Lattice path approach for busy period density of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si65.gif" overflow="scroll"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="italic">GI</mml:mi></mml:mrow><mml:mrow><mml:mi>a</mml:mi></mml:mrow></mml:msup><mml:mo>/</mml:mo><mml:msup><mml:mrow><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mi>b</mml:mi></mml:mrow></mml:msup><mml:mo>/</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math> queues using <mml:math xmlns:mml="http://www.w3.org/1998/Math/

Borkakaty, Bidisha; Agarwal, Mukesh; Sen, Kamalika

doi:10.1016/j.apm.2009.09.005

Cited by 3 publications

(1 citation statement)

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“…In [8], Borkakaty For arrivals of variable size following a Poisson distribution, Claeys et al [9] analyze the model M X /GI l,c /1, where the server remains idle until there is at least l customers waiting and can serve at most c customers simultaneously. With geometric distribution for arrivals and services, in [10], they present the model Geo X /Geo c /1 under two different policies: in the first, the server starts a new service although the number of clients does not reach c; in the second, the server waits until the number of clients reaches c. A related model, the GI/Geo/1 queue under N-policy, is analyzed by Lim et al [11].…”

Section: Introductionmentioning

confidence: 99%

Effect of Parameters on Geoa/Geob/1 Queues: Theoretical Analysis and Simulation Results

Soria-Lorente¹,

Sánchez²

2018

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This paper analyzes a discrete-time Geo a /Geo b /1 queuing system with batch arrivals of fixed size a, and batch services of fixed size b. Both arrivals and services occur randomly following a geometric distribution. The steady-state queue length distribution is obtained as the solution of a system of difference equations. Necessary and sufficient conditions are given for the system to be stationary. Besides, the uniqueness of the root of the characteristic polynomial in the interval (0, 1) is proven which is the only root needed for the computation of the theoretical solution with the proposed procedure. The theoretical results are compared with the ones observed in some simulations of the queuing system under different sets of parameters. The agreement of the results encourages the use of simulation for more complex systems. Finally, we explore the effect of parameters on the mean length of the queue as well as on the mean waiting time.

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Section: Introductionmentioning

confidence: 99%

Effect of Parameters on Geoa/Geob/1 Queues: Theoretical Analysis and Simulation Results

Soria-Lorente¹,

Sánchez²

2018

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Busy Period Analysis of $$\textit{GI/G/c}$$GI/G/c and $$\textit{MAP/G/c}$$MAP/G/c Queues

Chakravarthy

2018

Performance Prediction and Analytics of Fuzzy, Reliability and Queuing Models

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The busy period of an M/M/1 queue with balking and reneging

Ammar

Helan

Amri

2013

Applied Mathematical Modelling

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Lattice path approach for busy period density of GIa/Gb/1 queues using
Bidisha Borkakaty
¹
,
Mukesh Agarwal
²
,
Kamalika Sen
³

Cited by 3 publications

References 21 publications

Effect of Parameters on Geoa/Geob/1 Queues: Theoretical Analysis and Simulation Results

Effect of Parameters on Geoa/Geob/1 Queues: Theoretical Analysis and Simulation Results

Busy Period Analysis of $$\textit{GI/G/c}$$GI/G/c and $$\textit{MAP/G/c}$$MAP/G/c Queues

The busy period of an M/M/1 queue with balking and reneging

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Lattice path approach for busy period density of GIa/Gb/1 queues using Bidisha Borkakaty1, Mukesh Agarwal2, Kamalika Sen3

Cited by 3 publications

References 21 publications

Effect of Parameters on Geoa/Geob/1 Queues: Theoretical Analysis and Simulation Results

Effect of Parameters on Geoa/Geob/1 Queues: Theoretical Analysis and Simulation Results

Busy Period Analysis of $$\textit{GI/G/c}$$GI/G/c and $$\textit{MAP/G/c}$$MAP/G/c Queues

The busy period of an M/M/1 queue with balking and reneging

Contact Info

Product

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Lattice path approach for busy period density of GIa/Gb/1 queues using
Bidisha Borkakaty
¹
,
Mukesh Agarwal
²
,
Kamalika Sen
³