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Abstract-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.

Controller Area Network (CAN) • Section 4.6 has been added, providing formal proofs that the schedulability tests given in Sections 4.1, 4.2 and 4.3 are sufficient (Theorems 2 and 3) and selfsustainable (Theorems 4 and 5). This section also shows how more precise analysis can be achieved when the priorities of messages in a FIFO queue span those of messages in a priority queue or another FIFO queue, which is often the case in practice. Extended version• In Section 5.2, we have added a formal proof that transmission deadline monotonic priority ordering is optimal when all messages have the same maximum transmission time (Theorem 7).• In Section 7, we have extended the experimental evaluation to show how the performance degradation due to FIFO queues depends on the number of messages in each queue.• Sections 6.1 and 7.1 have been added, exploring the effects of implementing one or more FIFO queues in gateway nodes that are responsible for transferring messages from one network to another.

Controller Area Network (CAN) is widely used in automotive applications. With CAN, the network utilisation that may be obtained while ensuring that all messages meet their deadlines is strongly dependent on the policy used for priority (message identifier) assignment. This paper addresses the problem of priority assignment when some message identifiers are fixed. There are two variants of this problem: P1 where the gaps between fixed identifiers are large enough to accommodate the freely assignable messages and P2 when the gaps are too small. For problem P1, we provide algorithms that give optimal and robust priority orderings based on an adaptation of existing techniques. Problem P2 is more difficult to solve. We show via a counter example that the algorithms derived for P1 and others recently published can fail to find a schedulable priority ordering when the gaps are small, even though one exists. We derive an optimal and robust solution to this problem with respect to a simple form of schedulability analysis which assumes the same upper bound on the length of all messages.

Abstract-Engine control units in the automotive industry are particular challenging real-time systems regarding their real-time analysis. Some of the tasks of such an engine control unit are triggered by the engine, i.e. the faster the angular velocity of the engine, the more frequent the tasks are executed. Furthermore, the execution time of a task may vary with the angular velocity of the engine. As a result the worst case does not necessarily occur when all tasks are activated simultaneously. Hence this behavior cannot be addressed appropriately with the currently available real-time analysis methods. In this paper we make a first step towards a real-time analysis for an engine control unit. We present a sufficient real-time analysis assuming that the angular velocity of the engine is arbitrary but fixed.

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In real-time theory, basically two approaches for the computation of response-times exist. One of them is the busy window method, the other is the real-time calculus, an extension of the network calculus. While both can be used to compute the bounds of response-times, they have different properties that make them suitable for different system architectures. The busy window approach on the one hand is able to obtain tight bounds for scheduling policies like round-robin. It is also capable of considering offsets, therefore delivering better results in the relevant cases. Hierarchical scheduling on the other hand can be better accounted for by the real-time calculus, where this is an inherent feature of the underlying concept. The approach we present in this paper takes the theory of hierarchy from the realtime calculus and uses it to generalize the response-time analysis. This is implemented as an extension of the busy window method, which enables it to analyze scheduling hierarchies of an arbitrary depth.

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