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Extension of the loss probability formula to an overloaded queue with impatient customers
- Authors
- Kim, Bara; Kim, Jeongsim
- Issue Date
- 3월-2018
- Publisher
- ELSEVIER SCIENCE BV
- Keywords
- Impatient customers; Loss probability; Girsanov-type change of measure
- Citation
- STATISTICS & PROBABILITY LETTERS, v.134, pp.54 - 62
- Indexed
- SCIE
SCOPUS
- Journal Title
- STATISTICS & PROBABILITY LETTERS
- Volume
- 134
- Start Page
- 54
- End Page
- 62
- ISSN
- 0167-7152
- Abstract
- We consider a batch arrival M-X/G/1 queue with impatient customers. The loss probability is expressed in terms of the stationary waiting time distribution for the standard M-X/G/1 queue with no impatience. But this expression is only applicable when the offered load rho is less than 1. We give a formula for the loss probability applicable for any values of rho > 0, by proving that the loss probability is analytic in rho on (0, infinity) through a Girsanov-type change of measure. (C) 2017 Elsevier B.V. All rights reserved.
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