The discrete-time Geo/ Geo/1 queue with negative customers and disasters

The arrival of a negative customer to a queueing system causes one ordinary customer to be removed (or killed) if any is present. The arrival of a disaster, on the other hand, kills all the customers in the system if any. In this paper, we extend the queueing theory on negative arrivals and disaster...

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Bibliographic Details
Published in:Computers & operations research 2004-08, Vol.31 (9), p.1537-1548
Main Authors: Atencia, I., Moreno, P.
Format: Article
Language:English
Subjects:
Disasters
Discrete-time model
Ergodicity
Markov analysis
Markov chain
Mathematical models
Negative customers
Queuing
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Summary:The arrival of a negative customer to a queueing system causes one ordinary customer to be removed (or killed) if any is present. The arrival of a disaster, on the other hand, kills all the customers in the system if any. In this paper, we extend the queueing theory on negative arrivals and disasters to the discrete-time Geo/ Geo/1 queueing system. Specifically, we find the ergodicity condition and give explicit formulae for the stationary distribution. We also provide some numerical results to illustrate the effect of the parameters on several performance characteristics.
ISSN:0305-0548
1873-765X
0305-0548
DOI:10.1016/S0305-0548(03)00107-2