Evaluation of SJTA and DJTA Algorithms

This section evaluates the performances of the proposed joint static and dynamic task alloca- tion algorithms by comparing with the no-scheduling strategy and two other task allocation approaches:

• No scheduling strategy: The slave node only executes the first local tasks, the rest of the local tasks and the whole global tasks are done by the master node.

• Local Task Allocation (Local TA) [31]: It only provides the task solutions for the local application, the global tasks are fully completed by the master node itself.

• Global Task Allocation (Global TA): It only focuses on the global application task alloca- tion, the first local task is executed by the slave node and the rest are done by the master node.

Note that both Local TA and Global TA approaches run within each cluster as well as our proposed algorithms. The computational workload of the vertexes in the local and global DAG graphs are randomly generated within the ranges of [100, 500] KCCs and [10000, 50000] KCCs, respectively. The amount of the communicated data on the edges of the local and global DAGs

are distributed within the range of [100, 500] bits. The increases of the network lifetime by using the task allocation algorithms with respect to the no-scheduling strategy and the execution time of running them in Matlab 2017a are investigated by changing: a) The number of slave nodes, n; b) The number of local tasks, K; c) The number of global tasks, H; d) The execution period of global tasks, T . The configuration parameters are summarized in Table 5.3, and only one parameter is changed in each experiment.

Table 5.3: Configuration parameters of the simulations for estimation of the joint local and global task allocation.

Parameters Values

Default Varied

Number of slave nodes, n 10 {5, 10, 15, 20, 25}

The number of local tasks, K 10 {5, 10, 15, 20}

The number of global tasks, H 20 { 15, 20, 25, 3} Global task execution period, T 200 {50, 100, 200, 500, 1000}

The first set of simulations is conducted to investigate the performances of the proposed task allocation algorithms by changing the number of slave nodes, n. Fig. 5.9a illustrates that the increases of the network lifetime by applying the, Local TA, SJTA and DJTA become more significant as n changes from 5 to 25. In contrast, the improvement of network lifetime by using

Global TA decreases from 140% to 110% in average. The total workload of the local tasks of the slave nodes becomes larger as n increases, which makes the master node overburdened and die soon under no-scheduling strategy. While the energy consumption of the slave and master nodes are well balanced by Local TA,SJTAandDJTA. Moreover, the increase of the local task workload brings another consequence that only distributing the global tasks has less effect on extending the network lifetime. Due to the same reason, the superiority of DJTA and SJTA

over Local TA gets smaller. Regarding the algorithm runtime, as shown in Fig. 5.9b, the four approaches require more time for running the algorithm as the number of slave nodes increases. This is a common limitation of the centralized algorithms. For a large sized WSN, the clustering approaches are needed to group the network into small clusters. The detailed procedure will be illustrated in Chapter 6.

The second set of simulations is to evaluate the algorithm performances when changing the number of tasks in the local application, K. It can be seen in Fig. 5.10a that the gains of improving the network lifetime by using Local TA,SJTAandDJTAare slightly increased. Since the local tasks become more complex as K increases, there are more task allocation possibilities for the approaches which take the local task into account. In contrast, the Global TA only focuses on the global tasks, which is not affected by changing the local tasks. Meanwhile, the increasing

5 10 15 20 25 100

100.5 101 101.5

Number of slave nodes, n

N etw ork lif etime increase Local TA Global TA SJTA DJTA (a) 5 10 15 20 25 10−2 10−1 100

Number of slave nodes, n

Algor ithm runtime (sec.) Local TA Global TA SJTA DJTA (b)

Figure 5.9: Effect of the number of the slave nodes in the cluster on (a) network lifetime increase and (b) algorithm runtime (there are 20 and 10 tasks in global and local applications, respectively, and T = 200 rounds).

5 10 15 20

100 100.5 101

Number of local tasks, K

N etw ork lif etime increase Local TA Global TA SJTA DJTA (a) 5 10 15 20 10−2 10−1 100

Number of local tasks, K

Algor ithm runtime (sec.) Local TA Global TA SJTA DJTA (b)

Figure 5.10: Effect of the number of tasks in local application on (a) network lifetime increase and (b) algorithm runtime (there are 10 slave nodes in the network and 20 tasks in global application, and T = 200 rounds).

local tasks decreases the proportion of the global tasks in the whole local and global DAGs. The consequence is that the gain by using Global TA decreases from 136.63% to 123.89%. The corresponding algorithm runtime of Global TA is stable all the time while the Local TA consumes more time as K increases (see Fig. 5.10b). AlthoughSJTAprovides the static solution which is easier to implement in the slave and master nodes, DJTAachieves longer network lifetime and requires much less execution time. For example, when they are 20 local tasks, executingDJTA

needs 0.037 seconds and achieves 1060.23% network lifetime improvement, while executing

SJTArequires 0.528 seconds and extend the network lifetime 660.63% longer.

In addition to the local tasks, the impact of the number of global tasks, H, on the proposed algorithms is further estimated. The results are shown in Fig. 5.11. The gains of Global TA,

SJTAandDJTAon extending the network lifetime over the no-scheduling strategy increase while the gain of Local TA is slightly decreasing. This is due to the fact that Local TA only focuses on the workload distribution of local tasks. Correspondingly, its algorithm runtime remains the same as H increases from 15 to 30, while the others spend more time on executing the algorithms (see Fig. 5.11b). Besides,DJTAperforms better than SJTAon the network lifetime increase and execution time, which are consistent with the above-mentioned results. Note that, comparing with T = 200 rounds of local tasks, the workload of the global tasks is still relatively very small which leads to very small gains for Global TA. Thus, the next set of simulations adjusts the workload proportion of the global tasks by changing its execution period to evaluate the algorithm performance.

As the above depicted, changing the number of global tasks does not affect the algorithm too much when the execution period T = 200. The impact of T on the performance of the proposed algorithms is investigated in this part and the results are illustrated in Fig. 5.12. It is obvious that Global TA extends the network lifetime significantly when T is very small, i.e., the workload proportion of the global tasks is relatively large. It improves the network lifetime in average by 173% when T = 50. As the interval length of T increases, the performance of Global TA goes down. On the contrary, Local TA extends the network lifetime longer when T changes from 50 to 1000. Its performance is closer toSJTAandDJTAdue to the decreasing global task workload. SinceSJTAandDJTAtake both the local and global tasks into account, they prolong the network lifetime dramatically all the time. Meanwhile, their algorithm execution times decrease, as the global task workload is reducing when T increases.