Asymptotic Behavior of the Time-Dependent Solution of the M/G/1 Queueing Model with Second Optional Service

By studying the spectral properties of the underlying operator corresponding to the M / G / 1 queueing model with second optional service, we obtain that the time-dependent solution of the model strongly converges to its steady-state solution. We also show that the time-dependent queueing size at the departure point converges to the corresponding steady-state queueing size at the departure point.