How multiserver queues scale with growing congestion-dependent demand
成果类型：
Article
署名作者：
Whitt, W
署名单位：
Columbia University
刊物名称：
OPERATIONS RESEARCH
ISSN/ISSBN：
0030-364X
DOI：
10.1287/opre.51.4.531.16093
发表日期：
2003
页码：
531-542
关键词：
摘要：
We investigate how performance scales in the standard M/M/n queue in the presence of growing congestion-dependent customer demand. We scale the queue by letting the potential (congestion-free) arrival rate be proportional to the number of servers, n, and letting n increase. We let the actual arrival rate with n servers be of the form lambda(n) = f(xi(n))n, where f is a strictly-decreasing continuous function and xi(n) is a steady-state congestion measure. We consider several alternative congestion measures, such as the mean waiting time and the probability of delay. We show, under minor regularity conditions, that for each n there is a unique equilibrium pair (lambda(n)*, xi(n)*) such that xi(n)* is the steady-state congestion associated with arrival rate lambda(n)* and lambda(n)* = f(xi(n)*)n. Moreover, we show that, as n increases, the queue with the equilibrium arrival rate lambda(n)* is brought into heavy traffic, but the three different heavy-traffic regimes for multiserver queues identified by Halfin and Whitt (1981) each can arise depending on the congestion measure used. In considerable generality, there is asymptotic service efficiency: the server utilization approaches one as n increases. Under the assumption of growing congestion-dependent demand, the service efficiency can be achieved even if there is significant uncertainty about the potential demand, because the actual arrival rate adjusts to the congestion.