On regenerative and ergodic properties of the k-server queue with non-stationary Poisson arrivals
- 1 June 1985
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 22 (04) , 893-902
- https://doi.org/10.1017/s0021900200108125
Abstract
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 Zt = (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 Zt 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.Keywords
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