We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Large-time asymptotics for the G/ M/ s+ GI many-server fluid queue with abandonment.
- Authors
Liu, Yunan; Whitt, Ward
- Abstract
We previously introduced and analyzed the G/ M/ s+ GI many-server fluid queue with time-varying parameters, intended as an approximation for the corresponding stochastic queueing model when there are many servers and the system experiences periods of overload. In this paper, we establish an asymptotic loss of memory (ALOM) property for that fluid model, i.e., we show that there is asymptotic independence from the initial conditions as time t evolves, under regularity conditions. We show that the difference in the performance functions dissipates over time exponentially fast, again under the regularity conditions. We apply ALOM to show that the stationary G/ M/ s+ GI fluid queue converges to steady state and the periodic G/ M/ s+ GI fluid queue converges to a periodic steady state as time evolves, for all finite initial conditions.
- Subjects
QUEUING theory; ASYMPTOTIC theory of system theory; FLUID models in geophysics; STOCHASTIC analysis; ERGODIC theory
- Publication
Queueing Systems, 2011, Vol 67, Issue 2, p145
- ISSN
0257-0130
- Publication type
Article
- DOI
10.1007/s11134-010-9208-8