Performance analysis of retrial queue with server subject to two types of breakdowns and repairs

• Published in: Operational research Vol. 18; no. 2; pp. 521 - 559
• Main Authors: Krishna Kumar, B., Rukmani, R., Thanikachalam, A., Kanakasabapathi, V.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2018; Springer Nature B.V
• Subjects: Asymptotic properties; Breakdown; Breakdowns; Business and Management; Computational Intelligence; First principles; Maintenance; Management Science; Markov analysis; Markov processes; Operations Research; Operations Research/Decision Theory; Original Paper; Queues; Queuing theory; Laplace–Stieltjes transform; Orbit characteristics; Limiting behaviour; Steady-state condition; Retrial queue; First-step analysis; Random breakdowns; Generating functions; Stochastic decomposition; Repair time
• ISSN: 1109-2858; 1866-1505
• DOI: 10.1007/s12351-016-0275-4

This paper analyses a Markovian retrial queue where the server is subject to breakdowns and repairs. It is assumed that the breakdowns/repairs behaviour when the server is idle is different from the one when it is busy. Under the steady-state condition, explicit expressions for the partial probability generating functions of the server status and the number of customers in the orbit are obtained along with some key performance measures of the system. In addition, we study two new orbit characteristics, namely, the orbit idle period and the orbit busy period by using the first principle arguments. An approximate method of analysis for the system with losses is also suggested. The stochastic decomposition property is shown to hold good for the underlying retrial queueing system. Besides, we study the asymptotic behaviour of the system size under extreme conditions. Finally, some numerical results are illustrated.