Adaptation Ability of Scheme GA

We next investigate the adaptation ability of scheme GA against the change of the query profile.

To adapt the change of the query profile, an adaptive version of scheme GA (referred to as scheme Adaptive-GA) is proposed. In scheme Adaptive-GA, scheme GA is activated periodically, and we call each activation a run. In each run, scheme GA is executed for a predetermined time interval. The resulting population of the current run is taken as the initial population of the next run.

According to the observations in Section 5.2.7, the relative merits of scheme GREEDY and GA are in fact complementary rather than competitive. Therefore, we propose a scheme named

Augmented-0 5 10 15 20 25

1 5 9 13 17 21 25

Number of Runs

Average Access Time (sec)

GREEDY Adaptive-GA Augmented-GA OPT

Figure 17: The average access time with time varied

GA to take advantage of the respective merits of both schemes. In essence, scheme Augmented-GA is a revised version of scheme Adaptive-GA. In each run of scheme Augmented-GA, scheme GREEDY is executed and the result of scheme GREEDY is inserted into the population of the current run.

To compare the adaptation ability of scheme Adaptive-GA and Augmented-GA on the change of the query profile, we execute scheme GREEDY and scheme OPT in each run. We assume the time interval between runs to be one hour. The allowed time to execute scheme GA for each run is set to six seconds. In the first run, the value of θ is set to be 0.6. The value of θ is changed to 1.2 after a period which is, without loss of generality, eight hours. The order of the access probabilities of all queries is also changed. The value of θ is changed to 0.2 after more eight hours. The experiment executes for 24 hours. The average access times of scheme GREEDY, OPT, Adaptive-GA and Augmented-GA with time varied are shown in Figure 17.

In the first run, since the allowed time to execute scheme GA is short, scheme GREEDY outper-forms scheme Adaptive-GA. Since the result of scheme GREEDY is inserted into the population of scheme Augmented-GA, the result of scheme Augmented-GA is at least as good as that of scheme GREEDY. In the successive runs (from the second run to the eighth run), due to the convergence

prop-erty of GAs, the results of schemes Adaptive-GA and Augmented-GA become better and better. We observe that scheme Adaptive-GA outperforms scheme GREEDY after the fifth run. Due the insertion of the result of scheme GREEDY, the convergence speed of scheme Augmented-GA is faster than that of scheme Adaptive-GA. Hence, scheme Augmented-GA outperforms scheme Adaptive-GA. The re-sults of schemes GREEDY and OPT remain stable in the first eight runs since the query profile is not changed.

The first change of the query profile occurs in the ninth run. As the results shown in Section 5.2.6, the increase of skewness will increase the average access time. Hence, the average access times of schemes GREEDY and OPT decrease after the ninth run. Scheme Adaptive-GA is able to adapt the change of the query profile. However, since the allowed time to execute scheme GA is short, scheme GA in the ninth run is outperformed by scheme GREEDY. The results of schemes Adaptive-GA and Augmented-Adaptive-GA improve in the subsequent runs until the second change of the query profile.

Since the second change of the query profile occurs in the 17th run, the scenario between the 17th run and the 25th run is similar to that between the ninth run and the 16th run.

This experiment result shows that scheme Augmented-GA can successfully take advantages of the respective merits of scheme GREEDY and scheme GA to achieve better performance than pure GA-based schemes. In fact, with scheme Augmented-GA, one can either decrease the period of each run or increase the execution time to speed up adaptation and convergence.

6 Conclusion

Data broadcast is an important data dissemination technique on mobile computing environments. Gen-erating broadcast programs to effectively reduce the average waiting time is an important issue of data

broadcast. We explored in this paper the problem of broadcasting dependent data in multiple broadcast channels for unordered queries. By analyzing the model of dependent data broadcasting, we derived several theoretical properties for the average access time in a multiple channel environment. In light of the theoretical results, we developed scheme GA to generate broadcast programs for unordered queries.

To evaluate the effectiveness of scheme GA, we developed scheme OPT which is able to generate the optimal broadcast programs by exhaustive search. In addition, we also designed scheme GREEDY to efficiently generate broadcast programs for unordered queries in a greedy manner.

To measure the performance of scheme GA, several experiments were then conducted. Our exper-imental results showed that the theoretical results derived are able to guide the search of the genetic algorithm very effectively, thus leading to broadcast programs of very high quality. Specifically, the performance of the broadcast programs generated by scheme GA is close to that generated by scheme OPT (i.e., the performance of the optimal broadcast programs). After summarizing the experimental results, we observed that the relative merits of scheme GA and scheme GREEDY are in fact comple-mentary rather than competitive. As a result, we developed scheme Augmented-GA to take advantage of the respective merits of both schemes. Experimental results showed that scheme Augmented-GA can achieve better performance than pure GA-based schemes.

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