Heavy-traffic limits for the G/H2*/n/m queue

• 成果类型: Article
• 署名作者: Whitt, W
• 署名单位: Columbia University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.1040.0119
• 发表日期: 2005
• 页码: 1-27
• 关键词: diffusion-approximation

摘要

We establish heavy-traffic stochastic-process limits for queue-length, waiting-time and overflow stochastic processes in a class of G/GI/n/m queueing models with n servers and m extra waiting spaces. We let the arrival process be general, only requiring that it satisfy a functional central limit theorem. To capture the impact of the service-time distribution beyond its mean within a Markovian framework, we consider a special class of service-time distributions, denoted by H-2(*), which are mixtures of an exponential distribution with probability p and a unit point mass at 0 with probability 1 - p. These service-time distributions exhibit relatively high variability, having squared coefficients of variation greater than or equal to one. As in Halfin and Whitt (1981, Heavy-traffic limits for queues with many exponential servers, Oper Res. 29 567-588), Puhalskii and Reiman (2000, The multiclass GI/PH/N queue in the Halfin-Whitt regime. Adv. Appl. Probab. 32 564-595), and Garnett, Mandelbaum, and Reiman (2002. Designing a call center with impatient customers. Manufacturing Service Oper Management, 4 208-227), we consider a sequence of queueing models indexed by the number of servers, n, and let n tend to infinity along with the traffic intensities p(n) so that root n-(1 - p(n)) -> beta for - infinity < beta < infinity. To treat finite waiting rooms, we let m(n) / root n -> kappa for 0 < kappa <= infinity. With the special H-2(*) service-time distribution, the limit processes are one-dimensional Markov processes, behaving like diffusion processes with different drift and diffusion functions in two different regions, above and below zero. We also establish a limit for the G/M/n/m + M model, having exponential customer abandonments.