The rate of convergence to stationarity for M/G/1 models with admission controls via coupling [article]

Martin Kolb, Wolfgang Stadje, Achim Wübker
2012 arXiv   pre-print
We study the workload processes of two restricted M/G/1 queueing systems: in Model 1 any service requirement that would exceed a certain capacity threshold is truncated; in Model 2 new arrivals do not enter the system if they have to wait more than a fixed threshold time in line. For Model 1 we obtain several results concerning the rate of convergence to equilibrium. In particular we derive uniform bounds for geometric ergodicity with respect to certain subclasses. However, we prove that for
more » ... class of all Model 1 workload processes there is no uniform bound. For Model 2 we prove that geometric ergodicity follows from the finiteness of the moment-generating function of the service time distribution and derive bounds for the convergence rates in special cases. The proofs use the coupling method.
arXiv:1201.0532v1 fatcat:yjj5poi2cvbs5llfxzfqh7ekna