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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.

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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In this paper we present a real-time analysis for complex distributed systems. The event stream model describes the occurrences of events within arbitrary time intervals. We propose a method to explore the modification of these occurrences as the events are processed within a complex task system. By observing the effects of several tasks competing for the same resource, additional insight can be won on the density of the events generated by the individual tasks.

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