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.

扩展Kruk的结果（队列理论和网络应用.QTNA 2019.计算机科学讲座笔记，第11688卷.Springer，Cham，第263-275页，2019年），我们得出了单个服务器，单个客户类别的繁忙流量限制定理服务器使用从最繁忙的流量限制开始的最短剩余处理时间（SRPT）策略的队列，用于相应的最早截止时间优先队列系统。我们的分析允许相关的客户到达时间和服务时间以及重尾到达时间和服务时间分布，只要相应的随机原始过程在繁重的流量扩展下弱收敛到连续的极限即可。对于Grompll等人的SRPT大流量限制定理，我们的方法得出了简单明了的论据和新见解。（Stoch Syst 1（1）：1-16，2011）。