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PERFORMANCE EVALUATION OF QUEUING SYSTEMS WITH BALKING, RENEGING, FEEDBACK, IMPATIENT CUSTOMERS AND DOWNED SERVERS
Keywords:
model $M/M/2/N$, balking, reneging, feedback.DOI:
https://doi.org/10.17654/0972086324011Abstract
The objective of this work is to evaluate the performance of $M/M/2/N$ (finite $N$) Markovian queuing systems with balking, reneging, feedback, impatient customers and downed servers in order to be able to measure and appreciate the quality of service offered to customers. Firstly we used the Chapman-Kolmogorov equation to obtain the system of equilibrium equations called balance system of equations, secondly, we used the recursive method to obtain the probabilities of the state of the system which we consider as probabilistic performance measures of the system, thirdly, we used system state probabilities to show that the number of customers in the system has a limit and that this limit is 2 when the rate of distribution of server repair times increases, fourthly, we used the method of the generating functions of the probabilities to obtain the average performance measures of the system and finally, we showed by a numerical illustration, the influence of the parameters of the failures on the probabilities of the state of the system and on the measures of average performance of the system.
Received: September 11, 2023
Accepted: November 10, 2023
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