X hits on this document

20 views

0 shares

0 downloads

0 comments

6 / 8

average service capacity of source i and c = (c1, c2, c3, c4). The average service capacity of the whole network is then A(c) = (c1 + c2 + c3 + c4)/4. We change the heterogene- ity in service capacity by changing each ci, while keeping A(c) = 200kbps the same. We measure the degree of het- erogeneity in term of δ = Var{c}/A(c), the normalized standard deviation. We set δ to range from 0.05 to 0.7.

To demonstrate the impact of correlation in each fixed path, we use a class of AR-1 random processes to model the stochastic fluctuation in the service capacity. The values of ρ and (t) in (8) represents the degree of corre- lation and the noise term of the process respectively. It is reasonable to assume that if the average service capacity is large, the service capacity is more likely to fluctuate over a wider range. In this regard, we assume that the amount of fluctuation in Ci(t) is proportional to its mean value ci. Specifically, for path i, we set i(t) to be uni- f o r m l y d i s t r i b u t e d o v e r [ c i θ i , c i + θ i ] w h e r e θ i i s c h o s e n s u c h t h a t V a r { C i ( t ) } / E { C i ( t ) } r e m a i n s t h e s a m e f all i. o r

In our simulation, the network is modeled as a dis- crete time system where the length of each time slot (one period) is chosen to be 5 minutes. In reality, it is ex- pected that within such a period, there is no major event that triggers dramatic fluctuation in the service capacity. There may be small short-term fluctuations, on the order of seconds, in the service capacity due to the nature of the network protocol, such as TCP congestion window changes, or OS interrupt handling, etc. These changes however do not impose serious impact on the service ca- pacity. Thus, we are not interested in such small short- term variation, but are more interested in the fluctuation on a longer time scale caused by change in the number of connections at the source or change in network con- gestion status, which all usually last for longer time (say, minutes to hours).

We set the file size to 150MB, which is the typical size of some small video clips or multimedia files. As the av- erage service capacity (of the network) is 200kbps, we set the chunk-size for chunk-based switching to be 7.5 MB (= 200kbps × 5 minutes) to allow fair comparison between periodic switching and chunk-based switching. Although many modern P2P systems make the size of a “chunk” to be around 256KB or so, it is unlikely for a peer to switch to different peers after each chunk. Rather, a download- ing peer may receive several “chunks” consecutively from the same source peer. Hence the real data size down- loaded from the same source is not just 256KB, but will be usually larger.

We consider four possible download strategies, perma- nent, periodic switching, chunk-based switching and par- allel downloading. For permanent connection, the user initially choose one of four sources randomly and stay there until the download completes. For chunk-based switching, the peer switches to a new randomly selected source whenever a chunk is completed. Although we sim- ulate the system as a discrete time system, the user is

6

allowed to switch to a new source anytime within a time slot whenever it finishes the current chunk. For paral- lel download, the file is divided into 4 equal-sized pieces and the downloading peer connects to all 4 source and download each piece from each source peer simultane- ously. Finally, for periodic switching, a user switches to a new randomly chosen source every 5 minute to further download the remaining parts of the file.

300

Average Download Time (min)

250

200

150

100

50

Permanent (=0.5) Permanent (=0.95) Chunk−based (=0.5) Chunk−based (=0.95) Periodic (=0.5) Periodic (=0.95) Parallel (=0.5) Parallel (=0.95)

0.05

0.1

0.15 0.2 0.25 0.3 Degree of Heterogeneity ()

0.35

0.4

(a) Low degree of heterogeneity: 0 < δ < 0.4

350

Average Download Time (min)

300

250

200

150

100

Permanent (=0.5) Permanent (=0.95) Chunk−based (=0.5) Chunk−based (=0.95) Periodic (=0.5) Periodic (=0.95) Parallel (=0.5) Parallel (=0.95)

50 0.4

0.45

0.5 0.55 0.6 Degree of Heterogeneity ()

0.65

(b) High degree of heterogeneity: 0.4 < δ < 0.7

Figure 4: Average download time vs. degree of hetero- geneity under different download strategies and different degree of correlations.

Figures 4 (a)–(b) show the average download time vs. the degree of heterogeneity in the average service capac- ities (δ) when there is a single downloader in the net- work. Dashed lines are for strong correlations (ρ = 0.95) and solid lines represent the case of light correlations (ρ = 0.5). In Figure 4(a), when the degree of heterogene- ity is small, all three single-link download strategies (per- manent, chunk-based, periodic) under light correlations perform the same. This is well expected since the service capacities of all paths are almost i.i.d. over space and time, so switching doesn’t make any difference and the av- erage download time becomes F/A(c) = 150MB/200kbps = 100 minutes, as commonly used in practice. On the other hand, when there exists strong correlations in the service capacity, the download time is longer for all strate- gies except the periodic switching. For example, when δ = 0.1, the correlation alone can cause more than 20% of increase in the average download time. Thus, when the network is more like homogeneous (i.e., small δ), the temporal correlation in the service capacity of each path

Document info
Document views20
Page views20
Page last viewedWed Dec 07 16:48:17 UTC 2016
Pages8
Paragraphs387
Words6789

Comments