PADS: An approach to modeling resource demand and supply for the formal analysis of hierarchical scheduling

As real-time embedded systems become more complex, resource partitioning is increasingly used to guarantee real-time performance. Recently, several compositional frameworks of resource partitioning have been proposed using real-time scheduling theory with various notions of real-time tasks running under restricted resource supply environments. However, these real-time scheduling-based approaches are limited in their expressiveness in that, although capable of describing resource-demand tasks, they are unable to model resource supply. This paper describes a process algebraic framework PADS for reasoning about resource demand and resource supply inspired by the timed process algebra ACSR. In ACSR, real-time tasks are specified by enunciating their consumption needs for resources. To also accommodate resource-supply processes in PADS, given a resource cpu we write c̅p̅u ̅ to denote the availability of cpu for a requesting task process. Using PADS, we define a supply-demand relation where a pair (T , S) belongs to the relation if the demand process T can be scheduled under supply S. We develop a theory of compositional schedulability analysis as well as a technique for synthesizing an optimal supply process for a set of tasks. Furthermore, we define ordering relations between supplies which describe when a supply offers more resource capacity than another. With this notion it is possible to formally represent hierarchical scheduling approaches that assign more “generous” resource allocations to tasks in exchange for a simple representation. We illustrate our techniques via a number of examples. Comments Manuscript Number: TCS-D-10-00731R2 This journal article is available at ScholarlyCommons: http://repository.upenn.edu/cis_papers/486 PADS: An approach to modeling resource demand and supply for the formal analysis of hierarchical scheduling Anna Philippoua, Insup Leeb, Oleg Sokolskyb aDepartment of Computer Science, University of Cyprus, Nicosia, Cyprus bDepartment of Computer and Info. Science, University of Pennsylvania, Philadelphia, PA, U.S.A. Abstract As real-time embedded systems become more complex, resource partitioning is increasingly used to guarantee real-time performance. Recently, several compositional frameworks of resource partitioning have been proposed using real-time scheduling theory with various notions of real-time tasks running under restricted resource supply environments. However, these real-time scheduling-based approaches are limited in their expressiveness in that, although capable of describing resource-demand tasks, they are unable to model resource supply. This paper describes a process algebraic framework PADS for reasoning about resource demand and resource supply inspired by the timed process algebra ACSR. In ACSR, real-time tasks are specified by enunciating their consumption needs for resources. To also accommodate resource-supply processes in PADS, given a resource cpu, we write cpu to denote the availability of cpu for a requesting task process. Using PADS, we define a supply-demand relation where a pair (T, S) belongs to the relation if the demand process T can be scheduled under supply S. We develop a theory of compositional schedulability analysis as well as a technique for synthesizing an optimal supply process for a set of tasks. Furthermore, we define ordering relations between supplies which describe when a supply offers more resource capacity than another. With this notion it is possible to formally represent hierarchical scheduling approaches that assign more “generous” resource allocations to tasks in exchange for a simple representation. We illustrate our techniques via a number of examples.As real-time embedded systems become more complex, resource partitioning is increasingly used to guarantee real-time performance. Recently, several compositional frameworks of resource partitioning have been proposed using real-time scheduling theory with various notions of real-time tasks running under restricted resource supply environments. However, these real-time scheduling-based approaches are limited in their expressiveness in that, although capable of describing resource-demand tasks, they are unable to model resource supply. This paper describes a process algebraic framework PADS for reasoning about resource demand and resource supply inspired by the timed process algebra ACSR. In ACSR, real-time tasks are specified by enunciating their consumption needs for resources. To also accommodate resource-supply processes in PADS, given a resource cpu, we write cpu to denote the availability of cpu for a requesting task process. Using PADS, we define a supply-demand relation where a pair (T, S) belongs to the relation if the demand process T can be scheduled under supply S. We develop a theory of compositional schedulability analysis as well as a technique for synthesizing an optimal supply process for a set of tasks. Furthermore, we define ordering relations between supplies which describe when a supply offers more resource capacity than another. With this notion it is possible to formally represent hierarchical scheduling approaches that assign more “generous” resource allocations to tasks in exchange for a simple representation. We illustrate our techniques via a number of examples.