Feasibility Tests for Recurrent Real-Time Tasks in the Sporadic DAG Model

A model has been proposed in [Baruah et al., in Proceedings of the IEEE Real-Time Systems Symposium 2012] for representing recurrent precedence-constrained tasks to be executed on multiprocessor platforms, where each recurrent task is modeled by a directed acyclic graph (DAG), a period, and a relative deadline. Each vertex of the DAG represents a sequential job, while the edges of the DAG represent precedence constraints between these jobs. All the jobs of the DAG are released simultaneously and have to be completed within some specified relative deadline. The task may release jobs in this manner an unbounded number of times, with successive releases occurring at least the specified period apart. The feasibility problem is to determine whether such a recurrent task can be scheduled to always meet all deadlines on a specified number of dedicated processors. The case of a single task has been considered in [Baruah et al., 2012]. The main contribution of this paper is to consider the case of multiple tasks. We show that EDF has a speedup bound of 2-1/m, where m is the number of processors. Moreover, we present polynomial and pseudopolynomial schedulability tests, of differing effectiveness, for determining whether a set of sporadic DAG tasks can be scheduled by EDF to meet all deadlines on a specified number of processors

Offline and online variants of the Traveling Salesman Problem

In this thesis, we study several well-motivated variants of the Traveling Salesman Problem (TSP). First, we consider makespan minimization for vehicle scheduling problems on trees with release and handling times. 2-approximation algorithms were known for several variants of the single vehicle problem on a path. A 3/2-approximation algorithm was known for the single vehicle problem on a path where there is a fixed starting point and the vehicle must return to the starting point upon completion. Karuno, Nagamochi and Ibaraki give a 2-approximation algorithm for the single vehicle problem on trees. We develop a Polynomial Time Approximation Scheme (PTAS) for the single vehicle scheduling problem on trees which have a constant number of leaves. This PTAS can be easily adapted to accommodate various starting/ending constraints. We then extended this to a PTAS for the multiple vehicle problem where vehicles operate in disjoint subtrees. We also present competitive online algorithms for some single vehicle scheduling problems. Secondly, we study a class of problems called the Online Packet TSP Class (OP-TSP-CLASS). It is based on the online TSP with a packet of requests known and available for scheduling at any given time. We provide a 5/3 lower bound on any online algorithm for problems in OP-TSP-CLASS. We extend this result to the related k-reordering problem for which a 3/2 lower bound was known. We develop a κ+1-competitive algorithm for problems in OP-TSP-CLASS, where a κ-approximation algorithm is known for the offline version of that problem. We use this result to develop an offline m(κ+1)-approximation algorithm for the Precedence-Constrained TSP (PCTSP) by segmenting the n requests into m packets. Its running time is mf(n/m) given a κ-approximation algorithm for the offline version whose running time is f(n)

Asymptotically Optimal Approximation Algorithms for Coflow Scheduling

Many modern datacenter applications involve large-scale computations composed of multiple data flows that need to be completed over a shared set of distributed resources. Such a computation completes when all of its flows complete. A useful abstraction for modeling such scenarios is a {\em coflow}, which is a collection of flows (e.g., tasks, packets, data transmissions) that all share the same performance goal. In this paper, we present the first approximation algorithms for scheduling coflows over general network topologies with the objective of minimizing total weighted completion time. We consider two different models for coflows based on the nature of individual flows: circuits, and packets. We design constant-factor polynomial-time approximation algorithms for scheduling packet-based coflows with or without given flow paths, and circuit-based coflows with given flow paths. Furthermore, we give an $O(\log n/\log \log n)$-approximation polynomial time algorithm for scheduling circuit-based coflows where flow paths are not given (here $n$ is the number of network edges). We obtain our results by developing a general framework for coflow schedules, based on interval-indexed linear programs, which may extend to other coflow models and objective functions and may also yield improved approximation bounds for specific network scenarios. We also present an experimental evaluation of our approach for circuit-based coflows that show a performance improvement of at least 22% on average over competing heuristics.Comment: Fixed minor typo

Semi-autonomous Intersection Collision Avoidance through Job-shop Scheduling

In this paper, we design a supervisor to prevent vehicle collisions at intersections. An intersection is modeled as an area containing multiple conflict points where vehicle paths cross in the future. At every time step, the supervisor determines whether there will be more than one vehicle in the vicinity of a conflict point at the same time. If there is, then an impending collision is detected, and the supervisor overrides the drivers to avoid collision. A major challenge in the design of a supervisor as opposed to an autonomous vehicle controller is to verify whether future collisions will occur based on the current drivers choices. This verification problem is particularly hard due to the large number of vehicles often involved in intersection collision, to the multitude of conflict points, and to the vehicles dynamics. In order to solve the verification problem, we translate the problem to a job-shop scheduling problem that yields equivalent answers. The job-shop scheduling problem can, in turn, be transformed into a mixed-integer linear program when the vehicle dynamics are first-order dynamics, and can thus be solved by using a commercial solver.Comment: Submitted to Hybrid Systems: Computation and Control (HSCC) 201

Capacity Planning and Leadtime management

In this paper we discuss a framework for capacity planning and lead time management in manufacturing companies, with an emphasis on the machine shop. First we show how queueing models can be used to find approximations of the mean and the variance of manufacturing shop lead times. These quantities often serve as a basis to set a fixed planned lead time in an MRP-controlled environment. A major drawback of a fixed planned lead time is the ignorance of the correlation between actual work loads and the lead times that can be realized under a limited capacity flexibility. To overcome this problem, we develop a method that determines the earliest possible completion time of any arriving job, without sacrificing the delivery performance of any other job in the shop. This earliest completion time is then taken to be the delivery date and thereby determines a workload-dependent planned lead time. We compare this capacity planning procedure with a fixed planned lead time approach (as in MRP), with a procedure in which lead times are estimated based on the amount of work in the shop, and with a workload-oriented release procedure. Numerical experiments so far show an excellent performance of the capacity planning procedure