IEEE 802.1Qbv Gate Control List Synthesis Using Array Theory Encoding

Time Sensitive Networks (TSN) emerge as the set of sub-standards incorporating real-time support as an extension of standard Ethernet. In particular, IEEE 802.1Qbv defines a time-triggered communication paradigm with the addition of a time-aware shaper governing the selection of frames at the egress queues according to a predefined schedule, encoded in so-called Gate Control Lists (GCL). Nonetheless, the design of compositional systems with real-time demands requires a proper configuration of these mechanisms to truly achieve the temporal isolation of communication streams with end-to-end timeliness guarantees. In this paper we address how the synthesis of communication schedules for GCLs defined in IEEE 802.1Qbv can be formalized as a system of constraints expressed via first-order theory of arrays (T_A). We formulate the necessary constraints showing the suitability of the theory of arrays and discuss optimization opportunities arising from the underlying scheduling problem. Our evaluation using general-purpose SMT/OMT solvers proves the validity of the approach, scaling well for small-to medium-networks, and exposing trade-offs for the time needed to synthesize a schedule. Furthermore, we conduct a comparison against previous work and conclude the appropriateness of the method as the basis for future TSN scheduling tools.