SMT-based Task- and Network-level Static Schedule Generation for Time-Triggered Networked Systems

Abstract

In Ethernet-based time-triggered networks, like TTEthernet, a global communication scheme, for which the schedule synthesis is known to be an NP-complete problem, establishes contention-free windows for the exchange of messages with guaranteed low latency and minimal jitter. However, in order to achieve end-to-end determinism at the application level, software tasks running on the end-system nodes need to obey a similar execution scheme with tight dependencies towards the network domain. In this paper we address the simultaneous co-synthesis of network as well as application schedules for preemptive time-triggered tasks communicating in a switched multi-speed time-triggered network. We use Satisfiability Modulo Theories (SMT) to formulate the scheduling constraints and solve the resulting problem using a state-of-the-art SMT solver. Furthermore, we introduce a novel incremental scheduling approach, based on the demand bound test for asynchronous constrained-deadline periodic tasks, which significantly improves scalability for the average case without sacrificing schedulability. We demonstrate the performance of our approach using synthetic network topologies and system configurations. * The research leading to these results has received funding from the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement n o 610640 (DREAMS).

On the Scalability of Constraint Solving for Static/Off-Line Real-Time Scheduling

“…Our paper also develops over previous work on applying exact solving techniques (ILP/SMT/CP, more classical branch-and-cut, model checking) to off-line real-time scheduling problems [12,6,8]. These previous results all focus on either the (improved) modeling of a given scheduling problem or on the improvement of the solver algorithm.…”

“…As a baseline, we employ for all problems classical encodings, similar to the one of [6]. In the case of parallelized code running on homogenous architectures, this encoding is enriched with state-of-the-art symmetry-breaking constraints [13] that largely reduce solving time.…”

“…Constraints are generated from tasks graphs in a systematic way [6]. Tasks graphs are usually displaying some amount of parametric symmetry which allows us to produce even more constraints [13] (see Section 4.2).…”

“…We do not consider in this category the many other papers which discard exact solving techniques based on theoretical considerations, rather than experimental ones, because the issue is indeed to consider the potential gap between the two. -A few recent papers reporting the successful application of modern constraint solving tools to realistic real-time scheduling and compilation problems [12,6], due to increase in solver efficiency.…”

Synthesizing time-triggered schedules for switched networks with faulty links

“…Different techniques have been adopted for synthesis of time-triggered schedules for medium size systems, such as constraint programming (CP) solvers [25], integer linear programming (ILP) solvers [14], and satisfiability modulo theory (SMT) solvers [18]. For systems or larger size, SMT solvers have been combined with iterative/segmentation techniques yielding good results [11,4,26,23,12], even if compared to ILP.…”