Periodic scheduling of marked graphs using balanced binary words

This report presents an algorithm to statically schedule live and strongly connected Marked Graphs (MG). The proposed algorithm computes the best execution where the execution rate is maximal and place sizes are minimal. The proposed algorithm provides transition schedules represented as binary words. These words are chosen to be balanced. The contributions of this paper is the proposed algorithm itself along with the characterization of the best execution of any MG.Comment: No. RR-7891 (2012

Throughput and FIFO Sizing: an Application to Latency-Insensitive Design

RR-6919On-chip communications are a key concern for high end designs. Since latency issues cannot be avoided in deep-submicron technologies, design methodologies need to cope with it. In such a case, precise FIFO sizings are of high interest, to find the right trade-off in between area, power and throughput. This paper provides means to size optimally FIFOs while reaching maximum achievable throughput. We apply our algorithms to Latency-Insensitive Designs. Such algorithms can also be used to size FIFOs in other application fields, as for instance Networks-on-Chips. We also revisit the equalization process, which introduces as much latencies as possible in the system while preserving global system throughput. This algorithm point out where it is possible to introduce more stage of pipelines while ensuring the maximum throughput of the system. It allows for instance to postpone execution of IP(s) to limit dynamic power peak. We provide a modified algorithm that globally minimizes the number of such introduced latencies

Performance-preserving clustering of elastic controllers

Asynchronous and latency-insensitive circuits offer a similar form of elasticity that tolerates variations in the delays or the latencies of the computation and communication resources of a system. This flexibility comes at the expense of including a control layer that synchronizes the flow of information. This paper proposes a method for reducing the complexity of the control layer by clustering controllers with similar functionality. The approach reduces the control layer and the number of elastic buffers to a significantly smaller elastic skeleton that preserves the performance of the system. The method also takes into account layout information, thus avoiding optimizations that can be physically unfeasible. The experimental results indicate that drastic reductions in the complexity of the control can be obtained.Postprint (author's final draft

Statically scheduled Process Networks

Event/Marked Graphs (EG) form a strict subset of Petri Nets. They are fundamental models in Scheduling Theory, mostly because of their absence of alternative behaviors (or conflict-freeness). It was established in the past that, under broad structural conditions, behavior of Timed Event Graphs (TEG) becomes utterly regular (technically speaking: “ultimately k-periodic”). More recently it has been proposed to use this kind of regular schedulings as syntactic types for so-called N-synchronous processes. These types remained essentially user-provided. Elsewhere there have been proposals for adding control in a “light fashion” to TEGs, not as general Petri Nets, but with the addition of Merge/Select nodes switching the data flows. This was much in the spirit of Kahn process networks [8, 9]. But usually the streams of test values governing the switches are left unspecified, which may introduce phenomena of congestion or starvation in the system, as token flow preservation becomes an issue. In the present paper we suggest to restrict the Merge/Select condition streams to (binary) k-periodic patterns as well, and to study their relations with the schedules constructed as before for TEGs, but on the extended model. We call this model Kahn-extended Event Graphs (KEG). The main result is that flow preservation is now checkable (by abstraction into another model of Weighted Marked Graphs, called SDF in the literature). There are many potential applications of KEG models, as for instance in modern Systems-on-Chip (SoC) comprising on-Chip networks. Communication links can then be shared, and the model can represent the (regular) activity schedules of the computing as well as the communicating components, after a strict scheduling has been found. They can also be used as a support to help find the solution

Kahn-extended Event Graphs

Process Networks have long been used as formal Models of Computation in the design of dedicated hardware and software embedded systems and Systems-on-Chip. Choice-less models such as Marked/Event Graphs and their Synchronous Data Flow extensions have been considered to support periodic scheduling analysis. Those models do not hide dependency informations like regular sequential languages: they capture the communication topology through point-to-point channels. Those models are concurrent, formally defined, have a clear semantic but are limited due to static point-to-point channels. Then, further extensions such as Cyclo-Static Data Flow or Boolean-controlled Dataflow (BDF) graphs introduced routing switches, allowing internal choices while preserving conflict-freeness, in the tradition of Kahn Process Networks. We introduce a new model, which we term Kahn-extended Event Graphs (KEG). It can be seen as a specialization of both Cyclo-Static and BDF processes. It consists merely in the addition of Merge/Select routing nodes to former Marked/Event Graphs; but, most importantly, these new nodes are governed by explicit (ultimately periodic) binary-word switching patterns for routing directions. We introduce identities on Merge/Select expressions, and show how they build a full axiomatization for the flow-equivalence between the computation nodes. The transformations carry a strong intuitive meaning, as they correspond to sharing/unsharing the interconnect links. Such interconnect defines each time a precise Network-on-Chip topology, and the switching patterns drive the traffic. One can also compute the buffering space actually required at the various fifo locations. The example of a Sobel edge filter is discussed to illustrate the importance of this model

Latency-insensitive design and central repetitive scheduling

The theory of latency-insensitive design (LID) was recently invented to cope with the time closure problem in otherwise synchronous circuits and programs. The idea is to allow the inception of arbitrarily fixed (integer) latencies for data/signals traveling along wires or communication media. Then mechanisms such as shell wrappers and relaystations are introduced to “implement ” the necessary backpressure congestion control, so that data with shorter travel duration can safely await others with which they are to be consumed simultaneously by the same computing element. These mechanisms can themselves be efficiently represented as synchronous components in this global, asynchronouslyspirited environment. Despite their efficient form, relay-stations and backpressure mechanisms add complexity to a system whose behaviour is ultimately very repetitive. Indeed, the ”slowest” data loops regulate the traffic and organize the traffic to their pace. This specific repetitive scheduling has been extensively studied in the past under the name of “Central Repetitive Problem”, and results were established proving that so-called k-periodic optimal solutions could be achieved. But the “implementation ” using typical synchronous circuit elements in the LID context was never worked out. We deal with these issues here, using explicit representation of schedules as periodic words on {0, 1} ⋆ borrowed from the recently theory of N-synchronous systems.

Latency-insensitive design and central repetitive scheduling

The theory of latency-insensitive design (LID) was recently invented to cope with the time closure problem in otherwise synchronous circuits and programs. The idea is to allow the inception of arbitrarily fixed (integer) latencies for data/signals traveling along wires or communication media. Then mechanisms such as shell wrappers and relaystations are introduced to “implement ” the necessary backpressure congestion control, so that data with shorter travel duration can safely await others with which they are to be consumed simultaneously by the same computing element. These mechanisms can themselves be efficiently represented as synchronous components in this global, asynchronouslyspirited environment. Despite their efficient form, relay-stations and backpressure mechanisms add complexity to a system whose behaviour is ultimately very repetitive. Indeed, the ”slowest” data loops regulate the traffic and organize the traffic to their pace. This specific repetitive scheduling has been extensively studied in the past under the name of “Central Repetitive Problem”, and results were established proving that so-called k-periodic optimal solutions could be achieved. But the “implementation ” using typical synchronous circuit elements in the LID context was never worked out. We deal with these issues here, using explicit representation of schedules as periodic words on {0, 1} ⋆ borrowed from the recently theory of N-synchronous systems.