On Markovian Queueing Model as Birth-Death Process

1
Okoro Otonritse Joshua
Okoro Otonritse Joshua
1 UNIVERSITY OF IBADAN

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Markovian queueing model has so many application in real life situations. Places where Markovian queueing model can be applied include, Supermarket, Production system, Post office, data communication, parking place, assembly of printed circuit boards, call center of an insurance company, main frame computer, toll booths, traffic lights, e.t.c. Birth-death process has being markovian foundation on queueing models. This article is an eye opener to novice researchers, since it explore Markovian queueing model in real life situation. The fundamental of Markovian Queueing model as birth and death process is hereby reviewed in this article, with fundamental results applications in M / M / 1, M / M / S, M / M / 1/ K , and M / M / s / K. Here we reexamined; Average Number of Customers and average number of time in the system, waiting in the queue, in service respectfully. These summaries of these results are also tabulated.

14 Cites in Articles

References

  1. Sheldon Ross (2010). Introduction to Probability Models Tenth Edition Academic Press is an imprint of Elsevier 30 Corporate Drive, Suite 400.
  2. Hwei Hsu (2011). Probability, Random Variables, and Random Processes, Schaum's Series Outline.
  3. Brian Bunday (1996). An Introduction to Queueing Theory.
  4. Brian Bunday (1986). Basic Queueing Theory.
  5. Sheldon Ross (2010). Student's Manual to Accompany Introduction to Probability Models Tenth Edition.
  6. M Carlos,Carlos Hernandez-Suarez,Osval Castillo-Chavez,Karla Lopez,Hern Andez-Cuevas (2010). An Application Of Queuing Theory To SIS And SEIS Epidemic Models.
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  8. M Carlos,Carlos Hernandez-Suarez,Castillo-Chavez (1999). A basic result on the integral for birth-death Markov processes.
  9. Alan Krinik,Carrie Mortensen,Gerardo Rubino (2003). Connections Between Birth-Death Processes.
  10. Donald Gross,John Shortle,James Thompson,Carl Harris (2008). Fundamental of Queue Theory-Fourth Edition.
  11. Ivo Adan,Jacques Resing (2002). Queueing Theory.
  12. A Nasroallah Monte Carlo Simulation of Markov Chain Steady-state Distribution.
  13. J Banks,J Carson,B Nelson,D Nicol (2001). Discrete-Event System Simulation.
  14. F Hillier,G Lieberman (2001). Introduction to Operations Research.

Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

Ethical Approval

No ethics committee approval was required for this article type.

Data Availability

Not applicable for this article.

Okoro Otonritse Joshua. 2014. \u201cOn Markovian Queueing Model as Birth-Death Process\u201d. Global Journal of Science Frontier Research - F: Mathematics & Decision GJSFR-F Volume 13 (GJSFR Volume 13 Issue F11): .

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Issue Cover
GJSFR Volume 13 Issue F11
Pg. 21- 40
Journal Specifications

Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

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v1.2

Issue date

March 22, 2014

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English

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Markovian queueing model has so many application in real life situations. Places where Markovian queueing model can be applied include, Supermarket, Production system, Post office, data communication, parking place, assembly of printed circuit boards, call center of an insurance company, main frame computer, toll booths, traffic lights, e.t.c. Birth-death process has being markovian foundation on queueing models. This article is an eye opener to novice researchers, since it explore Markovian queueing model in real life situation. The fundamental of Markovian Queueing model as birth and death process is hereby reviewed in this article, with fundamental results applications in M / M / 1, M / M / S, M / M / 1/ K , and M / M / s / K. Here we reexamined; Average Number of Customers and average number of time in the system, waiting in the queue, in service respectfully. These summaries of these results are also tabulated.

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On Markovian Queueing Model as Birth-Death Process

Okoro Otonritse Joshua
Okoro Otonritse Joshua UNIVERSITY OF IBADAN

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