. The arrival and service pattern are assumed to follow the Poisson law. Queue length, variance, average waiting time and probabilities have been estimated using statistical tools, generating function technique and law of calculus. Extensive parametric study has been presented to show the efficacy of the present solution methodology. Present study demonstrates that the queuing theory provides a good approach to analyze the complicated probabilistic and deterministic systems.

Keywords

Queuing model, Poisson law, Variance, Probabilities.

References

[1] Jackson, R.R.P. 1954. Queuing systems with phase-type service. Operational Research Quarterly, 5, 109-120.
[2] Maggu, P.L. 1970. Phase type service queues with two servers in biseries. Journal of Operational Research Society of Japan, 13(1), 1- 6.
[3] Singh, T. P., Vinod, K., Rajinder, K., (2005). On transient behaviour of a queuing network with parallel biserial queues, JMASS, 1(2), 68-75.
[4] Gupta D., Singh, T.P., Rajinder, K., (2007). Analysis of a network queue model comprised of biserial and parallel channel linked with a common server. Ultra Science, 19(2) M, 407-418.
[5] Kumar, V., Singh, T. P. , and Kumar, R. 2006. Steady state behaviour of a queue model comprised of two subsystems with biserial channels linked with a common channel. Ref Des Era JSM, 1(2), 135-152.
[6] Gupta, D., Sharma, S. and Sharma, S. 2012. On linkage of a flowshop scheduling model including job block criteria with a parallel biserial queue network, Computer Engineering and Intelligent System, 3(2), 17-28
[7] Seema, Gupta, D. and Sharma, S. 2013. Analysis of biserial servers linked to a common server in fuzzy environment, International Journal of Computer Applications, 68(6), 26-32.