4.6 Simulation Results
4.6.3 Evaluations of CSTA , CDTA and DOOTA for Asymmetric WSNs
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Figure 4.9: Effect of the variation among the tasks on the (a) network lifetime increase and (b) algorithm runtime for CSTA, CDTA and DOOTA task allocation algorithms in symmetric networks, respectively (There are n = 10 slave node in the cluster and K = 10 tasks in the application, and the ratio of the battery energy of the master node to the slave node isRms =5.0, respectively).
slave node, due to the fact that the battery energy of the slave and master nodes are randomly generated for the asymmetric networks. 500 test instances are run for each simulation and the reported results correspond to the average values and the standard deviations.
Effect of the number of the slave nodes for asymmetric WSNs
In this part, a set of simulations are conducted to estimate the performance of the proposed algorithms for asymmetric networks when changing the number of the slave nodes.
The network lifetime increase by using the proposed task allocation algorithms with respect to the no-scheduling strategy and the corresponding algorithm runtime are depicted in Fig. 4.10.
Like the results in the symmetric networks, the network lifetime increases by using the three proposed algorithms become more significant when the number of slave nodes n increases, e.g., DOOTA extends the network lifetime in average 278.15% longer than the no-scheduling strategy whenn equals 5 and this gain increases to 859.78% whenn = 30. The reason is the same as presented in symmetric networks that the master node quickly gets overloaded using the no-scheduling strategy as n increased, which leads it die soon. While the workload of all the slave and master nodes can be efficiently allocated by the task allocation algorithms, which makes the network stay active for longer time. Due to the fact thatCSTAonly provides the static partition solution whileCDTAandDOOTA supply multiple partition solutions,CSTA performs the worst among these three algorithms on extending the network lifetime. Besides, DOOTA improves the network lifetime as long asCDTA, which again validates the analysis of the optimal task allocation solution in Section 4.5.1.
Unlike the results in symmetric networks shown in Fig. 4.6a, the superiority of CDTAand DOOTAoverCSTAon extending the network lifetime increases whennchanges from 5 to 30 for the asymmetric networks. Fig. 4.10a shows thatCDTAandDOOTAextend the network lifetime in average 71.53% longer than CSTA when nequals 5 with respect to no-scheduling strategy, while their gains increase to 206.95% whenn equals 30. Each slave node may have different partition solutions in the asymmetric networks due to different positions and battery energy. The partition solutions for each slave node provided byCDTAandDOOTA, which consist of multiple partition cuts and the corresponding weights, are better than the static partition cuts provided by CSTA. Therefore, whennincreases, the benefits of usingCDTAandDOOTAaccumulates.
Since it needs to consider the partition solutions for each slave nodes in the asymmetric networks, the execution time of runningCSTA,CDTAandDOOTAincreases asnbecomes larger.
TakingCSTAfor example, it takes in average 7.93×10−2seconds when there are 5 slave nodes, while 5.98×10−1seconds are needed asnchanges to 30. Although the trend of the algorithm runtime ofDOOTAincreases like the other two centralized algorithms, it is still 3 and 2 orders
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Figure 4.10: Effect of the number of slave nodes in the cluster on the (a) network lifetime increase and (b) algorithm runtime forCSTA,CDTAandDOOTAtask allocation algorithms, respectively (There are K = 10 tasks in the application and the middle variation level is selected, respectively).
of magnitude smaller thanCSTAandCDTA.
Effect of the number of the tasks in the application for asymmetric WSNs
The second set of simulations are conducted to investigate the effect of the number of tasks in the application,K, on the performance of the proposed algorithms for the asymmetric networks.
Fig. 4.11a shows the network lifetime increase by using the task allocation algorithms for asymmetric networks. The gains ofCSTA,CDTAandDOOTAwith respect to the no-scheduling strategy are slightly changed asK varies. This phenomenon is consistent with the results for symmetric networks, which can be explained by the same reasons.
The execution time of runningCSTA,CDTAandDOOTAtask allocation algorithms for asym-metric networks are illustrated in Fig. 4.11b. The centralized algorithms, CSTA and CDTA, require drastically more execution time when K becomes larger. Specifically, CSTA takes 4.99×10−2seconds in average asK equals 5 while it needs almost 1 second when there are 20 tasks. Since the partition cut is modeled as aK×1 binary vector as presented in Section 4.3.2,K determines the complexities of the centralized algorithms. For asymmetric networks, in which the slave nodes need individual partition solutions, the complexities of calculating the partition solutions are exponentially increases. In contrast to the centralized algorithms, the execution
time of runningDOOTAchanges less. The reason is thatDOOTAcalculates the optimal partition solutions based on the number of the important partition cuts. Although the number of the tasks in the application increase, the important partition cuts may not change or slightly changes.
Further more, the algorithm runtime ofDOOTAis still 3 and 2 orders of magnitude smaller than the centralized algorithmsCSTAandCDTA.
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Figure 4.11: Effect of the number of tasks in the application on the (a) network lifetime increase and (b) algorithm runtime forCSTA,CDTAandDOOTAtask allocation algorithms, respectively (There are n = 10 slave node in the cluster and the middle variation level is selected, respectively).
Effect of the variation among the tasks for asymmetric WSNs
The performance of the task allocation algorithms are further investigated by changing the variation levels among the tasks in the applications. The same three variation levels, low variation level, middle variation level and high variation level, are used in this set of simulations.
The trend of the network lifetime increase by usingCSTA,CDTAandDOOTAtask allocation algorithms are very similar to the results for the symmetric networks. Fig. 4.12a illustrates that both theCDTAandDOOTAalgorithms improve the network lifetime longer as the variation levels raise, i.e., they extend the network lifetime longer from 370.05% to 437.72% in average when it changes from the low variation level to the high variation level. On the contrary, the performance of CSTA becomes weaker where the variation level is higher. Since CSTA only
provides the static partition cut, which cannot achieve a fair workload balance among the slave and master nodes for the tasks with high variations. This drawback of the static task allocation can be solved by the dynamic task scheduling using multiple partition cuts. Thus,DOOTAand CDTAperforms much better thanCSTA.
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Figure 4.12: Effect of the variation among the tasks on the (a) network lifetime increase and (b) algorithm runtime for CSTA, CDTA and DOOTA task allocation algorithms, respectively (There are n = 10 slave node in the cluster and K = 10 tasks in the application, respectively).
Fig. 4.12b depicts the corresponding executing time of running these three task allocation algorithms. Since the algorithms need to consider the partition solution for each slave node, their algorithm running time are larger by comparing with running them for symmetric networks.
However, the variation levels do not change the number of the tasks as well as the number of the important partition cuts, the time requirements for runningCSTA,CDTAandDOOTAremain stable.