On regenerative and ergodic properties of the k-server queue with non-stationary Poisson arrivals

We consider the stable k- server queue with non-stationary Poisson arrivals and i.i.d. service times and show that the non-time-homogeneous Markov process Z t = (the queue length and residual service times at time t ) can be subordinated to a stable time-homogeneous regenerative process. As an application we show that if the system starts from given conditions at time s then the distribution of Z t stabilizes (but depends on t ) as s tends backwards to –∞. Also moment and stochastic domination results are established for the delay and recurrence times of the regenerative process leading to results on uniform rates of convergence.