Periodic Schedules for Bounded Timed Weighted Event Graphs

Abstract

Timed event graphs (TEGs) and timed weighted event graphs (TWEGs) which have multiple arc cardinalities, have been widely used for automated production systems such as robotized work cells or embedded systems. TWEGs are useful for modeling batch flows of entities such as batch arrivals or processing of jobs. Periodic schedules, that combine an explicit description of starting times and an easy implementation are particularly interesting, and have been proved to be optimal for ordinary timed event graphs (TEGs). In this paper, we present polynomial algorithms to check the existence of periodic schedules of bounded TWEGs and to compute their optimal throughput. These results can be considered as generalizations of those for ordinary timed event graphs. We then establish that periodic schedules are suboptimal for TWEGs and may not exist even for a live TWEG. The gap between optimal throughput and throughput of an optimal periodic schedule is experimentally investigated for a subclass of TWEGs, namely timed weighted circuits.

Relaxed subgraph execution model for the throughput evaluation of IBSDF graphs

“…A basic method to evaluate the IBSDF graph throughput is to compute the maximum throughput of its equivalent flat srSDF graph using ASAP schedule [8] and periodic schedule [9] based methods for SDF graphs.…”

“…There are many methods to compute the throughput of SDF graphs, which can be found in [6], [8], [9], [11], [12]. Most of these methods are based on two techniques: simulating a schedule, and analysing the graph structure.…”

“…Most of these methods are based on two techniques: simulating a schedule, and analysing the graph structure. In this paper we are interested in the two methods [8] and [9] based on the As Soon As Possible (ASAP) schedule and the Periodic schedule.…”

“…N b of graph iterations in one period T he duration of one period 2) Periodic Schedule [9]: It consists in defining a periodic execution for each actor. Hence, the starting time S σ a,t of all executions t of an actor a ∈ A are defined by the starting time of the first execution S σ a,0 and the execution period w σ a of a, such that:…”

“…A basic method to compute the throughput of an IBSDF graph is to transfomr it to a non hierarchical graph (flattening the hierarchy) and use [8] and [9] methods for SDF graphs. [10] shows that this transformation results in a exponential large graph for which basic methods fail to compute the throughput.…”