becomes a major factor that renders the average down- load time longer. However, the average download time remains the same under the random periodic switching.

Figure 4 (a) also shows the performance of parallel downloading. Intuitively, parallel downloading should perform better than single link downloading because (i) it utilizes more than one link at the same time and (ii) if the connection is poor, parallel downloading reduces the amount of data getting through that bad path. Since

there is

only a single

ity the

network can

user, it utilizes all the provide (c_{1 }+ c_{2 }+ c_{3 }

service

capac-

+ c_{4}).

In this

case, c_{2 }+ from

the average download time should be 150MB/(c_{1 }+ c_{3 }+ c_{4}) = 150MB/800kbps ≈ 25 minutes. We see Figure 4(a) that parallel downloading can actually

achieve the performance close to our expectation the service capacities of different paths are close to Still, parallel downloading is prone to the negative of correlations.

when i.i.d. effect

As the degree of heterogeneity increases, the average download time sharply increases for all the schemes ex- cept the periodic switching. Figure 4 (b) shows this when δ is between 0.4 and 0.7. Permanent and chunk-based switching both suffer from the negative effect of hetero- geneity. When both heterogeneity and correlation are high (δ = 0.65 and ρ = 0.95), permanent connection takes about 350 minutes to complete the download. This time is about 250 minutes, or 4 hours more than using the periodic switching! Even the chunk-based switching yields the average download time almost as twice much as the periodic switching. Further, the performance of parallel downloading degrades very fast as the degree of heterogeneity increases. At some point, even for a sin- gle downloading peer in the network, the performance of parallel downloading becomes worse than the chunk- based switching (single-link download) and close to that of permanent connection. When there is a large degree of heterogeneity, it is more likely that one of the parallel connections is ‘poor’ with very small capacity. Thus, even though the size of chunk over each path is smaller than the whole file (hence reducing the risk of staying with the bad path for too long), this is still not as good as the idea of averaging capacities all the time, as used in the periodic switching. We note that temporal correlations still negatively affect in all these three schemes. How- ever, it should be pointed out that the random periodic switching performs the same regardless of heterogeneity and correlations, and in fact it outperforms all the other schemes when the network is heterogeneous with a wide range of service capacities as in the current network.

# IV.B Multiple Downloaders with Competition

As seen earlier, when there is only one downloading peer in the network, the average download time can be reduced by randomly switching connections among paths with different average capacities. However, there are al- ways multiple users in a network and competition among peers is obvious. In this section, we consider the perfor- mance of different download strategies under a multi-user

7

environment. In the multi-user scenario, we set the num- ber of source peers to N = 100. The sources are divided into 4 groups and each source within the same group will have the same average service capacity. We set the cor- relation coefficient of each source to 0.5, which indicates light temporal correlations in the service capacity. The distribution of service capacity of each group is chosen to make δ = 0.6. In our simulation, if m users connect to a source offering service capacity C(t), then each of those m users receives service capacity of C(t)/m. The effect of dividing capacity among users gives us an idea of how different strategies will perform when users compete for limited resources in the network. To represent the level of competition, we use the source-user ratio, i.e. the ra- tio between the number of source peers to the number of users (downloading peers).

2500

# Average Download Time (min)

2000

1500

1000

500

0

0.5

Chunk−based Parallel(5) Parallel(All) Periodic Permanent

1

1.5

2

2.5

3

3.5

4

#

of Downloaders / # of Uploaders

Figure 5: Performance of different download strategies under if different levels of competition.

Figure 5 shows the average download time under differ- ent strategies as the number of downloaders increases (dif- ferent levels of competition). Because the total amount of service capacity in the network is fixed, users have to share this fixed amount of capacity and thus the aver- age download time will increase as the number of down- loaders increases for all possible strategies. In Figure 5, the periodic switching always yields the smallest average download time than all the other strategies regardless of the level of competition among downloading peers. Even under heavy competition, when the number of users is 4 times of the number of sources, periodic switching can re- duce at least 50% of the average download time compared to other strategies.

It is interesting to see that under heavy competition, parallel downloading is even worse than the single link download. As discussed earlier, in parallel downloading, the download time is determined by the chunk that fin- ishes the last. In other words, the download is complete when the chunk from the source offering the ‘worst’ ser- vice capacity is done. Under heavy competition, paral- lel downloading actually makes more users to share the ‘worst’ source, thus increasing the download time further. Thus, our study shows that, contrary to the common be-