Earliest-deadline-first service in heavy-traffic acyclic networks

Law of large numbers for the many-server earliest-deadline-first queue

A many-server queue operating under the earliest deadline first discipline, where the distributions of service time and deadline are generic, is studied at the law of large numbers scale. Fluid model equations, formulated in terms of the many-server transport equation and the recently introduced measure-valued Skorohod map, are proposed as a means of characterizing the limit. The main results are the uniqueness of solutions to these equations, and the law of large numbers scale convergence to the solutions.

Fluid limits for earliest-deadline-first networks

This paper analyzes fluid scale asymptotics of two models of generalized Jackson networks employing the earliest deadline first (EDF) policy. One applies the 'soft' EDF policy, where deadlines are used to determine priority but jobs do not renege, and the other implements 'hard' EDF, where jobs renege when deadlines expire, and deadlines are postponed with each migration to a new station. The arrival rates, deadline distribution and service capacity are allowed to fluctuate over time at the fluid scale. Earlier work on EDF network fluid limits, used as a tool to obtain stability of these netwo…

Fluid limits of G/G/1+G queues under the non-preemptive earliest-deadline-first discipline

A single-server queuing model is considered with customers that have deadlines. If a customer's deadline elapses before service is offered, the customer abandons the system (customers do not abandon while being served). When the server becomes available, it offers service to the customer having earliest deadline among those that are in the queue. We obtain a fluid limit of the queue length and abandonment processes and for the occupation measure of deadlines, in the form of measure-valued processes. We characterize the limit by means of a Skorohod problem in a time-varying domain, which has an…

Accuracy of state space collapse for earliest-deadline-first Queues

This paper presents a second-order heavy traffic analysis of a single server queue that processes customers having deadlines using the earliest-deadline-first scheduling policy. For such systems, referred to as real-time queueing systems, performance is measured by the fraction of customers who meet their deadline, rather than more traditional performance measures, such as customer delay, queue length or server utilization. To model such systems, one must keep track of customer lead times (the time remaining until a customer deadline elapses) or equivalent information. This paper reviews the e…

使用实时排队模型面向器官短缺弹性分配政策的肝移植研究

Toward organ shortage resilient allocation policies using real-time queueing models for liver transplantation

本文提出用实时排队模型优化肝移植器官分配，通过模拟虚构寿命的最早模拟截止时间优先（ESDF）策略，在器官短缺加剧时维持了不同适应症间的公平性，优于法国现行评分政策。

Heavy traffic analysis for EDF queues with reneging

This paper presents a heavy-traffic analysis of the behavior of a single-server queue under an Earliest-Deadline-First (EDF) scheduling policy in which customers have deadlines and are served only until their deadlines elapse. The performance of the system is measured by the fraction of reneged work (the residual work lost due to elapsed deadlines) which is shown to be minimized by the EDF policy. The evolution of the lead time distribution of customers in queue is described by a measure-valued process. The heavy traffic limit of this (properly scaled) process is shown to be a deterministic fu…