Server state-dependent customer impatience in single-server Markovian Queues with multiple vacation

In this paper, a single-server Markovian queuing model under multiple-vacation policy is analyzed, with a focus on server state-dependent customer impatience manifested through balking and reneging.Observations indicate that customers arriving to find long queues or extended waiting times may exhibit impatience through balking or reneging during both vacation and busy periods of the server, respectively.Notably, customer impatience intensifies when the server is in vacation state.During this state, implementing specific retention mechanisms can effectively reduce customer reneging.This research derives closed-form expressions for traditional and newly designed performance measures.In addition, sensitivity analysis is conducted to examine the impact of the system parameters on different performance metrics.This investigation contributes to understanding the customer behavior in queuing systems with intermittently available services.