Heavy traffic analysis for single-server SRPT and LRPT queues via EDF diffusion limits
研究了单服务器队列在最短剩余处理时间（SRPT）和最长剩余处理时间（LRPT）策略下的重流量极限定理，允许相关和重尾的到达与服务时间分布，为已有定理提供了简洁证明和新见解。
Abstract Extending the results of Kruk (Queueing theory and network applications. QTNA 2019. Lecture notes in computer science, vol 11688. Springer, Cham, pp 263–275, 2019), we derive heavy traffic limit theorems for a single server, single customer class queue in which the server uses the Shortest Remaining Processing Time (SRPT) policy from heavy traffic limits for the corresponding Earliest Deadline First queueing systems. Our analysis allows for correlated customer inter-arrival and service times and heavy-tailed inter-arrival and service time distributions, as long as the corresponding stochastic primitive processes converge weakly to continuous limits under heavy traffic scaling. Our approach yields simple, concise justifications and new insights for SRPT heavy traffic limit theorems of Gromoll et al. (Stoch Syst 1(1):1–16, 2011). Corresponding results for the longest remaining processing time policy are also provided.