Analytically elegant and computationally efficient results in terms of roots for the $$GI^{X}/M/c$$ G I X / M / c queueing system

Chaudhry, M. L.; Kim, James J.

doi:10.1007/s11134-015-9469-3

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Deriving the Root Equation: From Gi X /Geo/c To Gi X /M/c1

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Cited by 11 publications

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“…e equation (45) coincides with the root equation provided by Chaudhry and Kim [40] who consider the GI X / M/c with light-tailed inter-batch-arrival times. To compute the roots of (45) when the inter-batch-arrival times follow a continuous heavy-tailed distribution, we modify K(z) (1) with(plots):…”

Section: Deriving the Root Equation: From Gi X /Geo/c To Gi X /M/csupporting

confidence: 64%

Analytically Simple and Computationally Efficient Results for the GI^X/Geo/c Queues

Chaudhry

Kim

Banik

2019

Journal of Probability and Statistics

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A simple solution to determine the distributions of queue-lengths at different observation epochs for the model GIX/Geo/c is presented. In the past, various discrete-time queueing models, particularly the multiserver bulk-arrival queues, have been solved using complicated methods that lead to incomplete results. The purpose of this paper is to use the roots method to solve the model GIX/Geo/c that leads to a result that is analytically elegant and computationally efficient. This method works well even for the case when the inter-batch-arrival times follow heavy-tailed distributions. The roots of the underlying characteristic equation form the basis for all distributions of queue-lengths at different time epochs.

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Section: Deriving the Root Equation: From Gi X /Geo/c To Gi X /M/csupporting

confidence: 64%

Analytically Simple and Computationally Efficient Results for the GI^X/Geo/c Queues

Chaudhry

Kim

Banik

2019

Journal of Probability and Statistics

Self Cite

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Analysis of the Sojourn Time Distribution for M/GL/1 Queue with Bulk-Service of Exactly Size L

Tang

2018

Methodol Comput Appl Probab

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A New and Pragmatic Approach to the GIX/Geo/c/N Queues Using Roots

Kim

Chaudhry

Goswami

et al. 2020

Methodol Comput Appl Probab

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Analytically elegant and computationally efficient results in terms of roots for the $$GI^{X}/M/c$$ G I X / M / c queueing system

Cited by 11 publications

References 14 publications

Analytically Simple and Computationally Efficient Results for the GI^X/Geo/c Queues

Analytically Simple and Computationally Efficient Results for the GI^X/Geo/c Queues

Analysis of the Sojourn Time Distribution for M/GL/1 Queue with Bulk-Service of Exactly Size L

A New and Pragmatic Approach to the GIX/Geo/c/N Queues Using Roots

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Analytically elegant and computationally efficient results in terms of roots for the $$GI^{X}/M/c$$ G I X / M / c queueing system

Cited by 11 publications

References 14 publications

Analytically Simple and Computationally Efficient Results for the GIX/Geo/c Queues

Analytically Simple and Computationally Efficient Results for the GIX/Geo/c Queues

Analysis of the Sojourn Time Distribution for M/GL/1 Queue with Bulk-Service of Exactly Size L

A New and Pragmatic Approach to the GIX/Geo/c/N Queues Using Roots

Contact Info

Product

Resources

About

Analytically Simple and Computationally Efficient Results for the GI^X/Geo/c Queues

Analytically Simple and Computationally Efficient Results for the GI^X/Geo/c Queues