A closer look at the M/G/R PS model for TCP traffic

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1 A closer look at the M/G/R PS model for TCP traffic July 23, 2001 Institute of Communication etworks Munich University of Technology 1

2 Outline Simulation Scenario Sojourn Time Formulas Investigated Scenarios Simulation Results Conclusion and Further Issues 2

3 Simulation Scenario Important Parameters Clients Servers Data Flow Capacity r Capacity C Propagation Delay T P Simulation environment: network simulator version 2.1b7, TcpReno File interarrival time: neg. exp. distributed File length: hyperexp. distributed, mean: 22 kbytes Buffer size = 500 packets MSS = 500 bytes 3

4 Pure M/G/R PS Model E x r 2 M / G / R{ T ( x)} = 1+ Sojourn Time Formulas E ( R, Rρ) R(1 ρ) = x r f R x R ρ f R file length C/r link utilization delay factor Extended M/G/R PS Model (see PGTS 2000) E extended { T( l) } = log 2 l RTT + E MSS n* RTT + E M / G / R M / G / R { T ( l l )} { T( l l )} slow start start l l < l l slow start slow start with l l start = 2 log l MSS 1 MSS n ( ) MSS slow start = 1 2 *, n * = log w 2 *, C w* = RTT MSS available r = f peak R RTT MSS 4

5 Investigated Scenarios C r T prop ρ f R "Reference" 4100 kbps 256 kbps 10 ms "ong Delay" 4100 kbps 256 kbps 100 ms "ong Queuing" 1150 kbps 64 kbps 10 ms "High Utilization" 3800 kbps 256 kbps 10 ms

6 "Reference" Transfer Time 4 Mean Median Theory Time in seconds File Size in bytes 6

7 "Reference" Queue ength Distribution 0.3 Frequency 0.2 M/M/1/500 queuing system Queue ength in packets 7

8 "Reference" umber of Active Flows Frequency 0.04 M/G/R PS model umber of simultaneously active flows 8

9 "ong Delay" Transfer Time 4 Mean Extended Theory Theory Time in seconds File Size in bytes 9

10 "ong Delay" umber of Active Flows 0.08 M/G/R PS model 0.06 Frequency umber of simultaneously active flows 10

11 "ong Queuing" Transfer Time 15 Mean Extended Theory Theory Time in seconds File Size in bytes 11

12 "ong Queuing" umber of Active Flows 0.08 M/G/R PS model 0.06 Frequency umber of simultaneously active flows 12

13 "High Utilization" Transfer Time 8 Mean Extended Theory Theory Time in seconds File Size in bytes 13

14 "High Utilization" Queue ength Distribution 0.12 Frequency 0.08 M/M/1/500 queuing system Queue ength in packets 14

15 "High Utilization" umber of Active Flows 0.04 M/G/R PS model 0.03 Frequency umber of simultaneously active flows 15

16 Conclusions and Further Issues Pure M/G/R PS works fine for low utilization high bandwidth low propagation delay Use Extended M/G/R PS if RTT > E M/G/R {T(x)} small x if T buffer > E M/G/R {T(x)} small x use RTT estimates use buffer queue estimates Further Issues effect of packet loss packet-level characteristics 16

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