Sanjoy K. Baruah

Proportionate progress: A notion of fairness in resource allocation

Given a set ofn tasks andm resources, where each taskx has a rational weightx.w=x.e/x.p,0<x.w<1, aperiodic schedule is one that allocates a resource to a taskx for exactlyx.e time units in each interval [x.p·k, x.p·(k+1)) for allk∈N. We define a notion of proportionate progress, called P-fairness, and use it to design an efficient algorithm which solves the periodic scheduling problem.

Preemptively scheduling hard-real-time sporadic tasks on one processor

Consideration is given to the preemptive scheduling of hard-real-time sporadic task systems on one processor. The authors first give necessary and sufficient conditions for a sporadic task system to be feasible (i.e., schedulable). The conditions cannot, in general, be tested efficiently (unless P=NP). They do, however, lead to a feasibility test that runs in efficient pseudo-polynomial time for a very large percentage of sporadic task systems.<<ETX>>

Algorithms and complexity concerning the preemptive scheduling of periodic, real-time tasks on one processor

We investigate the preemptive scheduling of periodic, real-time task systems on one processor. First, we show that when all parameters to the system are integers, we may assume without loss of generality that all preemptions occur at integer time values. We then assume, for the remainder of the paper, that all parameters are indeed integers. We then give, as our main lemma, both necessary and sufficient conditions for a task system to be feasible on one processor. Although these conditions cannot, in general, be tested efficiently (unless P=NP), they do allow us to give efficient algorithms for deciding feasibility on one processor for certain types of periodic task systems. For example, we give a pseudo-polynomial-time algorithm for synchronous systems whose densities are bounded by a fixed constant less than 1. This algorithm represents an exponential improvement over the previous best algorithm. We also give a polynomial-time algorithm for systems having a fixed number of distinct types of tasks. Furthermore, we are able to use our main lemma to show that the feasibility problem for task systems on one processor is co-NP-complete in the strong sence. In order to show this last result, we first show the Simultaneous Congruences Problem to be NP-complete in the strong sense. Both of these last two results answer questions that have been open for ten years. We conclude by showing that for incomplete task systems, that is, task systems in which the start times are not specified, the feasibility problem is ∑2p-complete.

A proportional share resource allocation algorithm for real-time, time-shared systems

We propose and analyze a proportional share resource allocation algorithm for realizing real-time performance in time-shared operating systems. Processes are assigned a weight which determines a share (percentage) of the resource they are to receive. The resource is then allocated in discrete-sized time quanta in such a manner that each process makes progress at a precise, uniform rate. Proportional share allocation algorithms are of interest because: they provide a natural means of seamlessly integrating real and non-real-time processing; they are easy to implement; they provide a simple and effective means of precisely controlling the real-time performance of a process; and they provide a natural means of policing so that processes that use more of a resource than they request have no ill-effect on well-behaved processes. We analyze our algorithm in the context of an idealized system in which a resource is assumed to be granted in arbitrarily small intervals of time and show that our algorithm guarantees that the difference between the service time that a process should receive and the service time it actually receives is optimally bounded by the size of a time quantum. In addition, the algorithm provides support for dynamic operations, such as processes joining or leaving the competition, and for both fractional and non-uniform time quanta. As a proof of concept we have implemented a prototype of a CPU scheduler under FreeBSD. The experimental results shows that our implementation performs within the theoretical bounds and hence supports real-time execution in a general purpose operating system.

Static-priority scheduling on multiprocessors

The preemptive scheduling of systems of periodic tasks on a platform comprised of several identical processors is considered. A scheduling algorithm is proposed for static-priority scheduling of such systems; this algorithm is a simple extension of the uniprocessor rate-monotonic scheduling algorithm. It is proven that this algorithm successfully schedules any periodic task system with a worst-case utilization no more than a third the capacity of the multiprocessor platform. It is also shown that no static-priority multiprocessor scheduling algorithm (partitioned or global) can guarantee schedulability for a periodic task set with a utilization higher than one half the capacity of the multiprocessor platform.

Priority-driven scheduling of periodic task systems on multiprocessors

The scheduling of systems of periodic tasks upon multiprocessor platforms is considered. Utilization-based conditions are derived for determining whether a periodic task system meets all deadlines when scheduled using the earliest deadline first scheduling algorithm (EDF) upon a given multiprocessor platform. A new priority-driven algorithm is proposed for scheduling periodic task systems upon multiprocessor platforms: this algorithm is shown to successfully schedule some task systems for which EDF may fail to meet all deadlines.

Proportionate progress: a notion of fairness in resource allocation

Given a set ofn tasks andm resources, where each taskx has a rational weightx.w=x.e/x.p,0<x.w<1, aperiodic schedule is one that allocates a resource to a taskx for exactlyx.e time units in each interval [x.p·k, x.p·(k+1)) for allk∈N. We define a notion of proportionate progress, called P-fairness, and use it to design an efficient algorithm which solves the periodic scheduling problem.

Generalized Multiframe Tasks

A new model for sporadic task systems is introduced. This model— the generalized multiframe task model—further generalizes both the conventional sporadic-tasks model, and the more recent multiframe model of Mok and Chen. A framework for determining feasibility for a wide variety of task systems is established; this framework is applied to this task model to obtain a feasibility-testing algorithm that runs in time pseudo-polynomial in the size of the input for all systems of such tasks whose densities are bounded by a constant less than one.

Response-Time Analysis for Mixed Criticality Systems

Many safety-critical embedded systems are subject to certification requirements. However, only a subset of the functionality of the system may be safety-critical and hence subject to certification, the rest of the functionality is non safety-critical and does not need to be certified, or is certified to a lower level. The resulting mixed criticality system offers challenges both for static schedulability analysis and run-time monitoring. This paper considers a novel implementation scheme for fixed priority uniprocessor scheduling of mixed criticality systems. The scheme requires that jobs have their execution times monitored (as is usually the case in high integrity systems). An optimal priority assignment scheme is derived and sufficient response-time analysis is provided. The new scheme formally dominates those previously published. Evaluations illustrate the benefits of the scheme.

Dynamic- and Static-priority Scheduling of Recurring Real-time Tasks

The recurring real-time task model for hard-real-time task is studied from a feasibility-analysis perspective. This model generalizes earlier models such as the sporadic task model and the generalized multiframe task model. Algorithms are presented for the static-priority and dynamic-priority feasibility-analysis of systems of independent recurring real-time tasks in a preemptive uniprocessor environment.