A Dynamic Boundary Guarding Problem with Translating Targets

We introduce a problem in which a service vehicle seeks to guard a deadline (boundary) from dynamically arriving mobile targets. The environment is a rectangle and the deadline is one of its edges. Targets arrive continuously over time on the edge opposite the deadline, and move towards the deadline at a fixed speed. The goal for the vehicle is to maximize the fraction of targets that are captured before reaching the deadline. We consider two cases; when the service vehicle is faster than the targets, and; when the service vehicle is slower than the targets. In the first case we develop a novel vehicle policy based on computing longest paths in a directed acyclic graph. We give a lower bound on the capture fraction of the policy and show that the policy is optimal when the distance between the target arrival edge and deadline becomes very large. We present numerical results which suggest near optimal performance away from this limiting regime. In the second case, when the targets are slower than the vehicle, we propose a policy based on servicing fractions of the translational minimum Hamiltonian path. In the limit of low target speed and high arrival rate, the capture fraction of this policy is within a small constant factor of the optimal.Comment: Extended version of paper for the joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conferenc

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

This paper presents a heavy traffic analysis of the behavior of multi-class acyclic queueing networks in which the customers have deadlines. We assume the queueing system consists of J stations, and there are K different customer classes. Customers from each class arrive to the network according to independent renewal processes. The customers from each class are assigned a random deadline drawn from a deadline distribution associated with that class and they move from station to station according to a fixed acyclic route. The customers at a given node are processed according to the earliest-deadline-first (EDF) queue discipline. At any time, the customers of each type at each node have a lead time, the time until their deadline lapses. We model these lead times as a random counting measure on the real line. Under heavy traffic conditions and suitable scaling, it is proved that the measure-valued lead-time process converges to a deterministic function of the workload process

Truthful Online Scheduling with Commitments

We study online mechanisms for preemptive scheduling with deadlines, with the goal of maximizing the total value of completed jobs. This problem is fundamental to deadline-aware cloud scheduling, but there are strong lower bounds even for the algorithmic problem without incentive constraints. However, these lower bounds can be circumvented under the natural assumption of deadline slackness, i.e., that there is a guaranteed lower bound $s > 1$ on the ratio between a job's size and the time window in which it can be executed. In this paper, we construct a truthful scheduling mechanism with a constant competitive ratio, given slackness $s > 1$. Furthermore, we show that if $s$ is large enough then we can construct a mechanism that also satisfies a commitment property: it can be determined whether or not a job will finish, and the requisite payment if so, well in advance of each job's deadline. This is notable because, in practice, users with strict deadlines may find it unacceptable to discover only very close to their deadline that their job has been rejected

Comparison of Flow Scheduling Policies for Mix of Regular and Deadline Traffic in Datacenter Environments

Datacenters are the main infrastructure on top of which cloud computing services are offered. Such infrastructure may be shared by a large number of tenants and applications generating a spectrum of datacenter traffic. Delay sensitive applications and applications with specific Service Level Agreements (SLAs), generate deadline constrained flows, while other applications initiate flows that are desired to be delivered as early as possible. As a result, datacenter traffic is a mix of two types of flows: deadline and regular. There are several scheduling policies for either traffic type with focus on minimizing completion times or deadline miss rate. In this report, we apply several scheduling policies to mix traffic scenario while varying the ratio of regular to deadline traffic. We consider FCFS (First Come First Serve), SRPT (Shortest Remaining Processing Time) and Fair Sharing as deadline agnostic approaches and a combination of Earliest Deadline First (EDF) with either FCFS or SRPT as deadline-aware schemes. In addition, for the latter, we consider both cases of prioritizing deadline traffic (Deadline First) and prioritizing regular traffic (Deadline Last). We study both light-tailed and heavy-tailed flow size distributions and measure mean, median and tail flow completion times (FCT) for regular flows along with Deadline Miss Rate (DMR) and average lateness for deadline flows. We also consider two operation regimes of lightly-loaded (low utilization) and heavily-loaded (high utilization). We find that performance of deadline-aware schemes is highly dependent on fraction of deadline traffic. With light-tailed flow sizes, we find that FCFS performs better in terms of tail times and average lateness while SRPT performs better in average times and deadline miss rate. For heavy-tailed flow sizes, except for tail times, SRPT performs better in all other metrics.Comment: Technical Repor

Mayle v. Felix

Following his murder conviction, Felix filed a pro se habeas petition alleging Sixth Amendment violations at trial The petition was filed within the one-year Antiterrorism and Effective Death Penalty Act deadline. He was later appointed counsel, who filed an amended petition alleging Fifth Amendment violations; but that petition was filed five months after the AEDPA deadline had passed. The Court held that the amended petition was not saved by the Relation Back doctrine because it did not share with the earlier claims a common core of operative facts

Mayle v. Felix

Following his murder conviction, Felix filed a pro se habeas petition alleging Sixth Amendment violations at trial The petition was filed within the one-year Antiterrorism and Effective Death Penalty Act deadline. He was later appointed counsel, who filed an amended petition alleging Fifth Amendment violations; but that petition was filed five months after the AEDPA deadline had passed. The Court held that the amended petition was not saved by the Relation Back doctrine because it did not share with the earlier claims a common core of operative facts