Transient and steady-state analysis of hybrid arrivals of single and batch customers queueing systems with switch-off period

Abstract

In this paper, we analyze the transient behavior of a novel single server queueing system with hybrid arrivals of single and state-dependent batch of customers. Whenever the system becomes empty the server undergoes the switch-off state for random duration of time. Explicit expressions for transient probabilities of the status of the server and system size are obtained. In addition, the first-passage-time probability density function is determined along with its first two moments. We have also derived analytical results for time-dependent performance measures of the system. Further, under stability condition, the corresponding steady-state probabilities and key performance measures of the system are also discussed. Finally, we have provided extensive numerical illustrations to visualize the behaviors of system performance measures graphically by varying the values of system parameters.