Poisson vs' Periodic Probing Or Does PASTA matter

1
Poisson vs. Periodic Probing(Or Does PASTA
matter?)

• Muhammad Mukarram Bin Tariq ltmtariq_at_cc.gatech.edugt
  
• Amogh Dhamdhere
• Constantine Dovrolis
• Mostafa Ammar
• College of Computing
• Georgia Tech

2
The PASTA Property and Active NW Measurements

• PASTA Poisson Arrivals See Time Averages
• fraction of time a stochastic system
  spends in state X
• fraction of Poisson arrivals (out of N)
  that see system in state X, then
• Application to Active Network Measurements
• Stream of Poisson Probes will observe time
  average of delay, loss rate(?), available bw.

3
Poisson Vs. Periodic Probing

• Poisson Probing seems to be the right way to
  probe
• But, Periodic probing has a number of advantages
• Existing utilities e.g., ping
• In-band measurements many applications send data
  periodically
• Amenable to frequency domain analysis
• Are Periodic probing measurements different from
  Poisson probing?
• We focus on three path performance metrics
• RTT
• Loss rate
• Packet pair dispersion
• We measure differences between Poisson and
  Periodic Estimates
• Median values
• Distribution of measurements (goodness-of-fit
  test)
• Note We focus only on the relative difference
• Measurements may be potentially wrong!

4
Experimental Setup

• Probing sessions on 53 different paths between
  23 diverse Planetlab hosts
• Measurement Session
• 600 Poisson 600 Periodic probes interleaved
• Six different inter-arrivals I 10, 20, 50,
  100, 500, 1000 ms
• Four different packet sizes L 32, 64, 480,
  800, 1400 bytes
• We only consider sessions for which loss rate
• 892 sessions for RTT and loss
• 749 sessions for Dispersion
• The packets are time-stamped at receivers using
  kernel level libpcap time stamps

5
Comparing the Distributions

• Null Hypothesis Two distributions are same
• P-value probability of error if we reject null
  hypothesis
• Typical threshold for safe rejection 5-10

• Kolmogorov-Smirnov (KS) test is sensitive to
  discontinuities
• e.g., many packets seeing minimum (propagation)
  delays
• KS focuses on maximum vertical diff. b/w two
  distributions

6
Kullback-Liebler Distance based Goodness-of-Fit
Test

• Kullback-Liebler (KL) distance, aka, relative
  entropy, is a measure of difference between two
  distributions

• Distribution with Poisson
• Distribution with Periodic
• We randomly partition in twodisjoint parts,
  , and compute distribution of
  
  (boot-strapping)
• P-value

7
RTT Measurements

• Median RTT Estimates
• Estimate with Poisson Probes
• Estimate with Periodic Probes
• Relative Difference

8
Loss-rate Measurements

• Difference in loss-rate estimates
• loss-rate estimate with Poisson
• loss-rate estimate with Periodic
• Difference
• There is some loss
  but not more than
  10

9
Caveats in Estimating Loss-rate

• Fraction of lost Poisson Probes converges to
  fraction of time that queue is full
• May not be equal to fraction of packets lost
• Loss-event queue is full there is an arrival
• Conditions are independent only for Poisson
  arrivals (memoryless)
• The average loss rate, and the loss rate for
  individual flows, depends on burstiness of
  traffic
• Periodic Probes may miss effects that occur at
  smaller time scales than probing period
• e.g., underestimate bursty losses in Drop-tail
  queue

10
PASTA and NW of Queues

• Poisson probes may not arrive as Poisson process
  at bottleneck link
• Probe inter-arrivals become correlated (e.g.,
  output of M/D/1 is not Poisson)
• Interfering traffic distorts their inter-arrival
  times
• Strictly speaking PASTA does not apply in
  multihop paths

11
Summary

• Do Poisson and Periodic Probes measure
  significantly different RTT, loss-rate and
  dispersion?
• Our experiments indicate that they dont
• There is no significant difference in either the
  median values or the distributions for these
  three metrics
• There are some caveats loss-rate measurements
• Poisson probes do not measure the loss rates
• Probes do not arrive Poisson on bottleneck link
  due to correlations introduced by queues and
  interfering traffic

12
Dispersion Measurements

• We send probe pairs
• Inter-arrival between pairs being exponential
  (for Poisson), and fixed for periodic probes.
• Measure dispersal between packets of a pair
• Median Dispersion Estimates
• Estimate with Poisson Probes
• Estimate with Periodic Probes
• Relative Difference

• KL-test indicates no statistically significant
  difference for 95 of sessions
• Null Hypothesis Distributions with Poisson and
  Periodic Probing are same

13
Loss-rate Simulation
Queue Service Rate 5.9 pps (fixed) Net
Arrival Rate 6 pps Buffer 10 packets
Discipline FCFS Drop Drop-Tail
14
Summary

• Do Poisson Arrivals see significantly different
  time averages, from Periodic Arrivals, in the
  context of active Internet measurements
• We perform experiments to measure RTT
  Packet Pair Dispersion Packet Loss
  Rates using a finite stream of Poisson and
  Periodically arriving probes
• Empirically, there seems to be no significant
  difference in either the median values or the
  distributions of these metrics estimated using
  Poisson or Periodic probes