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

M. Kolb, W. Stadje, A. Wübker, Stochastic Models 32 (2015) 121–135.

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Journal Article | Published | English
Author
Kolb, MartinLibreCat; Stadje, Wolfgang; Wübker, Achim
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Abstract
We study the workload processes of two M/G/1 queueing systems with restricted capacity: 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. For Model 2 geometric ergodicity follows from the finiteness of the moment-generating function of the service time distribution. We derive bounds for the convergence rates in special cases. The proofs use the coupling method.
Publishing Year
Journal Title
Stochastic Models
Volume
32
Issue
1
Page
121-135
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Kolb M, Stadje W, Wübker A. The rate of convergence to stationarity for M/G/1 models with admission controls via coupling. Stochastic Models. 2015;32(1):121-135. doi:http://dx.doi.org/10.1080/15326349.2015.1090322
Kolb, M., Stadje, W., & Wübker, A. (2015). The rate of convergence to stationarity for M/G/1 models with admission controls via coupling. Stochastic Models, 32(1), 121–135. http://dx.doi.org/10.1080/15326349.2015.1090322
@article{Kolb_Stadje_Wübker_2015, title={The rate of convergence to stationarity for M/G/1 models with admission controls via coupling}, volume={32}, DOI={http://dx.doi.org/10.1080/15326349.2015.1090322}, number={1}, journal={Stochastic Models}, publisher={INFORMS}, author={Kolb, Martin and Stadje, Wolfgang and Wübker, Achim}, year={2015}, pages={121–135} }
Kolb, Martin, Wolfgang Stadje, and Achim Wübker. “The Rate of Convergence to Stationarity for M/G/1 Models with Admission Controls via Coupling.” Stochastic Models 32, no. 1 (2015): 121–35. http://dx.doi.org/10.1080/15326349.2015.1090322.
M. Kolb, W. Stadje, and A. Wübker, “The rate of convergence to stationarity for M/G/1 models with admission controls via coupling,” Stochastic Models, vol. 32, no. 1, pp. 121–135, 2015, doi: http://dx.doi.org/10.1080/15326349.2015.1090322.
Kolb, Martin, et al. “The Rate of Convergence to Stationarity for M/G/1 Models with Admission Controls via Coupling.” Stochastic Models, vol. 32, no. 1, INFORMS, 2015, pp. 121–35, doi:http://dx.doi.org/10.1080/15326349.2015.1090322.

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