Palm Calculus Part 1 The Importance of the Viewpoint JY Le Boudec 1 May 2015.

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Presentation transcript:

Palm Calculus Part 1 The Importance of the Viewpoint JY Le Boudec 1 May 2015

1. Event versus Time Averages Consider a simulation, state S t Assume simulation has a stationary regime Consider an Event Clock: times T n at which some specific changes of state occur Ex: arrival of job; Ex. queue becomes empty Event average statistic Time average statistic 2

Example: Gatekeeper; Average execution time Real time t (ms) job arrival Execution time for a job that arrives at t (ms) Viewpoint 1: System Designer Viewpoint 2: Customer

Example: Gatekeeper; Average execution time Real time t (ms) job arrival Execution time for a job that arrives at t (ms) Viewpoint 1: System Designer Viewpoint 2: Customer

Sampling Bias W s and W c are different A metric definition should mention the sampling method (viewpoint) Different sampling methods may provide different values: this is the sampling bias Palm Calculus is a set of formulas for relating different viewpoints Can often be obtained by means of the Large Time Heuristic 5

Large Time Heuristic Explained on an Example 6

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This is Palm Calculus ! 11

A.Sn = 90, 10, 90, 10, 90; Xn = 5000, 1000, 5000, 1000, 5000 B.S n = 90, 10, 90, 10, 90; X n = 1000, 5000, 1000, 5000, 1000 C.Both D.None E.I don’t know 12

Solution 13

The Large Time Heuristic Formally correct if simulation is stationary It is a robust method, i.e. independent of assumptions on distributions (and on independence) 14

Other «Clocks» 15 Flow 1 Flow 2 Flow 3 Distribution of flow sizes for an arbitrary flow for an arbitrary packet

Which curves are for the per-packet viewpoint ? A.A B.B C.It depends D.I don’t know 16

Solution Answer A There are more packets in the large flows. So more packets experience a large flow size. 17

18 Load Sensitive Routing of Long-Lived IP Flows Anees Shaikh, Jennifer Rexford and Kang G. Shin Proceedings of Sigcomm'99 ECDF, per flow viewpoint ECDF, per packet viewpoint

19 Flow 1 Flow 2 Flow 3 Distribution of flow sizes for an arbitrary flow for an arbitrary packet

Large «Time» Heuristic 20

Large «Time» Heuristic 21 Flow n=1 Flow n=2 Flow n=3 p=1 p=2 p=3 p=4 p=5p=6 p=7 p=8 p=9

Large «Time» Heuristic 3.Compare 22 Flow n=1 Flow n=2 Flow n=3 p=1 p=2 p=3 p=4 p=5p=6 p=7 p=8 p=9

Large «Time» Heuristic for PDFs of flow sizes Put the packets side by side, sorted by flow 1.How do we evaluate these metrics in a simulation ? 23 Flow n=1 Flow n=2 Flow n=3

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Cyclist’s Paradox On a round trip tour, there is more uphill than downhill 26

The km clock vs the standard clock 27

BorduRail claims that only 5% of trains arrivals are late BorduKonsum claims that 30% of train users suffer from late train arrivals 28

29 Solution