Abstract
To develop future cyber-physical systems, like networks of autonomous vehicles, the modeling and simulation of huge networks of collaborating systems acting together on large-scale topologies is required. Probabilistic Timed Graph Transformation Systems (PTGTSs) have been introduced as a means of modeling a high-level view of these systems of systems. In our previous work, we proposed a simulation scheme based on local search incremental graph matching that can handle large-scale real-world topologies. However, the prohibitive complexity of the graph matching problem underlying the simulation of any GTS variant makes this setup potentially problematic.
In this paper, we present an improved simulation algorithm and identify restrictions that hold for PTGTS high-level models of cyber-physical systems and real-world topologies, for which we can establish favorable worst-case complexity bounds. We show that the worst-case amortized complexity per simulation step is only logarithmic in the number of active collaborating systems (like vehicles) and constant concerning the size of the topology. The theoretical results are confirmed by experiments.
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Notes
- 1.
Note that the additional restrictions in the following definition, compared to [13], do not restrict the expressiveness of PTGTSs as (a) lower bounds for invariants can be replaced by additional conditions with clock constraints for all PTGT rules and (b) higher priority PTGT rules with constraints for the clocks can be emulated by additional pre-conditions for all lower-priority PTGT rules.
- 2.
The experiments were run on a server with 256Â GB RAM and two Intel Xeon E5-2643 CPUs (4 cores/3.4Â GHz). Our single-threaded implementation runs using Java 1.8.
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Zöllner, C., Barkowsky, M., Maximova, M., Giese, H. (2021). On the Complexity of Simulating Probabilistic Timed Graph Transformation Systems. In: Gadducci, F., Kehrer, T. (eds) Graph Transformation. ICGT 2021. Lecture Notes in Computer Science(), vol 12741. Springer, Cham. https://doi.org/10.1007/978-3-030-78946-6_14
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