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http://dx.doi.org/10.5351/KJAS.2015.28.1.033

Approximation on the Distribution of the Overshoot by the Property of Erlang Distribution in the M/En/1 Queue  

Lee, Sang-Gi (Sampling Division, Statistics Korea)
Bae, Jongho (Department of Information and Statistics, Chungnam National University)
Publication Information
The Korean Journal of Applied Statistics / v.28, no.1, 2015 , pp. 33-47 More about this Journal
Abstract
We consider an $M/E_n/1$ queueing model where customers arrive at a facility with a single server according to a Poisson process with customer service times assumed to be independent and identically distributed with Erlang distribution. We concentrate on the overshoot of the workload process in the queue. The overshoot means the excess over a threshold at the moment where the workload process exceeds the threshold. The approximation of the distribution of the overshoot was proposed by Bae et al. (2011); however, but the accuracy of the approximation was unsatisfactory. We derive an advanced approximation using the property of the Erlang distribution. Finally the newly proposed approximation is compared with the results of the previous study.
Keywords
Queueing model; Erlang distribution; workload process; overshoot;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
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