CONTINUITY OF A QUEUEING INTEGRAL REPRESENTATION IN THE M1 TOPOLOGY

• 成果类型: Article
• 署名作者: Pang, Guodong; Whitt, Ward
• 署名单位: Columbia University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/09-AAP611
• 发表日期: 2010
• 页码: 214-237
• 关键词: heavy-traffic limits; queues

摘要

We establish continuity of the integral representation y(t) = x(t) + integral(t)(0)h(y(s)) ds, t >= 0, mapping a function x into a function y when the underlying function space D is endowed with the Skorohod M-1 topology. We apply this integral representation with the continuous mapping theorem to establish heavy-traffic stochastic-process limits for many-server queueing models when the limit process has jumps unmatched in the converging processes as can occur with bursty arrival processes or service interruptions. The proof of M-1-continuity is based on a new characterization of the M-1 convergence, in which the time portions of the parametric representations are absolutely continuous with respect to Lebesgue measure, and the derivatives are uniformly bounded and converge in L-1.