The week's pick
Reseach Article
Two Server (s, S) Inventory System with Positive Service Time, Positive Lead Time, Retrial Customers and Negative Arrivals
| International Journal of Computer Applications |
| Foundation of Computer Science (FCS), NY, USA |
| Volume 62 - Number 10 |
| Year of Publication: 2013 |
| Authors: Hannah Revathy. P, Muthu Ganapathi Subramanian |
10.5120/10115-4784
|
Hannah Revathy. P, Muthu Ganapathi Subramanian . Two Server (s, S) Inventory System with Positive Service Time, Positive Lead Time, Retrial Customers and Negative Arrivals. International Journal of Computer Applications. 62, 10 ( January 2013), 9-13. DOI=10.5120/10115-4784
Abstract
This paper deals with a two server (s,S) inventory system with positive service time, positive lead time, retrial of customers and negative arrivals. In this system, arrival of customers form a Poisson process, lead time and service time are exponentially distributed. The system starts with S units of inventory on hand. Each arriving customer is served a single unit of the item by any one of the servers. When the inventory level reaches s, an order is placed for (S-s) units. If the inventory level is zero or both servers are busy, then the arriving customer goes to orbit and becomes a source of repeated calls. Assume that the capacity of the orbit is infinite. The negative arrival plays an important role in this paper and it controls the congestion in the orbit by removing one customer from the orbit and further it is assumed that it removes the customer from the orbit only if inventory level is zero or both servers are busy. It is also assumed that the access from orbit to the service facility is governed by the classical retrial policy. This model is solved by using Direct Truncation Method. Numerical and graphical studies have been done for analysis of mean number of customers in the orbit, average inventory level, Truncation level, mean number of busy servers and system performance measures. A suitable cost function is defined.
References
- J. R. Artalejo and Antonio Gomez-Corral, Retrial Queueing Systems, Springer, 2008.
- Artalejo. J. R and A. Gomez corral (1999). On a single server queue with negative arrivals and repeated request, Journal of Applied Probability 36, pp 907-918.
- G. I. Falin, "A survey of retrial queues," Queueing Systems, vol. 7, no. 2, pp. 127–167, 1990.
- G. I. Falin and J. G. C. Templeton, Retrial Queues, Chapman & Hall, London, UK, 1997.
- Gelenbe (1991). Product forms queueing networks with negative and positive customers, Journal of Applied Probability, 28, pp 656-663.
- P. G. Harrison and E. Pitel(1993). Sojourn times in single-server queue with negative customers, Journal of Applied Probability 30, pp 943-963.
- A. Krishnamoorthy and K. P. Jose, "Three Production Inventory Systems with Service, Loss and Retrial of Customers" Information and Management Sciences, Volume 19, Number 3, pp. 367-389, 2008
- J. R. Artalejo, A. Krishnamoorthy, and M. J. Lopez-Herrero, "Numerical analysis of (s,S) inventory systems with repeated attempts," Annals of Operations Research, vol. 141, no. 1, pp. 67–83, 2006.
- A. Krishnamoorthy and M. E. Islam, "(s,S) inventory system with postponed demands," Stochastic Analysis and Applications, vol. 22, no. 3, pp. 827–842, 2004.
- A. Krishnamoorthy and K. P. Jose, "An (s,S) inventory system with positive lead-time, loss and retrial of customers ," Stochastic Modelling and Applications, vol. 8, no. 2, pp. 56–71, 2005.
- A. Krishnamoorthy and K. P. Jose "Comparison of Inventory Systems with Service, Positive Lead-Time, Loss, and Retrial of Customers" Journal of Applied Mathematics and Stochastic Analysis Volume 2007.
- A. Muthu Ganapathi Subramanian, G. Ayyappan, G. Sekar. "M/M/1 Retrial queueing system with negative arrival under non-preemptive priority service", Journal of Fundamental Sciences Vol 5, No 2 230-146, 2009
- P. V. Ushakumari, "On (s,S) inventory system with random lead time and repeated demands," Journal of Applied Mathematics and Stochastic Analysis, vol. 2006
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