A Single-Server Queue with Vacations and Non-Gated Time-Limited Service

We analyze an M/G/1 queue with server vacations and non-gated time-limited service. This work is complementary to our previous work [6] where the same model but with gated time-limited service is studied. As in that paper, we first derive a functional equation which characterizes the system behavior, then solve the equation by a numerical technique that approximates the unknown function by a weighted sum of Laguerre functions with unknown coefficients. The functional equation is transformed into a set of linear equations from which the coefficients can be computed. By the work-decomposition and PASTA properties, the average customer waiting time can be readily obtained. Numerical examples are included to demonstrate the validity of the technique.