CapProbe: A Simple and Accurate Capacity Estimation Technique

Kapoor et al., SIGCOMM ‘04

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

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

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 decreases—a.k.a. compression

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 pair—a.k.a. expansion

– Can occur anywhere on the link

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

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

Effect of Packet Size

Decreasing probability of cross-traffic induced delays will improve CapProbe’s effectiveness

Want to consider the relationship between probe packets’ sizes and probability of delay

Effect of Probing Packet Size

Queuing probability of second packet:– Second packet departs L/C (= dispersal) time units after

first packet—known as “vulnerability window”– If cross-traffic arrives during vulnerability window,

capacity estimation accuracy will decrease

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

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

Effects of Probing Packet Sizes

Simulation: narrow link = 4 Mbps

a) packet size = 100 bytes b) packet size = 1500 bytes

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

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%

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

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

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 =

λ = traffic arrival rate, μ = service rate, τ = dispersion

Deterministic Cross-traffic

Probability of no queuing =

λ= traffic arrival rate,

τ = dispersion,

tx = transmission time of cross-traffic packet

Pareto On/Off Cross-traffic

If tx < 1/2λ < tx + τ, a good sample can only arrive during an OFF period.

If 1/2λ > tx + τ, a good sample can occur in both ON and OFF periods

If 1/2λ < tx, good samples can only occur in OFF periods with idle time longer than the dispersion τ (see figure below)

Long Range Dependent Cross-traffic

Effect of cross-traffic packet size on requisite number of samples. Mix = 50%, 25%, 25%

6-hop LRD Cross-traffic

Above: a) persistentb) non-persistent

Minimum Delay Sum Condition

Want to determine accuracy of estimations– Accuracy based on absence of delay—best 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

Minimum Sum Delay Condition

Probability of an unqueued sample for pairs and single packets

Minimum Delay Sum Condition

Percentage increase in probability of unqueued sample when using single packets instead of packet pairs

Minimum Delay Sum Condition

Effect of probe packet size on the number of samples required to satisfy the minimum delay condition

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 @ packet sizes around 700 and 900 bytes; if estimations are within 5% of each other, algorithm stops; else, it restarts

Simulation Results

Simulation Results

Simulation Results

Simulation Results

Simulation Results

Simulation Results—Comparison to Other Techniques

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/

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