FORMACIÓN Y EMPLEO

3.2 Contention-aware mapping . . . . 31

3.2.1 Task mapping . . . 32 3.2.2 Application mapping . . . 34

3.3 WCTT and mapping baseline references . . . . 37

Chapter 2 has shown different NoCs architectures that provide different classes of QoS. Re- gardless of the NoC architecture, in distributed hard real-time systems, the WCTT of all the packets generated by a flow must be lower than a predetermined deadline. Such real-time packet schedulability analysis have been done for various types of networks by taking into account the type of contentions that can occur between flows. The challenge lies in the abil- ity to define analysis techniques that have a limited complexity, in order to give results in a

reasonable amount of time, and at the same time compute WCTT values that are not too pes- simistic. The complexity of the analysis depends on the NoC concepts implemented. Virtual circuit switching relying on a TDMA leads to WCTT that can be easily computed. In fact, no contention can therefore occur. However, in wormhole networks, the analysis of the system behavior becomes more complex due to different types of interferences. Thus, in this chapter, we focus on approaches used to compute the WCTT over wormhole networks. Even we have assumed a BE NoC architecture in the remainder of the work, we focus in this chapter not only on BE wormhole networks but also on priority-based wormhole networks. Actually, we are in- terested to present how the existing approaches model the behavior of the wormhole switching. Besides, we show how they consider the different types of interferences in the computation of the WCTT. On the other hand, the WCTT depends on the mapping of the application. Thus, another challenge lies in the ability to reduce the congestion incurred by the flows, whether be- longing to the same application or not. At the end of the chapter, we present a state-of-the-art on the mapping strategies used to reduce the contentions between flows and thus their WCTT.

3.1

WCTT over wormhole networks

In this section, we present a state-of-the art on the approaches used to analyze the WCTT on priority-based wormhole networks and BE wormhole networks.

3.1.1

Priority-based wormhole networks

Real-time communication over wormhole networks were studied before NoCs were introduced. The most important mechanism in a wormhole real-time network is the use of virtual chan- nels. Moreover, coupled with a mechanism for preemptive priorities, it allows a message to temporarily stop the transmission of another lower priority message.

The first approaches to upper-bound the latency of transmitted packets over a priority-based wormhole switching with virtual channels were proposed in [Mut94, HO97]. Using these ap-

3.1. WCTT over wormhole networks 27

proaches, the priority of flows is mapped over the priority bits of VCs. At each router, links are assigned to VCs of the highest priority that have a flit ready to be transmitted. [HO97] presents a feasibility test that determines whether a set of messages can be transmitted in a given network respecting the deadlines of all messages. Each message is periodic and has a different priority level. Each physical link includes a virtual channel for each message that uses it. The principle to compute the worst-case delay of a message mi is to compute the delays of

transmission of the messages mj having higher priorities than mi and sharing at least one link

with mi. Moreover, as the messages are periodic, multiple instances of the same message can

block mi. The authors propose to consider the entire path of a given message as a single shared

resource, i.e. as one link which is must be free of any message of highest priority than mi.

Kim et al. [KKHL98] noticed that neither of those approaches consider the impact of indirect interference. An indirect interference happens when a message shares at least one link with mj

but does not share any link with mi, and thus could have an impact on the latency bounds of mi.

[KKHL98] proposes an algorithm to compute WCTT of flows over priority-based wormhole networks. Compared to [Mut94, HO97], the authors use a dependency graph between flows to identify both the direct and indirect contentions a flow may suffer. When an indirect flow is identified, the accuracy of WCTT values is improved, as the blocking effect of indirect flows can thus be modeled to occur only when other (periodic) blocking flows are released simultaneously. Otherwise, this indirect message can not interfere and its impact is not counted in the computation of the upper bound. However, [Shi09] shows that this method still introduces excessive interference to the studied flow. Actually, they show on an example that possible parallel communication will take place on disjoint links which reduces the possible interference from higher priority flows.

[LJS05] proposed another improved algorithm. The defect in the approaches in [Mut94, HO97] is that they aggregate all the links used by the studied flow and the flows that interfere with it in a single resource. This resource must be fully reserved for the studied flow in order to be transmitted. Thus, if two flows in conflict with the studied flow do not intersect, they can be transferred simultaneously. Therefore, the authors in [LJS05] distinguish direct from

indirect contentions but by utilizing a contention tree. This tree is further used to identify when parallel transmissions of flows on disjoint concurrent paths can occur, reducing the contention interferences.

Priority-based wormhole was also applied in the context of NoC. [SB08] is based on previous works and provides another method for verifying the schedulability of a set of messages. It presents a method for computing the WCTT of flows which integrates both direct and indirect interferences of higher-priority flows. The computation proposed by [SB08] is based on the assumption that a message is undergoing its worst-case delay if it is transmitted at the same time with all higher priority messages. The authors then provide an iterative method and separately compute the delays due to direct and indirect interference. Indirect interferences are treated as additional release jitter on flows that directly interfere with the analyzed flow. They also show that their method provides tighter bounds than [HO97], but it is not optimal when simultaneous interference exists. Besides, they show that values obtained in [LJS05] can be optimistic, as the worst case scenario do not occur when flows are released simultaneously. However, the authors imply that it is not possible to obtain an exact bound in this case. Both algorithms proposed in [SB08] and [LJS05] assume that all flows that are in indirect contentions have an impact.

[Shi09] is an evolution of [SB08] in the aim to reduce the number of priority levels necessary to the proper functioning of this type of network. Indeed, the virtual channels are expensive in terms of memory and power consumption. So the authors propose to share a given priority level between several messages. They also provide a method to compute the transmission delay of a flow in this model. The principle of the computation is as follows: at each priority level, they treat all flows having this level as a single message that must reserve all links used by the messages of the same level in order to be transmitted. The WCTT for this "aggregate message" is then calculated according to the method presented in [SB08]. The delay for a message is given by the sum of the delay for the "aggregate message" and the delay for the message from the source node.

3.1. WCTT over wormhole networks 29

tioning approach but where runtime migrations are decided by the applications themselves. As paths of flows cannot be known at design time, the size of the search space of the worst-case scenario is higher. Compared to [SB08], a lower complexity but more pessimistic method is thus used.