Open AccessM/M/1 Queueing Model with Working Vacation and Two Type of Server Breakdown
Author(s) -
Praveen Agrawal,
Anamika Jain,
Madhu Jain
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1849/1/012021
Subject(s) - computer science , queueing system , queueing theory , queue , exponential distribution , geometric distribution , rendering (computer graphics) , real time computing , duration (music) , markovian arrival process , service (business) , state (computer science) , computer network , probability distribution , mathematics , statistics , algorithm , artificial intelligence , physics , economy , economics , acoustics
In this paper the steady state probability distribution of the number of customers in single server Markovian queue is obtained by using matrix geometric approach with working vacation where server may breakdown in working vacation state as well as in busy state. The arrival of the customer is depends upon the server’s state and arrival follows FCFS discipline. The server is made available for rendering alternate service to customers. The inter-arrival time of the customers, service time, vacation duration, and lifetime and repair time of the server follows an exponential distribution. Numerical illustrations are made to examine the validity of analytical results. Sensitivity analysis is also made of in order to discover the outcome of various parameters on the system performance physical appearance.