Considered distributing a file of F = 20 Gbits to N peers. The server has an upl

Question

Considered distributing a file of F = 20 Gbits to N peers. The server has an upload rate of us = 40 Mbps, and each peer has a download rate of di = 3 Mbps an upload rate of u. For N = 2000 u=(300 kbps for even clients, 400 kbps for odd clients) and (2500 mbps for even clients and 3500 mbps for odd clients). With this information prepare a chart (table) giving the minimum distribution time for each of the combinations of N and u for both, client-server distribution and P2P distribution. To obtain full credit, you must show how you arrive to the calculation and you must provide the formulas you used.

Write the formula for DCS and P2P min. distribution.

DCSmd =

P2Pmd =

Write the variables that you will use. For example, N = 2000:

In the table below, write the individual terms (in the first row of DCS and P2P) and show your work

DCS (N=2000)

P2P (N=2000)

DCS (N=2000)

Explanation / Answer

DCSmd =max { NF / us , F / dmin }

                                                             

P2Pmd =max{ F / us , F / dmin , NF / (us + ui) }

                                                               i

Given F = 20 Gbits = 20 * 1024 Mbits =20480 Mbits

us = 40 Mbps

di = 3 Mbps

N = 2000

Write the variables that you will use. For example, N = 2000:

In the table below, write the individual terms (in the first row of DCS and P2P) and show your work

DCS (N=2000)

10

100

1000

2000

300

6826.66

51200

512000

102400

400

6826.66

51200

512000

102400

2500

6826.66

51200

512000

102400

3500

6826.66

51200

512000

102400

P2P (N=2000)

10

100

1000

2000

300

400

2500

3500

Dcs=Max{20*1024)(10)/40 , (20)(1024)/3} = MAX ={ 5120,6826.66)

like we can can calculate Dcs

For p2p

For n=10

For 300kbps=MAX{(20*1024)/40,(20*1024)/3,(20*1024)(10)/(40+3)} = Max{512,6826.66,4762.79} = 6826.66

For 400 kbps= MAX{(20*1024)/40 , (20*1024)/3 , (20*1024)(10)/(40+4)}=Max{512,6826.26,4654.54}=6826.66

For 2500 Mbps= MAX{(20*1024)/40 , (20*1024)/3 , (20*1024)(10)/(40+25000)}=Max{512,6826.66,8.1789}=6826.66

For 3500 kbps= MAX{(20*1024)/40 , (20*1024)/3 , (20*1024)(10)/(40+35000)}=Max{512,6826.66, 5.844}=6826.66

For n=100

For 300 kbps= MAX{(20*1024)/40 , (20*1024)/3 , (20*1024)(100)/(40+30)}=

Max{512,6826.66,29257.14}=29257

For 400 kbps= MAX{(20*1024)/40 , (20*1024)/3 , (20*1024)(100)/(40+40)}=

Max{512,6826.66,25600}=25600

For 2500 Mbps= MAX{(20*1024)/40 , (20*1024)/3 , (20*1024)(100)/(40+250000)}=

Max{512,6826.66,8.190}=6826

For 3500 kbps= MAX{(20*1024)/40 , (20*1024)/3 , (20*1024)(100)/(40+350000)}=

Max{512,6826.66,5.850}=6826

For n=1000

For 300 kbps= MAX{(20*1024)/40 , (20*1024)/2 , (20*1024)(1000)/(40+300)}=

Max{512,6826.66,60235.29}=60235

For 400 kbps= MAX{(20*1024)/40 , (20*1024)/2 , (20*1024)(1000)/(40+400)}=

Max{512,6826.66,46545.45}=46545

For 2500 Mbps= MAX{(20*1024)/40 , (20*1024)/2 , (20*1024)(1000)/(40+2500000)}=

Max{512,6826.66,8.19}=6826

For 3500 kbps= MAX{(20*1024)/40 , (20*1024)/2 , (20*1024)(1000)/(40+3500000)}=

Max{512,6826.66,5.85}=6826

For n=2000

For 300 kbps= MAX{(20*1024)/40 , (20*1024)/2 , (20*1024)(2000)/(40+300*2)}=

Max{512,6826.66,64000}=64000

For 400 kbps= MAX{(20*1024)/40 , (20*1024)/2 , (20*1024)(2000)/(40+400*2)}=

Max{512,6826.66,48761}=48761

For 2500 Mbps= MAX{(20*1024)/40 , (20*1024)/2 , (20*1024)2000)/(40+2500000*2)}=

Max{512,6826.66,8.19}=6826

For 3500 kbps= MAX{(20*1024)/40 , (20*1024)/2 , (20*1024)(2000)/(40+3500000*2)}=

Max{512,6826.66,5.19}=6826

DCS (N=2000)

10

100

1000

2000

300

6826.66

51200

512000

102400

400

6826.66

51200

512000

102400

2500

6826.66

51200

512000

102400

3500

6826.66

51200

512000

102400

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