Queuing time and utilization ratio in markov queuing systems

Authors

DOI:

https://doi.org/10.15587/1729-4061.2014.24901

Keywords:

queuing system, Markov chain, queuing time, downtime, utilization ratio of states

Abstract

In many cases two variables such as utilization ratio (relative characteristic) and queuing time (absolute characteristic) are enough to assess the efficiency of a queuing system. The literature contains formulas for calculating utilization and downtime ratios as constants.

In the paper, queuing time and utilization ratio are obtained as a function of time. This allows to investigate them in dynamics.

For the queuing system S, set as a Markov chain with continuous time and finite number of states where n is the number of system state, the formulas for calculating the queuing time (downtime) in any state are obtained. Queuing time in the i-th state for the time interval  can be calculated using the formula.

The formulas for calculating the time of appearance and disappearance of queues, time intervals of the queue existence in any state of the system are obtained. The formulas for calculating the time of the beginning, end and duration of service in any state are obtained. The formulas of dependencies of utilization ratio of any system state on the time are obtained.

Calculating the above functions for the unloading terminal of freight rail hub is given as an example of using the obtained formulas.

Author Biographies

Семен Давыдович Бронза, Ukrainian State Academy of Railway Transport Feerbaha, 7, Kharkov, Ukraine, 61050

Docent, Candidate of physico-mathematical sciences

Department of Mathematics

Наталия Семеновна Юрчак, Ukrainian State Academy of Railway Transport Feyerbakh Area, 7, Kharkiv, Ukraine, 61050

Docent, Candidate of technical sciences

Department of Mathematics

Ольга Александровна Гончарова, Ukrainian State Academy of Railway Transport Feerbaha, 7, Kharkov, Ukraine, 61050

Senior lecturer, Candidate of physico-mathematical sciences

Department of Mathematics

Мурад Жораевич Овчиев, Ukrainian State Academy of Railway Transport Feerbaha, 7, Kharkov, Ukraine, 61050

Graduate student

Department Office of freight and commercial work

References

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Published

2014-06-20

How to Cite

Бронза, С. Д., Юрчак, Н. С., Гончарова, О. А., & Овчиев, М. Ж. (2014). Queuing time and utilization ratio in markov queuing systems. Eastern-European Journal of Enterprise Technologies, 3(4(69), 10–15. https://doi.org/10.15587/1729-4061.2014.24901

Issue

Vol. 3 No. 4(69) (2014): Mathematics and Cybernetics - applied aspects

Section

Mathematics and Cybernetics - applied aspects

License

Copyright (c) 2014 Семен Давыдович Бронза, Наталия Семеновна Юрчак, Ольга Александровна Гончарова, Мурад Жораевич Овчиев

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