Single Counter Markovian Queuing Model with
Multiple Inputs

Gajendra k. Saraswat

doi:https://doi.org/10.14445/22315373/IJMTT-V60P533

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 60 | Number 4 | Year 2018 | Article Id. IJMTT-V60P533 | DOI : https://doi.org/10.14445/22315373/IJMTT-V60P533

Single Counter Markovian Queuing Model with Multiple Inputs

Gajendra k. Saraswat

Citation :

Gajendra k. Saraswat, "Single Counter Markovian Queuing Model with Multiple Inputs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 60, no. 4, pp. 205-219, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V60P533

Abstract

This paper analyzes a M/M/1 queueing model with multiple input, where the rate of arrival and service capacity follow Poisson distribution. The arrival process of the model remains in three stages said to be state I, II, and III. The system remains in three state for a random time which is exponentially distributed. The queue discipline is first-in-first-out. Laplace transforms of the various probability generating functions are obtained and the steady state results are derived. The probability that the arrival process (input) will be. In state I, II and III is also analyzed.

Keywords

- Queuing Theory, Markovian Process, Exponential Distribution, Poisson distribution and Probability Generating Function.

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