EDGE SCHEDULING in Visual Studio .NET

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73 EDGE SCHEDULING This section analyzes the theoretical background of the fundamental technique to achieve contention awareness in scheduling: edge scheduling (Sinnen and Sousa [172, 179]) The utilization of edge scheduling in contention aware heuristics and the interaction with task scheduling are treated in the next section Edge scheduling is the adoption of the task scheduling principle in the communication domain In contrast to the classic model of the target system (De nition 43), communication resources are treated like processors, in the sense that only one communication can be active on each resource at a time Thus, edges are scheduled onto the communication links for the time they occupy them To schedule an edge on a link, a start time and a nish time are assigned to the edge The corresponding notations from node scheduling (Section 41) are adopted De nition 76 (Edge Start, Communication and Finish Time on Link) Let G = (V, E, w, c) be a task graph and TG = (N, P, D, H, b) a communication network according to De nition 75 The start time ts (e, L) of an edge e E on a link L L (L = D H) is the function ts : E L Q+ 0 The communication time of e on L is (e, L) = c(e) b(L)
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(71)
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The nish time of e on L is tf (e, L) = ts (e, L) + (e, L) (72)
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So the time during which link L is occupied with the transfer of the data associated with the edge e is denoted by the communication time (e, L) As links might have heterogeneous data rates (De nition 73), the communication time is a function of the edge e and the link L This also brings a change to the interpretation of the edge cost c(e) (De nition 44) De nition 77 (Communication Cost Network Model) Let G = (V, E, w, c) be a task graph and TG = (N, P, D, H, b) a communication network The communication cost c(e) of edge e is the average time the communication represented by e occupies a link of L for its transfer Like a processor, a link is exclusively occupied by one edge Condition 71 (Link Constraint) Let G = (V, E, w, c) be a task graph and TG = (N, P, D, H, b) a communication network For any two edges e, f E scheduled
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on link L L: ts (e, L) tf (e, L) ts ( f , L) tf ( f , L) or ts ( f , L) tf ( f , L) ts (e, L) tf (e, L) (73)
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Despite its similarity with task scheduling, edge scheduling differs in one important aspect In general, a communication route between two processors consists of more than one link An edge is scheduled on each link of the route, while a node is only scheduled on one processor (with the exception of node duplication, Section 62) The scheduling of an edge along the links of the route is signi cantly determined by the routing in the network 731 Scheduling Edge on Route In Section 72 the network model of the target system was carefully developed in a way that encapsulates and hides all the details about the network topology from edge scheduling For any communication between two distinct processors, edge scheduling only sees the communication route in the form of an ordered list of involved links This list is provided by the routing algorithm of the network model, when it is given the two communicating processors De nition 78 (Route) Let TG = (N, P, D, H, b) be a communication network For any two distinct processors Psrc and Pdst , Psrc , Pdst P, the routing algorithm of TG returns a route R TG from Psrc to Pdst in the form of an ordered list of links R = L1 , L2 , , Ll , Li L for i = 1, , l In De nition 78 the route depends only on the source and the destination processor of a communication and not on the traf c state of the network This conforms to the network model s property of static routing (De nition 75) Since the network model also supposes circuit switching, the entire communication is transmitted on the returned route Hence, the edge e of the communication is scheduled on each link of the route The type of link (eg, half or full duplex) is irrelevant to edge scheduling Data traverses the links in the order of the route, which must be considered in the scheduling of the edges Condition 72 (Causality) Let G = (V, E, w, c) be a task graph and TG = (N, P, D, H, b) a communication network For the start and nish times of edge e E on the links of the route R = L1 , L2 , , Ll , R TG, tf (e, Lk 1 ) tf (e, Lk ), ts (e, L1 ) ts (e, Lk ), for 1 < k l (74) (75)
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