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Optimizing the Estimation of the Traffic Intensity Parameter of Queuing Model $M/M/1$ under Bayeian, E-Bayesian and Hierarchical Bayesian estimation Methods and based on Stationary Probability and System Cost Function
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Shahram Yaghoobzadeh Shahrastani *   , Amrollah Jafari |
| Payame Noor University |
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Abstract: (1889 Views) |
In this article, queunig model $M/M/1$ is Considered, in which the innterarrival of customers have an exponenial disributon with the parameter $lambda$ and the service times have an exponenial disributon with the parameter $mu$ and are independent of the interarrival times. it is also assumed that the system is active until $T$. Then, under this stopping time Bayesian, $E$-Bayesian and hierarchical Bayesian estimations of the traffic intensity parameter of this queuing model are obtained under the general entropy loss function and considering the gamma and erlang prior distributions for parameters $lambda$ and $mu$, respicctively. Then, using numerical analysis and based on a new index, Bayesian, $E$-Bayesian and hierarchical Bayesian estimations are compared. |
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| Keywords: Stationary probability, Cost function, $E$-Bayesian estimation, Hierarchical Bayesian estimation, The $M/1/1$ queuing system. |
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Full-Text [PDF 262 kb]
(837 Downloads)
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Type of Study: Research |
Subject:
Special
Received: 2023/06/28 | Accepted: 2024/03/5 | Published: 2024/03/15
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