# Network Analysis of Biserial Queues Linked with a Flowshop Scheduling System

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 246)

## Abstract

This paper is an attempt to establish a linkage between networks of queues consisting of two parallel biserial servers connected with a common server in series and a multistage flowshop scheduling system having m machines. In the queue network, both the arrival and service patterns follow Poisson law. The objective of this paper is to develop an algorithm minimizing the total elapsed time with minimum completion time, average waiting time, and minimum queue length for the proposed queuing–scheduling linkage model. The efficiency of the proposed algorithm is tested by a numerical illustration.

### Keywords

Biserial servers Mean queue length Linkage network Flowshop scheduling Elapsed time Completion time

### References

1. 1.
A. K. Erlang, “The theory of probabilities and telephone conversations”, Nyt Tidsskrift fur Matematik, Vol. B, No. 20, pp. 33, 1909.Google Scholar
2. 2.
R. R. P. Jackson, “Queuing system with phase type service”, O. R.Quat., Vol. 5, pp. 109–120, 1954.Google Scholar
3. 3.
D. C. John, “A proof of queuing formula: “L = λW””, Operation Research, Vol. 13, pp. 400–412, 1965.Google Scholar
4. 4.
P. L. Maggu, “Phase type service queue with two channels in Biserial”, J.OP. Res. Soc. Japan, Vol. 13, No. 1, 1970.Google Scholar
5. 5.
K. Vinod, T. P. Singh and 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.Google Scholar
6. 6.
D. Gupta, T.P Singh and 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, pp. 407–418, 2007.Google Scholar
7. 7.
S. Sharma, D. Gupta and S. Sharma, “Analysis of linkage network of queues with a multistage flowshop scheduling system”, International journal of Operation Research, Accepted for publication, 2013.Google Scholar
8. 8.
S. M. Johnson, “Optimal two & three stage production schedules with set up times includes”, Nav. Res. Log. Quart., Vol. 1, pp. 61–68, 1954.Google Scholar
9. 9.
T. P. Singh and V. Kumar, “On linkage of a scheduling system with biserial queue network”, Arya Bhatta Journal of Mathematics & Informatics, Vol. 1, No. 1, pp. 71–76, 2009.Google Scholar
10. 10.
S. Sharma, D. Gupta and S. Sharma, “Analysis of network of biserial queues linked with a common server”, International journal of Computing and Mathematics, Accepted for publication, 2013a.Google Scholar
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