期刊
ANNALS OF APPLIED PROBABILITY
卷 23, 期 4, 页码 1291-1317出版社
INST MATHEMATICAL STATISTICS
DOI: 10.1214/12-AAP870
关键词
Stability; common quadratic Lyapunov function; Lyapunov function; piecewise OU process; multi-server queues; customer abandonment; Halfin-Whitt regime; phase-type distribution
资金
- NSF [EEC-0926308]
- Oberwolfach Leibniz fellowship
We study the positive recurrence of piecewise Ornstein-Uhlenbeck (OU) diffusion processes, which arise from many-server queueing systems with phase-type service requirements. These diffusion processes exhibit different behavior in two regions of the state space, corresponding to overload (service demand exceeds capacity) and underload (service capacity exceeds demand). The two regimes cause standard techniques for proving positive recurrence to fail. Using and extending the framework of common quadratic Lyapunov functions from the theory of control, we construct Lyapunov functions for the diffusion approximations corresponding to systems with and without abandonment. With these Lyapunov functions, we prove that piecewise OU processes have a unique stationary distribution.
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