CapProbe: A Simple and Accurate Capacity Estimation Technique

1
CapProbe A Simple and Accurate Capacity
Estimation Technique

• Kapoor et al., SIGCOMM 04

2
Capacity Estimation Techniques

• Monitor delays of packet pairs and trains
• Monitor dispersions of packet pairs and trains
• CapProbe uses both dispersion measurements for
  estimation, delay measurements to filter out
  inaccurate estimations

3
Dispersion The Packet Pair Algorithm

• If two packets sent back-to-back are queued one
  after the other at a narrow link, they will exit
  the link with dispersion T given by
• T L / B,
• L size of second packet,
• B bandwidth of narrow link

4
Packet Pair Algorithm Inaccuracies

• Capacity over-estimation
• Observed dispersion smaller than what would have
  been introduced by the narrow link
• If the first packet queued after narrow link
  while the second packet experiences less queue
  delay after narrow link, observable dispersion
  decreasesa.k.a. compression

5
Packet Pair Algorithm Inaccuracies

• Capacity under-estimation
• Observed dispersion larger than what would have
  been introduced by narrow link
• Can occur if cross-traffic packets serviced
  between packets of a paira.k.a. expansion
• Can occur anywhere on the link

6
CapProbe Observation

• CapProbe is based on the simple observation that
  a packet pair which produces either an over- or
  under-estimation of capacity must have incurred a
  cross-traffic induced delay at some link

7
CapProbe Observation

• For each packet pair, CapProbe calculates delay
  sum
• delay(packet_1) delay(packet_2)
• A packet pair which incurs no cross-traffic
  delays exhibits the minimum delay sum its
  dispersion measurement can produce an error-free
  capacity estimation
• Given a set of packet pair probes, the probe
  which exhibits the smallest delay sum will
  provide the most accurate capacity estimate

8
Effect of Packet Size

• Decreasing probability of cross-traffic induced
  delays will improve CapProbes effectiveness
• Want to consider the relationship between probe
  packets sizes and probability of delay

9
Effect of Probing Packet Size

• Queuing probability of second packet
• Second packet departs L/C ( dispersal) time
  units after first packetknown as vulnerability
  window
• If cross-traffic arrives during vulnerability
  window, capacity estimation accuracy will
  decrease

10
Effect of Probing Packet Size

• Queuing probability of second packet
• Can be reduced by decreasing probe packet sizes
• Eg halving the packet size shrinks the
  vulnerability window, which reduces the
  probability that the second packet will incur a
  delay, thereby decreasing the probability of
  capacity under-estimation

11
Effect of Probing Packet Size

• Small packet sizes decreases probability of delay
  for second packet, but probability of delay for
  the first packet remains the same
• Thus the relative probability of delay for the
  first packet w.r.t. the second packet increases
  as size decreases
• Results in an increase in the probability of
  over-estimation
• Small packet sizes also increase the magnitude of
  over-estimation
• Consider the case when the first packet suffers
  more queuing than the second, leading to
  compression
• Compression ratio will be larger when the
  original dispersion is smaller

12
Effects of Probing Packet Sizes

• Simulation narrow link 4 Mbps
• a) packet size 100 bytes
  b) packet size 1500 bytes

13
Effects of Small Probing Packets

• Smaller packet sizes lead to a higher chance of
  over-estimation
• Capacity mode occurs with relative frequency of
  25
• Higher chance of accurate estimate
• Probability of no queuing delay 13
• Harder for OS clocks to accurately measure
  dispersion for small packets

14
Effects of Large Probing Packets

• Under-estimation is predominant
• Capacity mode occurs with a relative frequency of
  4
• Probability of no queuing delay 1.5

15
Effect of Probing Packet Size on Cross-Traffic
Queuing

• Effect of probe size on the probability of not
  queuing when cross-traffic size 550 bytes

16
CapProbe Convergence

• CapProbe provides accurate estimates if no
  cross-traffic delays introduced
• Desirable to understand the probability of
  obtaining delay-free measurements
• Also want to determine the average number of
  samples needed before a delay-free measurement is
  made (convergence rate)
• Two cases when cross-traffic poses a problem
• Cross-traffic present upon arrival of first
  packet
• Cross-traffic arrives between the packet pair

17
Poisson Cross-traffic

• Probability P1 that first packet arrives to empty
  system
• Probability P0 that no traffic arrives between
  pair
• Probability of no queuing
• Expected of samples needed
• ? traffic arrival rate, µ service rate, t
  dispersion

18
Deterministic Cross-traffic

• Probability of no queuing
• ? traffic arrival rate,
• t dispersion,
• tx transmission time of cross-traffic packet

19
Pareto On/Off Cross-traffic

• If tx lt 1/2? lt tx t, a good sample can only
  arrive during an OFF period.
• If 1/2? gt tx t, a good sample can occur in both
  ON and OFF periods
• If 1/2? lt tx, good samples can only occur in OFF
  periods with idle time longer than the dispersion
  t (see figure below)

20
Long Range Dependent Cross-traffic
Effect of cross-traffic packet size on requisite
number of samples. Mix 50, 25, 25
21
6-hop LRD Cross-traffic
Above a) persistent b) non-persistent
22
Minimum Delay Sum Condition

• Want to determine accuracy of estimations
• Accuracy based on absence of delaybest estimate
  comes from probe pair w/ minimum delay sum
  delay(P_first) delay(P_second)
• It is more likely that a single packet will not
  experience queuing than it is that neither of a
  pair of packets will experience queuing
• If the observed minimum delay sum is greater than
  the observed minimum possible delay, i.e. the
  minimum delay sum is greater than the sum of the
  minimum delays of individual packets, then the
  probe incurred some delay and is not as accurate
  as possible

23
Minimum Sum Delay Condition
Probability of an unqueued sample for pairs and
single packets
24
Minimum Delay Sum Condition
Percentage increase in probability of unqueued
sample when using single packets instead of
packet pairs
25
Minimum Delay Sum Condition
Effect of probe packet size on the number of
samples required to satisfy the minimum delay
condition
26
CapProbe Algorithm

• Initialization period of 40 samples
• If MDSC is not satisfied in less than 100
  samples, then
• If large variation in estimates, increase packet
  size 20 to improve OS timing accuracy
• Else, decrease packet size 20 to decrease
  cross-traffic delay probability
• Obtain 2 sequential MDSC-compliant measurements
  _at_ packet sizes around 700 and 900 bytes if
  estimations are within 5 of each other,
  algorithm stops else, it restarts

27
Simulation Results
28
Simulation Results
29
Simulation Results
30
Simulation Results
31
Simulation Results
32
Simulation ResultsComparison to Other Techniques
33
CapProbe Extensions

• TCP Probe A TCP with Built-in Path Capacity
  Estimation
• End-to-end Asymmetric Link Capacity Estimation
• http//nrl.cs.ucla.edu/CapProbe/

34
Conclusion

• CapProbe relies on novel combination of packet
  pair dispersion measurements to estimate link
  capacities and packet pair delays to filter out
  distorted estimates
• Accurate much faster than other techniques
• Has problems with cross-traffic consisting of
  small packets
• Has problems with high-load UDP cross-traffic