Queueing System with Negative Customers and Partial Protection of Service : 부분적인 서비스 보호와 부정적인 고객을 고려한 대기행렬 모형

다국어 초록 (Multilingual Abstract)

A multi-server queueing system with finite buffer is considered. The input flow is the BMAP (Batch Markovian Arrival Process). The service time has the PH (Phase) type distribution. Customers from the BMAP enter the system according to the discipline of partial admission. Besides ordinary (positive) customers, the Markovian flow (MAP) of negative customers arrives to the system. A negative customer can delete an ordinary customer in service if the state of its PH-service process belongs to some given set. In opposite case the ordinary customer is considered to be protected of the effect of negative customers. The stationary distribution and the main performance measures of the considered queueing system are calculated.

목차 (Table of Contents)

• 1. Introduction
• 2. Model Descriptions
• 3. Stationary Distributions
• 4. Performance Measures
• 5. Numerical Examples
• 6. Conclusion
• References

참고문헌 (Reference)

1 E, "“Product from network with negative and positive customers ” J. of Applied Prob." 656-663, 1991.

2 D. M, "“New results on the single server queue with a batch markovian arrival process" 1-46, 1991.

3 Chakravarthy, "The batch Markovian arrival process: a review and future work Advances in Probability Theory and Stochastic Process" Notable Publications 21-49, 2001.

4 Dudin, "Stable algorithm for stationary distribution calculation for a BMAP/SM/1 queueing system with markovian input of disasters" 42 : 547-556, 2004.

5 M. F, "Matrix-Geometric Solutions in Stochastic Models - An Algorithmic Approach" Johns Hopkins University Press 1981.

6 Klimenok, "Lack of invariant property of Erlang BMAP/ PH/N/0 model" 49 : 187-213, 2005

7 Graham, "Kronecker Products and Matrix Calculus with Applications" 1981.

8 Artalejo, "G-networks : A versatile approach for work removal in queueing networks" 126 : 233-249, 2000.

9 Bocharov, "G-network:Development of the product form networks theory" 64 : 718-746, 2003.

10 Anisimov V. V, "Analysis of Markov multi-server retrial queues with negative arrivals" 39 : 271-298, 2001.

11 Dudin, "An optimal multithreshold control for the input flow of the GI/PH/1 queuing system with BMAP flow of negative customers" 65 : 1417-1428, 2004.

12 Li, "A MAP/G/1 queue with negative customers" 47 : 5-43, 2004.