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

Abstract

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 steadystate 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.

Work Interruption: The Moderate Effect of Workload and Queue Length in the Manufacturing Industry

“…Distracted attention, difficult work transition (Altmann & Trafton, 2007) Depressed mood (Cai, Gong, Lu, & Zhong, 2018;Ockenfels, Sliwka, & Werner, 2015) Reduced proficiency or forgetfulness (Froehle & White, 2014;Teyarachakul, Chand, & Ward, 2011) Time pressure (Leroy & Glomb, 2018) H1(-) In a production line, queue length faced by employees may affect their operation behaviors. Many research models based on queue theory and interruption theory have explored the impact of interruptions on the queue system (Krishnamoorthy, Pramod, & Chakravarthy, 2014;Kumar, Rukmani, Thanikachalam, & Kanakasabapathi, 2018). However, there are no studies that have explored how interruptions influence worker performance under different queue lengths.…”

On a retrial queue with negative customers, passive breakdown, and delayed repairs

“…Since then, the retrial queues with breakdowns and repairs have been studied extensively from stability and reliability perspectives. Krishna et al [10] introduced a Markovian retrial queue with two types of breakdowns in which the server breaks down at different Poisson rates during an idle or busy period. They derived some performance measures and analyzed the orbit characteristics.…”