The rate of convergence to stationarity for M/G/1 models with admission controls via coupling
Autor(en): | Kolb, Martin Stadje, Wolfgang Wuebker, Achim |
Stichwörter: | Admission control; coupling; M/G/1; MARKOV-PROCESSES; Mathematics; QUEUE; rate of convergence; spectral gap; stationary; Statistics & Probability; STRONG ERGODICITY; TIME; uniform geometric ergodicity; workload process | Erscheinungsdatum: | 2016 | Herausgeber: | TAYLOR & FRANCIS INC | Journal: | STOCHASTIC MODELS | Volumen: | 32 | Ausgabe: | 1 | Startseite: | 121 | Seitenende: | 135 | Zusammenfassung: | 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. |
ISSN: | 15326349 | DOI: | 10.1080/15326349.2015.1090322 |
Show full item record