NOVEL HEAVY-TRAFFIC REGIMES FOR LARGE-SCALE SERVICE SYSTEMS

作者：Janssen A J E M^*; Van Leeuwaarden J S H; Mathijsen B W J

来源：SIAM Journal on Applied Mathematics, 2015, 75(2): 787-812.

DOI：10.1137/140960815

• heavy-traffic approximation
• heavy-traffic regimes
• large service systems
• queueing theory
• asymptotic analysis
• saddle point method
• Riemann zeta function

We introduce a family of heavy-traffic regimes for large-scale service systems, presenting a range of scalings that include both moderate and extreme heavy traffic, as compared to classical heavy traffic. The heavy-traffic regimes can be translated into capacity sizing rules that lead to economies-of-scales, so that the system utilization approaches 100% while congestion remains limited. We obtain heavy-traffic approximations for stationary performance measures in terms of asymptotic expansions, using a nonstandard saddle point method, tailored to the specific form of integral expressions for the performance measures, in combination with the heavy-traffic regimes.

• 出版日期2015