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

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

2012-01-02

arxiv.org/abs/1201.0532v1

Mathematics

Probability

14 pages

Scientific paper

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 the 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.

Affiliated with

Also associated with

No associations

Rating

The rate of convergence to stationarity for M/G/1 models with admission controls via coupling does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The rate of convergence to stationarity for M/G/1 models with admission controls via coupling, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The rate of convergence to stationarity for M/G/1 models with admission controls via coupling will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-183217