Effect of Cache Size - 6 Performance Evaluation

6 Performance Evaluation

6.7 Effect of Cache Size

This experiment evaluates the effect of cache size on average access time and average tuning time, and the experimental results are shown in Figure 14. Similar to [8], cache size is determined as “cache size ratio×the summation of the sizes of all data items.” The case that the value of cache size ratio is set to zero indicates the case that the server does not employ cache.

As shown in Figure 14a, average access time decreases as the value of cache size ratio increases. When the cache size is large, many data items are cached and can be obtained by the server without being fetched from the data servers. In addition, when the cache size is large enough, the benefit of increasing cache size diminishes since data items with high access rates are cached in the server cache. We also observe from Figure 14a that employing server cache, which is neglected in the prior studies on data indexing for on-demand data broadcasting [13], is able to effectively reduce average access time.

As the observations in Section 4.2, when it comes to average tuning time, cases with short average access time favor schemes with small values of degree. Hence, scheme Static-2 outperforms scheme Static-8 especially when the value of cache size ratio is large. This observation agrees with the results shown in Figure 14b. When the value of cache size ratio is small, both schemes do not perform well since the value of degree in scheme Static-2 is too small and the value of degree in scheme Static-8 is too large. On the other hand, scheme AIDOA is able to dynamically adjust the value of degree to attain better performance, showing the advantage of scheme AIDOA.

7 Conclusion

We proposed in this paper an energy-conserving on-demand data broadcasting system employing the data indexing technique. Different from the prior work, power consumption of turning on and turning off the wireless network interfaces was considered. In addition, we also employed server cache to reduce the effect of data fetch time. Specifically, we first analyzed the access time and tuning time of data requests and proposed algorithm AIDOA to adjust the degree of buckets according to system workload.

We also devised an approximation method to estimate the effect of increasing and decreasing the values of degree, and employed the approximation method to guide the adjustment of algorithm AIDOA. In addition, the companion program generation algorithm and cache replacement policy were proposed to cooperate with algorithm AIDOA. Several experiments were then conducted to evaluate the performance of algorithm AIDOA. Experimental results showed that algorithm AIDOA is able to greatly reduce power consumption at the cost of a slight increase in average access time and dynamically adjust the index and data organization to adapt to change of system workload.

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I_i(1) I_i(2) I_i(3) D_i(1) D_i(2) D_i(3)

I_i(1) I_i(2) I_i(3) I_i(4) D_i(1) D_i(2) D_i(3) D_i(4)

A F N A

t_End t_Start t_Sleep(i) t_WakeUp(i)

A F N A

t_End t_Start t_Sleep(i) t_WakeUp(i)

Bucket(i)

Time

Figure 15: An example scenario of Type I data requests that d_Curr.= 3 and dNext = 4

Appendix

Proof of Lemma 1:

Consider the cases that d_Next > d_Curr.. Figure 15 shows an example of Type I data requests. When the degree of buckets is set from d_Curr. to dNext, dNext− d_Curr. index item(s) and dNext− d_Curr. data item(s) will be appended to each index segment and data segment, respectively. As observed from Figure 15, setting the degree of buckets from d_Curr.to d_Next increases the average access time of Type I data requests by ^(d^Next^−d_B^Curr.^)×S^I. In addition, we also observe that appending d_Next− d_Curr. index items into each index segment does not affect the average tuning time of Type I requests. Hence, from the above observations, we have

Stat_I^d^Next.AvgAT = Stat_I.AvgAT + (d_Next− d_Curr.) ×S_I B, and Stat_I^d^Next.AvgT T = Stat_I.AvgT T.

We then apply the above equations as the approximations of Stat_I^d^Next.AvgAT and Stat_I^d^Next.AvgT T in the cases that d_Next < d_Curr., and hence, prove Lemma 1. Q.E.D.

Proof of Lemma 2:

Consider the example probe bucket of Type II data requests shown in Figure 16. Suppose that t_Start follows a uniform distribution between Bucket_i.Start and Bucket_i.End. Therefore, as observed from Fig-ure 16, the probabilities of a Type II data request to be Type II.I and Type II.II are _S ^S^I

I+S_D and _S^S^D

I+S_D,

A F N

Figure 16: An example scenario of Type II data requests that d_Curr.= 3 and dNext = 4 on the probe bucket respectively. Therefore, by the definition of Stat_II^d^Next.AvgAT P and Stat_II^d^Next.AvgT T P, we have

Stat_II^d^Next.AvgAT P = SI

We now consider the cases that d_Next > d_Curr. and derive the approximations of Stat_II.I^d^Next.AvgAT P, Stat_II.I^d^Next.AvgT T P, Stat_II.II^d^Next.AvgAT P and Stat_II.II^d^Next.AvgT T P. When the degree of buckets is set to from d_Curr.

to d_Next, d_Next− d_Curr. index item(s) and d_Next− d_Curr.data item(s) will be appended to each index segment and data segment. As observed from Figure 16, setting the degree of buckets from d_Curr. to dNextincreases the average access time and average tuning time of the probe buckets of Type II.I data requests (i.e., Stat_II.I^d^Next.AvgAT P and Stat_II.I^d^Next.AvgT T P) by ^(d^Next^−d^Curr._B^)×(S^I^+S^D⁾ and ^(d^Next^−d_B^Curr.^)×S^I, respectively. Hence,

In addition, we also observe that increasing the degree of buckets from d_Curr. to d_Next increases both

the average access time and average tuning time of the probe buckets of Type II.II data requests (i.e., Stat_II.II^d^Next.AvgAT P and Stat_II.II^d^Next.AvgT T P) by ^(d^Next^−d^Curr._B^)×(S^I^+S^D⁾. Therefore, we have

Stat_II.II^d^Next.AvgAT P = Stat_II.AvgAT P + (d_Next− d_Curr.) ×S_D B , and

Stat_II.II^d^Next.AvgT T P = Stat_II.AvgT T P + (d_Next− d_Curr.) ×S_D B .

We then apply the above equations to the approximations of Stat_II.I^d^Next.AvgAT P, Stat_II.I^d^Next.AvgT T P, Stat_II.II^d^Next.AvgAT P and Stat_II.II^d^Next.AvgT T P in the cases that d_Next < d_Curr., and hence, prove Lemma 2.

Q.E.D.

Proof of Lemma 3:

In the cases that the degree of buckets is d_Curr., since one data item and the corresponding index item contribute StatII.AvgAT S by ^S^I^+S_B ^D, the average number of data items in Type II data requests is Stat_II.AvgAT S ×_S ^B

I+S_D.

Consider the cases that set the degree of buckets to d_Next. For each Type II data request, on aver-age, d_Next− d_Curr. index items and d_Next− d_Curr. data items move from the search buckets to the probe bucket. Therefore, the average number of index and data items in Type II data requests both become StatII.AvgAT S ×_S ^B

I+SD− (dNext− d_Curr.). Since each search bucket contains dNext index items and dNext

data items, the average number of search buckets of Type II data requests is

AvgSBNoNext= StatII.AvgAT S × B

S_I+ S_D− (dNext− d_Curr.).

Finally, according to the derivations in Section 3.2.2, since each Type II data request contains AvgSBNo_Next search buckets on average, we have

Stat_II^d^Next.AvgAT S = AvgSBNo_Next× d_Next×(S_I+ S_D) B , and

Stat_II^d^Next.AvgT T S = AvgSBNoNext× µ

dNext×S_I

B + TO f f+ TOn

¶ .

Q.E.D.

Proof of Lemma 4:

A F N Time Bucket(j)

I_j(1) I_j(2) I_j(3) D_j(1) D_j(2) D_j(3)

A t_End t_Sleep(j) t_WakeUp(j)

A F N Time

Bucket(j)

I_j(1) I_j(2) I_j(4) D_j(1) D_j(2)

A t_End

t_Sleep(j) t_WakeUp(j)

I_j(3) D_j(3) D_j(4)

Figure 17: An example scenario of Type II data requests that d_Curr. = 3 and dNext = 4 on the retrieval bucket

Consider the cases that d_Next> d_Curr.and the example Type II data request shown in Figure 17. When the degree of buckets is set to from d_Curr.to d_Next, d_Next−d_Curr.index item(s) and d_Next−d_Curr.data item(s) will be appended to each index segment and data segment, respectively. As observed from Figure 17, setting the degree of buckets from d_Curr. to d_Next increases the average access time of each Type II data request on the retrieval bucket by ^(d^Next^−d_B^Curr.^)×S^I. In addition, we also observe that appending dNext− d_Curr.

index items into each index segment does not affect the average tuning time of each Type II request on the retrieval bucket. Hence, from the above observations, we have

Stat_II^d^Next.AvgAT R = Stat_II.AvgAT R + (d_Next− d_Curr.) ×S_I B, and Stat_II^d^Next.AvgT T R = StatII.AvgT T R.

We then apply the above equations as the approximations of Stat_II^d^Next.AvgAT R and Stat_II^d^Next.AvgT T R in the cases that d_Next< d_Curr., and hence, prove Lemma 4. Q.E.D.

在文檔中 AIDOA: An Adaptive and Energy-Conserving Indexing Method for On-Demand Data Broadcasting Systems (頁 29-35)