Schedulability tests for tasks with Variable Rate-dependent Behaviour under fixed priority scheduling

Automotive embedded real-time systems such as Engine Management utilise cyclic tasks that are activated periodically based on angular rotation rather than time. As well as having variable inter-arrival times, these tasks also have deadlines and worst-case execution times that are dependent on angular velocity i.e. engine speed or rpm. Such tasks exhibit Variable Rate-dependent Behaviour (VRB). In this paper, we introduce response time analysis for systems comprising VRB and sporadic tasks under fixed priority scheduling. Sufficient schedulability tests are introduced; from simple linear upper bounds on interference, to a more complex analysis using information about the physical limitations of the system to provide constraints for an ILP formulation of the problem.