International Journal of Statistics and Applied Mathematics
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International Journal of Statistics and Applied Mathematics

2020, Vol. 5, Issue 2, Part A

Markovian analysis of a birth-death process


Author(s): Hudson Nyang’wara Ongiri

Abstract: Markovian models basically refers to models which, largely, relies on the present state to predict the future. A birth process refers to the arrival of a customer to a system and a death process explains the departure of a customer from a system. This study modelled queues at the revenue collection points using the Markovian birth-death analytical models. The traffic intensity and waiting times were estimated from the secondary data collected from the revenue collection point. The focus was on Markovian queuing systems with infinite capacity that is M/M/m models, where m≥1. The queuing model employed at Bus Park Revenue collection point was identified to be M/M/2. The traffic intensity of the service station was estimated and it was discovered that the Birth rate > death rate, that is ρ2 =1.029412, indicating that the system was unstable. This indicated that the queue could grow indefinitely. As a result it was difficult to obtain other performance parameters. As a remedy, this study resorted to addition of a server with same rate of service, 70 customers/hr, to the system. This study assumed that the service distribution was the same for all the servers. On addition of a server the estimated number of customers in the system reduced significantly. After conducting queue analysis, this study concluded that the system at Bus Park Revenue collection point was not stable. This study recommended the addition of a server to the revenue collection point. Additionally, future researchers should conduct a non Markovian analysis of a birth-death process to determine if the same results could be realized.

Pages: 22-25 | Views: 541 | Downloads: 31

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How to cite this article:
Hudson Nyang’wara Ongiri. Markovian analysis of a birth-death process. Int J Stat Appl Math 2020;5(2):22-25.
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