Energy latency tradeoffs for medium access and sleep scheduling in wireless sensor networks.  Page 85 
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As seen from the above discussion, the endtoend delay for flow m depends on both the path and the slot assignment. Active Flows Communication: For a sensor network application, at any specific time, not all nodes have sampling data to report to the base station: there are only a limited number of active flows in the network. Here, it would be of interest to minimize the average delay of the active flows in the network, which is defined as follows: Definition 5: Average Delay (Davg P,f ): For a given graph G = (V,E), number of slots k, a slot assignment function f and paths P for M flows, the average delay is defined as P m2M d(Pm), where d(Pm)) is the delay along the path Pm under the given slot assignment function f. In active flows communication, our design goal is the following: Definition 6: Minimum Latency joint Scheduling and Routing (MLSR) Given a graph G = (V,E), the number of slots k and M flows, find a path Pm for each flow, and an slot assignment function f that minimizes the average delay (Davg f ) i.e. f = arg min P0,f 0 {Davg P0,f 0} (5.3) Figure 5.2 shows an example of separate routing and scheduling solution. When there is a new flow request, the routing algorithm will find a route first, then on the given route, if a schedule is achievable, the following data forwarding will use the route and scheduling to forward data report. If the scheduling process fails, then the routing algorithm is asked to find a new route. Figure 5.3 shows an example of scheduling and routing for two active flows. In figure 5.3(a), first there is only one active flow. If we run a shortest hop routing algorithm, it will find the path of A ! B ! C ! D ! E ! Z. A schedule can be assigned on the nodes on the path. The delay is 8. If using the link delay as the weight of the link, however, shortest path routing algorithm now select A ! B ! C ! H ! I ! J ! Z which has a latency of only 6. Now assume there is another flow request from node F to node Z. Suppose the flow want to use route F ! G ! I ! J ! Z. However at link (i, j), there is no slot that both i and j are free, so the flow is forced to choose route F ! G ! K ! L ! M ! N ! Z which has a delay of 8. So the total delay for the two active flows is 14 in figure 5.3(b). However, as shown in figure 5.3(c), if source A use route A ! B ! C ! D ! E ! Z and source F use route F ! G ! I ! J ! Z. A schedule can be achieved with total delay of only 12. This example shows that latency reduction by joint scheduling and routing. Intuitively, in MLSR, the objective is to color a graph with the given K colors such that the desired global objective (minimizing the delay diameter in the former and the average delay diameter in the 72
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Title  Energy latency tradeoffs for medium access and sleep scheduling in wireless sensor networks.  Page 85 
Repository email  cisadmin@lib.usc.edu 
Full text  As seen from the above discussion, the endtoend delay for flow m depends on both the path and the slot assignment. Active Flows Communication: For a sensor network application, at any specific time, not all nodes have sampling data to report to the base station: there are only a limited number of active flows in the network. Here, it would be of interest to minimize the average delay of the active flows in the network, which is defined as follows: Definition 5: Average Delay (Davg P,f ): For a given graph G = (V,E), number of slots k, a slot assignment function f and paths P for M flows, the average delay is defined as P m2M d(Pm), where d(Pm)) is the delay along the path Pm under the given slot assignment function f. In active flows communication, our design goal is the following: Definition 6: Minimum Latency joint Scheduling and Routing (MLSR) Given a graph G = (V,E), the number of slots k and M flows, find a path Pm for each flow, and an slot assignment function f that minimizes the average delay (Davg f ) i.e. f = arg min P0,f 0 {Davg P0,f 0} (5.3) Figure 5.2 shows an example of separate routing and scheduling solution. When there is a new flow request, the routing algorithm will find a route first, then on the given route, if a schedule is achievable, the following data forwarding will use the route and scheduling to forward data report. If the scheduling process fails, then the routing algorithm is asked to find a new route. Figure 5.3 shows an example of scheduling and routing for two active flows. In figure 5.3(a), first there is only one active flow. If we run a shortest hop routing algorithm, it will find the path of A ! B ! C ! D ! E ! Z. A schedule can be assigned on the nodes on the path. The delay is 8. If using the link delay as the weight of the link, however, shortest path routing algorithm now select A ! B ! C ! H ! I ! J ! Z which has a latency of only 6. Now assume there is another flow request from node F to node Z. Suppose the flow want to use route F ! G ! I ! J ! Z. However at link (i, j), there is no slot that both i and j are free, so the flow is forced to choose route F ! G ! K ! L ! M ! N ! Z which has a delay of 8. So the total delay for the two active flows is 14 in figure 5.3(b). However, as shown in figure 5.3(c), if source A use route A ! B ! C ! D ! E ! Z and source F use route F ! G ! I ! J ! Z. A schedule can be achieved with total delay of only 12. This example shows that latency reduction by joint scheduling and routing. Intuitively, in MLSR, the objective is to color a graph with the given K colors such that the desired global objective (minimizing the delay diameter in the former and the average delay diameter in the 72 