A Geometric Approach to Scheduling of Concurrent Real-time Processes Sharing Resources

Abstract

With the decreasing cost of embedded systems, product designers now ask for more functionalities from them. Parallel programming is a way to handle their complexity, and embedded platforms can support such programming, such as in C or Java. When more than one thread is being used in a program, the threads are running concurrently and are known as concurrent processes. Concurrent programs can allow more effective use of a computer's resources but require greater effort on the part of the developer to design them. On the other hand, a key feature of embedded systems is that they interact with a physical environment in real time. Indeed, parallel programming in a real-time context is rather new. Simple extensions of existing analysis tools for sequential processes are not sufficient: parallelism with threads involves purely parallel-specific phenomena, like deadlocks. In this chapter we examine the behavior of a class of concurrent processes sharing resources, from the point of view of the worst-case response time (WCRT). To address this complex issue, we introduce a model, called timed PV diagram, and exploit its geometric nature in order to deal with the state explosion problem arising in the analysis of concurrent processes. This idea is inspired by the results in the analysis of concurrent programs using PV diagrams, a model introduced by Dijkstra [9]. It has been used, since the beginning of the 90's, for the analysis of concurrent programs [13,11] (see [15] for a good survey). We focus on a particular problem: finding a schedule which is safe (that is, without deadlocks) and short. To this end, one needs to resolve the conflicts between two or more processes that happen when their simultaneous demand for the same resource exceeds the serving capacity of that resource. The motivations of this scheduling problem are: • The process under study might be part of a global system (for example, the body of an infinite loop in a program) and subject to a deadline. If no precise timing analysis result is available, one often estimates the WCRT by sequentializing all the processes and taking the sum of the WCRTs of each process considered individually. This measure can easily be greater than the deadline, while the real WCRT is probably much smaller. We are thus interested in providing a better estimation of the real WCRT. In addition, from the schedule, the designer can gain a lot of insight about other properties, e.g. the frequency and duration of waits. O pe n A cc es s D at ab as e w w w .ite ch on lin e. co m