The week's pick
Reseach Article
Stochastic Analysis of Bulk Production with Bulk and Catastrophic Sales System using Matrix Geometric Approach
| International Journal of Computer Applications |
| Foundation of Computer Science (FCS), NY, USA |
| Volume 107 - Number 7 |
| Year of Publication: 2014 |
| Authors: Ramshankar.r, Ramanarayanan.r |
10.5120/18763-0049
|
Ramshankar.r, Ramanarayanan.r . Stochastic Analysis of Bulk Production with Bulk and Catastrophic Sales System using Matrix Geometric Approach. International Journal of Computer Applications. 107, 7 ( December 2014), 16-21. DOI=10.5120/18763-0049
Abstract
This paper studies two stochastic Models (A) and (B) with bulk production and bulk sales of products with catastrophe. The system has infinite storing capacity and the production and sales sizes are finite valued random variables with finite maximum production and sales sizes. When a catastrophe occurs the entire stocks are sold. Matrix partitioning method is used to study the models. In Model (A) the maximum production size is greater than the maximum sales size and the infinitesimal generator is partitioned as blocks of the maximum production size for analysis and in Model (B) the maximum production size is less than the maximum sales size and the latter is for partition. The stationary stock level probabilities, its expected values, its variances and probabilities of empty level are derived for the two models using the rate matrix iterated. Numerical examples are presented for illustration. Bulk arrival and bulk service queue becomes a special case of the model considered.
References
- Aissani. A. and Artalejo. J. R. 1998. On the single server retrial queue subject to break downs, Queueing System . 30, 309-321.
- Ayyappan. G, Muthu Ganapathy Subramanian. A and Gopal Sekar. 2010. M/M/1 retrial queueing system with loss and feedback under pre-emptive priority service, IJCA, Vol. 2, N0. 6, 27-34.
- D. Bini, G. Latouche, and B. Meini. Numerical Methods for Structured Markov Chains. Numerical Mathematics and Scientific Computation. Oxford University Press, Oxford, 2005. 327 pages.
- Chakravarthy. S. R and Neuts. M. F. 2014. Analysis of a multiserver queueing model with MAP arrivals of special customers, Simulation Modelling Practice and Theory, vol. 43, 79-95,
- Gaver, D. , Jacobs, P. , Latouche, G, 1984. Finite birth-and-death models in randomly changing environments. Advances in Applied Probability 16, 715–731
- Latouche. G, and Ramaswami . V, (1998). Introduction to Matrix Analytic Methods in Stochastic Modeling, SIAM. Philadelphia, PA.
- Neuts . M. F. 1981. Matrix- Geometric Solutions in Stochastic Models: An algorithmic Approach, The Johns Hopkins Press, Baltimore
- Neuts. M. F and Nadarajan. R, 1982. A multi-server queue with thresholds for the acceptance of customers into service, Operations Research, Vol. 30, No. 5, 948-960.
- Noam Paz, and Uri Yechali, 2014 An M/M/1 queue in random environment with disaster, Asia- Pasific Journal of Operational Research 01/2014;31(30. DOI: 101142/S021759591450016X
- William J. Stewart, The matrix geometric/analytic methods for structured Markov Chains, www. sti. uniurb/events/sfmo7pe/slides/Stewart-2pdfN. C. State University
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