John P. Lehoczky

Priority inheritance protocols: an approach to real-time synchronization

An investigation is conducted of two protocols belonging to the priority inheritance protocols class; the two are called the basic priority inheritance protocol and the priority ceiling protocol. Both protocols solve the uncontrolled priority inversion problem. The priority ceiling protocol solves this uncontrolled priority inversion problem particularly well; it reduces the worst-case task-blocking time to at most the duration of execution of a single critical section of a lower-priority task. This protocol also prevents the formation of deadlocks. Sufficient conditions under which a set of periodic tasks using this protocol may be scheduled is derived. >

The rate monotonic scheduling algorithm: exact characterization and average case behavior

An exact characterization of the ability of the rate monotonic scheduling algorithm to meet the deadlines of a periodic task set is represented. In addition, a stochastic analysis which gives the probability distribution of the breakdown utilization of randomly generated task sets is presented. It is shown that as the task set size increases, the task computation times become of little importance, and the breakdown utilization converges to a constant determined by the task periods. For uniformly distributed tasks, a breakdown utilization of 88% is a reasonable characterization. A case is shown in which the average-case breakdown utilization reaches the worst-case lower bound of C.L. Liu and J.W. Layland (1973).<<ETX>>

Optimal portfolio and consumption decisions for a “small investor” on a finite horizon

A general consumption/investment problem is considered for an agent whose actions cannot affect the market prices, and who strives to maximize total expected discounted utility of both consumption ...

Fixed priority scheduling of periodic task sets with arbitrary deadlines

Consideration is given to the problem of fixed priority scheduling of period tasks with arbitrary deadlines. A general criterion for the schedulability of such a task set is given. Worst case bounds are given which generalize the C.L. Liu and J.W. Layland (1973) bound. The results are shown to provide a basis for developing predictable distributed real-time systems.<<ETX>>

Martingale and duality methods for utility maximization in a incomplete market

The problem of maximizing the expected utility from terminal wealth is well understood in the context of a complete financial market. This paper studies the same problem in an incomplete market containing a bond and a finite number of stocks whose prices are driven by a multidimensional Brownian motion process W. The coefficients of the bond and stock processes are adapted to the filtration (history) of W, and incompleteness arises when the number of stocks is strictly smaller than the dimension of W. It is shown that there is a way to complete the market by introducing additional “fictitious” stocks so that the optimal portfolio for the thus completed market coincides with the optimal portfolio for the original incomplete market. The notion of a “least favorable” completion is introduced and is shown to be closely related to the existence question for an optimal portfolio in the incomplete market. This notion is expounded upon using martingale techniques; several equivalent characterizations are provided...

Real Time Scheduling Theory: A Historical Perspective

In this 25th year anniversary paper for the IEEE Real Time Systems Symposium, we review the key results in real-time scheduling theory and the historical events that led to the establishment of the current real-time computing infrastructure. We conclude this paper by looking at the challenges ahead of us.

A resource allocation model for QoS management

Quality of service (QoS) has been receiving wide attention in many research communities including networking, multimedia systems, real-time systems and distributed systems. In large distributed systems such as those used in defense systems, on-demand service and inter-networked systems, applications contending for system resources must satisfy timing, reliability and security constraints as well as application-specific quality requirements. Allocating sufficient resources to different applications in order to satisfy various requirements is a fundamental problem in these situations. A basic yet flexible model for performance-driven resource allocations can therefore be useful in making appropriate tradeoffs. We present an analytical model for QoS management in systems which must satisfy application needs along multiple dimensions such as timeliness, reliable delivery schemes, cryptographic security and data quality. We refer to this model as Q-RAM (QoS-based Resource Allocation Model). The model assumes a system with multiple concurrent applications, each of which can operate at different levels of quality based on the system resources available to it. The goal of the model is to be able to allocate resources to the various applications such that the overall system utility is maximized under the constraint that each application can meet its minimum needs. We identify resource profiles of applications which allow such decisions to be made efficiently and in real-time. We also identify application utility functions along different dimensions which are composable to form unique application requirement profiles. We use a video-conferencing system to illustrate the model.

On task schedulability in real-time control systems

Most real-time computer-controlled systems are built in two separate steps, each in isolation: controller design and its digital implementation. Computational tasks that realize the control algorithms are usually scheduled by treating their execution times and periods as unchangeable parameters. Task scheduling therefore depends only on the limited computing resources available. On the other hand, controller design is primarily based on the continuous-time dynamics of the physical system being controlled. The set of tasks resulting from this controller design may not be schedulable with the limited computing resources available. Even if the given set of tasks is schedulable, the overall control performance may not be optimal in the sense that they do not make a full use of the computing resource. We propose an integrated approach to controller design and task scheduling. Specifically, task frequencies (or periods) are allowed to vary within a certain range as long as such a change does not affect critical control functions such as maintenance of system stability. We present an algorithm that optimizes task frequencies and then schedules the resulting tasks with the limited computing resources available. The proposed approach is also applicable to failure recovery and reconfiguration in real-time control systems.

The deferrable server algorithm for enhanced aperiodic responsiveness in hard real-time environments

Most existing scheduling algorithms for hard real-time systems apply either to periodic tasks or aperiodic tasks but not to both. In practice, real-time systems require an integrated, consistent approach to scheduling that is able to simultaneously meet the timing requirements of hard deadline periodic tasks, hard deadline aperiodic (alert-class) tasks, and soft deadline aperiodic tasks. This paper introduces the Deferrable Server (DS) algorithm which will be shown to provide improved aperiodic response time performance over traditional background and polling approaches. Taking advantage of the fact that, typically, there is no benefit in early completion of the periodic tasks, the Deferrable Server (DS) algorithm assigns higher priority to the aperiodic tasks up until the point where the periodic tasks would start to miss their deadlines. Guaranteed alert-class aperiodic service and greatly reduced response times for soft deadline aperiodic tasks are important features of the DS algorithm, and both are obtained with the hard deadlines of the periodic tasks still being guaranteed. The results of a simulation study performed to evaluate the response time performance of the new algorithm against traditional background and polling approaches are presented. In all cases, the response times of aperiodic tasks are significantly reduced (often by an order of magnitude) while still maintaining guaranteed periodic task deadlines. >

Real-time synchronization protocols for multiprocessors

The authors investigate the synchronization problem in the context of priority-driven preemptive scheduling on shared-memory multiprocessors. Unfortunately, a direct application of synchronization mechanisms such as the Ada rendezvous, semaphores, or monitors can lead to uncontrolled priority inversion: a high job being blocked by a lower priority job for an indefinite period of time. A task allocation scheme based on the generalized protocol is outlined.<<ETX>>