Modeling of Concurrent Task Execution in a Distributed System for Real-Time Control
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Task-execution times are one of the most important parameters in scheduling tasks. Most scheduling algorithms are based on the assumption that either worst-case task-execution times are known to the scheduler or no information on execution times is available at all. While scheduling tasks based on worst-case execution times can guarantee to meet their timing requirements, it may lead to severe under-utilization of CPUs because worst-case execution times could be one or two orders of magnitude larger than the corresponding actual values. Scheduling tasks based on the execution time distribution (instead of worst-case execution times) is known to improve system utilization significantly.In this paper, we propose a model to predict task execution times in a distributed system. The model considers several factors which affect the execution time of each task. These factors are classified into two groups: intrinsic and extrinsic. The intrinsic factors control the flow within a task, while the extrinsic factors include communication and synchronization delays between tasks. By simplifying the extrinsic factors, we represent a distributed system with a simple queuing model. The proposed queuing model consists of two stations: one for computation and the other for communication and synchronization. Information on system utilization can be obtained by converting this queuing model to a Markov chain. The execution time of a task is then derived from the information on system utilization in the form of average and distribution. The model is extended to describe the effects of multiple tasks assigned to a single processing node. The utility of the model is demonstrated with an example.