RTP Media Congestion Avoidance Techniques D. Hayes, Ed.
Internet-Draft University of Oslo
Intended status: Experimental S. Ferlin
Expires: September 22, 2016 Simula Research Laboratory
M. Welzl
K. Hiorth
University of Oslo
March 21, 2016
Shared Bottleneck Detection for Coupled Congestion Control for RTP
Media.
draft-ietf-rmcat-sbd-04
Abstract
This document describes a mechanism to detect whether end-to-end data
flows share a common bottleneck. It relies on summary statistics
that are calculated by a data receiver based on continuous
measurements and regularly fed to a grouping algorithm that runs
wherever the knowledge is needed. This mechanism complements the
coupled congestion control mechanism in draft-ietf-rmcat-coupled-cc.
Status of This Memo
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1. The signals . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.1. Packet Loss . . . . . . . . . . . . . . . . . . . . . 3
1.1.2. Packet Delay . . . . . . . . . . . . . . . . . . . . 3
1.1.3. Path Lag . . . . . . . . . . . . . . . . . . . . . . 4
2. Definitions . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1. Parameters and their Effect . . . . . . . . . . . . . . . 7
2.2. Recommended Parameter Values . . . . . . . . . . . . . . 8
3. Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.1. SBD feedback requirements . . . . . . . . . . . . . . . . 9
3.1.1. Feedback when all the logic is placed at
the sender . . . . . . . . . . . . . . . . . . . . . 10
3.1.2. Feedback when the statistics are
calculated at the receiver and SBD at
the sender . . . . . . . . . . . . . . . . . . . . . 10
3.1.3. Feedback when bottlenecks can be
determined at both senders and
receivers . . . . . . . . . . . . . . . . . . . . . . 11
3.2. Key metrics and their calculation . . . . . . . . . . . . 11
3.2.1. Mean delay . . . . . . . . . . . . . . . . . . . . . 11
3.2.2. Skewness Estimate . . . . . . . . . . . . . . . . . . 11
3.2.3. Variability Estimate . . . . . . . . . . . . . . . . 12
3.2.4. Oscillation Estimate . . . . . . . . . . . . . . . . 12
3.2.5. Packet loss . . . . . . . . . . . . . . . . . . . . . 13
3.3. Flow Grouping . . . . . . . . . . . . . . . . . . . . . . 13
3.3.1. Flow Grouping Algorithm . . . . . . . . . . . . . . . 13
3.3.2. Using the flow group signal . . . . . . . . . . . . . 15
3.4. Removing Noise from the Estimates . . . . . . . . . . . . 15
3.4.1. Oscillation noise . . . . . . . . . . . . . . . . . . 15
3.4.2. Clock skew . . . . . . . . . . . . . . . . . . . . . 16
3.5. Reducing lag and Improving Responsiveness . . . . 16
3.5.1. Improving the response of the skewness estimate . 17
3.5.2. Improving the response of the variability estimate 19
4. Measuring OWD . . . . . . . . . . . . . . . . . . . . . . . . 19
4.1. Time stamp resolution . . . . . . . . . . . . . . . . . . 19
5. Implementation status . . . . . . . . . . . . . . . . . . . . 20
6. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . 20
7. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 20
8. Security Considerations . . . . . . . . . . . . . . . . . . . 20
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9. Change history . . . . . . . . . . . . . . . . . . . . . . . 20
10. References . . . . . . . . . . . . . . . . . . . . . . . . . 21
10.1. Normative References . . . . . . . . . . . . . . . . . . 21
10.2. Informative References . . . . . . . . . . . . . . . . . 21
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 22
1. Introduction
In the Internet, it is not normally known if flows (e.g., TCP
connections or UDP data streams) traverse the same bottlenecks. Even
flows that have the same sender and receiver may take different paths
and share a bottleneck or not. Flows that share a bottleneck link
usually compete with one another for their share of the capacity.
This competition has the potential to increase packet loss and
delays. This is especially relevant for interactive applications
that communicate simultaneously with multiple peers (such as multi-
party video). For RTP media applications such as RTCWEB,
[I-D.ietf-rmcat-coupled-cc] describes a scheme that combines the
congestion controllers of flows in order to honor their priorities
and avoid unnecessary packet loss as well as delay. This mechanism
relies on some form of Shared Bottleneck Detection (SBD); here, a
measurement-based SBD approach is described.
1.1. The signals
The current Internet is unable to explicitly inform endpoints as to
which flows share bottlenecks, so endpoints need to infer this from
whatever information is available to them. The mechanism described
here currently utilises packet loss and packet delay, but is not
restricted to these.
1.1.1. Packet Loss
Packet loss is often a relatively rare signal. Therefore, on its own
it is of limited use for SBD, however, it is a valuable supplementary
measure when it is more prevalent.
1.1.2. Packet Delay
End-to-end delay measurements include noise from every device along
the path in addition to the delay perturbation at the bottleneck
device. The noise is often significantly increased if the round-trip
time is used. The cleanest signal is obtained by using One-Way-Delay
(OWD).
Measuring absolute OWD is difficult since it requires both the sender
and receiver clocks to be synchronised. However, since the
statistics being collected are relative to the mean OWD, a relative
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OWD measurement is sufficient. Clock skew is not usually significant
over the time intervals used by this SBD mechanism (see [RFC6817] A.2
for a discussion on clock skew and OWD measurements). However, in
circumstances where it is significant, Section 3.4.2 outlines a way
of adjusting the calculations to cater for it.
Each packet arriving at the bottleneck buffer may experience very
different queue lengths, and therefore different waiting times. A
single OWD sample does not, therefore, characterize the path well.
However, multiple OWD measurements do reflect the distribution of
delays experienced at the bottleneck.
1.1.3. Path Lag
Flows that share a common bottleneck may traverse different paths,
and these paths will often have different base delays. This makes it
difficult to correlate changes in delay or loss. This technique uses
the long term shape of the delay distribution as a base for
comparison to counter this.
2. Definitions
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
document are to be interpreted as described in RFC 2119 [RFC2119].
Acronyms used in this document:
OWD -- One Way Delay
MAD -- Mean Absolute Deviation
RTT -- Round Trip Time
SBD -- Shared Bottleneck Detection
Conventions used in this document:
T -- the base time interval over which measurements are
made.
N -- the number of base time, T, intervals used in some
calculations.
M -- the number of base time, T, intervals used in some
calculations.
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sum_T(...) -- summation of all the measurements of the variable
in parentheses taken over the interval T
sum(...) -- summation of terms of the variable in parentheses
sum_N(...) -- summation of N terms of the variable in parentheses
sum_NT(...) -- summation of all measurements taken over the
interval N*T
E_T(...) -- the expectation or mean of the measurements of the
variable in parentheses over T
E_N(...) -- the expectation or mean of the last N values of the
variable in parentheses
E_M(...) -- the expectation or mean of the last M values of the
variable in parentheses, where M <= N.
max_T(...) -- the maximum recorded measurement of the variable in
parentheses taken over the interval T
min_T(...) -- the minimum recorded measurement of the variable in
parentheses taken over the interval T
num_T(...) -- the count of measurements of the variable in
parentheses taken in the interval T
num_VM(...) -- the count of valid values of the variable in
parentheses given M records
PB -- a boolean variable indicating the particular flow
was identified transiting a bottleneck in the
previous interval T (i.e. Previously Bottleneck)
skew_est -- a measure of skewness in a OWD distribution.
skew_base_T -- a variable used as an intermediate step in
calculating skew_est.
var_est -- a measure of variability in OWD measurements.
var_base_T -- a variable used as an intermediate step in
calculating var_est.
freq_est -- a measure of low frequency oscillation in the OWD
measurements.
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p_l, p_f, p_mad, c_s, c_h, p_s, p_d, p_v -- various thresholds
used in the mechanism
M and F -- number of values related to N
.
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2.1. Parameters and their Effect
T T should be long enough so that there are enough packets
received during T for a useful estimate of short term mean
OWD and variation statistics. Making T too large can limit
the efficacy of freq_est. It will also increase the response
time of the mechanism. Making T too small will make the
metrics noisier.
N & M N should be large enough to provide a stable estimate of
oscillations in OWD. Usually M=N, though having M mean_delay) skew_base_T--
The mean_delay does not include the mean of the current T interval to
enable it to be calculated iteratively.
skew_est = sum_MT(skew_base_T)/num_MT(OWD)
where skew_est is a number between -1 and 1
Note: Care must be taken when implementing the comparisons to ensure
that rounding does not bias skew_est. It is important that the mean
is calculated with a higher precision than the samples.
3.2.3. Variability Estimate
Mean Absolute Deviation (MAD) delay is a robust variability measure
that copes well with different send rates. It can be implemented in
an online manner as follows:
var_base_T = sum_T(|OWD - E_T(OWD)|)
where
|x| is the absolute value of x
E_T(OWD) is the mean OWD calculated in the previous T
var_est = MAD_MT = sum_MT(var_base_T)/num_MT(OWD)
For calculation of freq_est p_v=0.7
For the grouping threshold p_mad=0.1
3.2.4. Oscillation Estimate
An estimate of the low frequency oscillation of the delay signal is
calculated by counting and normalising the significant mean,
E_T(OWD), crossings of mean_delay:
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freq_est = number_of_crossings / N
where we define a significant mean crossing as a crossing that
extends p_v * var_est from mean_delay. In our experiments we
have found that p_v = 0.7 is a good value.
Freq_est is a number between 0 and 1. Freq_est can be approximated
incrementally as follows:
With each new calculation of E_T(OWD) a decision is made as to
whether this value of E_T(OWD) significantly crosses the current
long term mean, mean_delay, with respect to the previous
significant mean crossing.
A cyclic buffer, last_N_crossings, records a 1 if there is a
significant mean crossing, otherwise a 0.
The counter, number_of_crossings, is incremented when there is a
significant mean crossing and decremented when a non-zero value is
removed from the last_N_crossings.
This approximation of freq_est was not used in [Hayes-LCN14], which
calculated freq_est every T using the current E_N(E_T(OWD)). Our
tests show that this approximation of freq_est yields results that
are almost identical to when the full calculation is performed every
T.
3.2.5. Packet loss
The proportion of packets lost over the period NT is used as a
supplementary measure:
pkt_loss = sum_NT(lost packets) / sum_NT(total packets)
Note: When pkt_loss is small it is very variable, however, when
pkt_loss is high it becomes a stable measure for making grouping
decisions.
3.3. Flow Grouping
3.3.1. Flow Grouping Algorithm
The following grouping algorithm is RECOMMENDED for SBD in the RMCAT
context and is sufficient and efficient for small to moderate numbers
of flows. For very large numbers of flows (e.g. hundreds), a more
complex clustering algorithm may be substituted.
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Since no single metric is precise enough to group flows (due to
noise), the algorithm uses multiple metrics. Each metric offers a
different "view" of the bottleneck link characteristics, and used
together they enable a more precise grouping of flows than would
otherwise be possible.
Flows determined to be transiting a bottleneck are successively
divided into groups based on freq_est, var_est, skew_est and
pkt_loss.
The first step is to determine which flows are transiting a
bottleneck. This is important, since if a flow is not transiting a
bottleneck its delay based metrics will not describe the bottleneck,
but the "noise" from the rest of the path. Skewness, with proportion
of packet loss as a supplementary measure, is used to do this:
1. Grouping will be performed on flows that are inferred to be
traversing a bottleneck by:
skew_est < c_s
|| ( skew_est < c_h & PB ) || pkt_loss > p_l
The parameter c_s controls how sensitive the mechanism is in
detecting a bottleneck. C_s = 0.0 was used in [Hayes-LCN14]. A
value of c_s = 0.05 is a little more sensitive, and c_s = -0.05 is a
little less sensitive. C_h controls the hysteresis on flows that
were grouped as transiting a bottleneck last time. If the test
result is TRUE, PB=TRUE, otherwise PB=FALSE.
These flows, flows transiting a bottleneck, are then progressively
divided into groups based on the freq_est, var_est, and skew_est
summary statistics. The process proceeds according to the following
steps:
2. Group flows whose difference in sorted freq_est is less than a
threshold:
diff(freq_est) < p_f
3. Group flows whose difference in sorted E_M(var_est) (highest to
lowest) is less than a threshold:
diff(var_est) < (p_mad * var_est)
The threshold, (p_mad * var_est), is with respect to the highest
value in the difference.
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4. Group flows whose difference in sorted skew_est is less than a
threshold:
diff(skew_est) < p_s
5. When packet loss is high enough to be reliable (pkt_loss > p_l),
group flows whose difference is less than a threshold
diff(pkt_loss) < (p_d * pkt_loss)
The threshold, (p_d * pkt_loss), is with respect to the highest
value in the difference.
This procedure involves sorting estimates from highest to lowest. It
is simple to implement, and efficient for small numbers of flows (up
to 10-20).
3.3.2. Using the flow group signal
Grouping decisions can be made every T from the second T, however
they will not attain their full design accuracy until after the
2*N'th T interval. We recommend that grouping decisions are not made
until 2*M T intervals.
Network conditions, and even the congestion controllers, can cause
bottlenecks to fluctuate. A coupled congestion controller MAY decide
only to couple groups that remain stable, say grouped together 90% of
the time, depending on its objectives. Recommendations concerning
this are beyond the scope of this draft and will be specific to the
coupled congestion controllers objectives.
3.4. Removing Noise from the Estimates
The following describe small changes to the calculation of the key
metrics that help remove noise from them. Currently these "tweaks"
are described separately to keep the main description succinct. In
future revisions of the draft these enhancements may replace the
original key metric calculations.
3.4.1. Oscillation noise
When a path has no bottleneck, var_est will be very small and the
recorded significant mean crossings will be the result of path noise.
Thus up to N-1 meaningless mean crossings can be a source of error at
the point a link becomes a bottleneck and flows traversing it begin
to be grouped.
To remove this source of noise from freq_est:
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1. Set the current var_base_T = NaN (a value representing an invalid
record, i.e. Not a Number) for flows that are deemed to not be
transiting a bottleneck by the first skew_est based grouping test
(see Section 3.3.1).
2. Then var_est = sum_MT(var_base_T != NaN) / num_MT(OWD)
3. For freq_est, only record a significant mean crossing if flow
deemed to be transiting a bottleneck.
These three changes can help to remove the non-bottleneck noise from
freq_est.
3.4.2. Clock skew
Generally sender and receiver clock skew will be too small to cause
significant errors in the estimators. Skew_est and freq_est are the
most sensitive to this type of noise due to their use of a mean OWD
calculated over a longer interval. In circumstances where clock skew
is high, basing skew_est only on the previous T's mean and ignoring
freq_est provides a noisier but reliable signal.
A more sophisticated method is to estimate the effect the clock skew
is having on the summary statistics, and then adjust statistics
accordingly. There are a number of techniques in the literature,
including [Zhang-Infocom02].
3.5. Reducing lag and Improving Responsiveness
Measurement based shared bottleneck detection makes decisions in the
present based on what has been measured in the past. This means that
there is always a lag in responding to changing conditions. This
mechanism is based on summary statistics taken over (N*T) seconds.
This mechanism can be made more responsive to changing conditions by:
1. Reducing N and/or M -- but at the expense of having less accurate
metrics, and/or
2. Exploiting the fact that more recent measurements are more
valuable than older measurements and weighting them accordingly.
Although more recent measurements are more valuable, older
measurements are still needed to gain an accurate estimate of the
distribution descriptor we are measuring. Unfortunately, the simple
exponentially weighted moving average weights drop off too quickly
for our requirements and have an infinite tail. A simple linearly
declining weighted moving average also does not provide enough weight
to the most recent measurements. We propose a piecewise linear
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distribution of weights, such that the first section (samples 1:F) is
flat as in a simple moving average, and the second section (samples
F+1:M) is linearly declining weights to the end of the averaging
window. We choose integer weights, which allows incremental
calculation without introducing rounding errors.
3.5.1. Improving the response of the skewness estimate
The weighted moving average for skew_est, based on skew_est in
Section 3.2.2, can be calculated as follows:
skew_est = ((M-F+1)*sum(skew_base_T(1:F))
+ sum([(M-F):1].*skew_base_T(F+1:M)))
/ ((M-F+1)*sum(numsampT(1:F))
+ sum([(M-F):1].*numsampT(F+1:M)))
where numsampT is an array of the number of OWD samples in each T
(i.e. num_T(OWD)), and numsampT(1) is the most recent; skew_base_T(1)
is the most recent calculation of skew_base_T; 1:F refers to the
integer values 1 through to F, and [(M-F):1] refers to an array of
the integer values (M-F) declining through to 1; and ".*" is the
array scalar dot product operator.
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To calculate this weighted skew_est incrementally:
Notation: F_ - flat portion, D_ - declining portion, W_ - weighted
component
Initialise: sum_skewbase = 0, F_skewbase=0, W_D_skewbase=0
skewbase_hist = buffer length M initialize to 0
numsampT = buffer length M initialzed to 0
Steps per iteration:
1. old_skewbase = skewbase_hist(M)
2. old_numsampT = numsampT(M)
3. cycle(skewbase_hist)
4. cycle(numsampT)
5. numsampT(1) = num_T(OWD)
6. skewbase_hist(1) = skew_base_T
7. F_skewbase = F_skewbase + skew_base_T - skewbase_hist(F+1)
8. W_D_skewbase = W_D_skewbase + (M-F)*skewbase_hist(F+1)
- sum_skewbase
9. W_D_numsamp = W_D_numsamp + (M-F)*numsampT(F+1) - sum_numsamp
+ F_numsamp
10. F_numsamp = F_numsamp + numsampT(1) - numsampT(F+1)
11. sum_skewbase = sum_skewbase + skewbase_hist(F+1) - old_skewbase
12. sum_numsamp = sum_numsamp + numsampT(1) - old_numsampT
13. skew_est = ((M-F+1)*F_skewbase + W_D_skewbase) /
((M-F+1)*F_numsamp+W_D_numsamp)
Where cycle(....) refers to the operation on a cyclic buffer where
the start of the buffer is now the next element in the buffer.
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3.5.2. Improving the response of the variability estimate
Similarly the weighted moving average for var_est can be calculated
as follows:
var_est = ((M-F+1)*sum(var_base_T(1:F))
+ sum([(M-F):1].*var_base_T(F+1:M)))
/ ((M-F+1)*sum(numsampT(1:F))
+ sum([(M-F):1].*numsampT(F+1:M)))
where numsampT is an array of the number of OWD samples in each T
(i.e. num_T(OWD)), and numsampT(1) is the most recent; skew_base_T(1)
is the most recent calculation of skew_base_T; 1:F refers to the
integer values 1 through to F, and [(M-F):1] refers to an array of
the integer values (M-F) declining through to 1; and ".*" is the
array scalar dot product operator. When removing oscillation noise
(see Section 3.4.1) this calculation must be adjusted to allow for
invalid var_base_T records.
Var_est can be calculated incrementally in the same way as skew_est
in Section 3.5.1. However, note that the buffer numsampT is used for
both calculations so the operations on it should not be repeated.
4. Measuring OWD
This section discusses the OWD measurements required for this
algorithm to detect shared bottlenecks.
The SBD mechanism described in this draft relies on differences
between OWD measurements to avoid the practical problems with
measuring absolute OWD (see [Hayes-LCN14] section IIIC). Since all
summary statistics are relative to the mean OWD and sender/receiver
clock offsets should be approximately constant over the measurement
periods, the offset is subtracted out in the calculation.
4.1. Time stamp resolution
The SBD mechanism requires timing information precise enough to be
able to make comparisons. As a rule of thumb, the time resolution
should be less than one hundredth of a typical path's range of
delays. In general, the lower the time resolution, the more care
that needs to be taken to ensure rounding errors do not bias the
skewness calculation.
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Typical RTP media flows use sub-millisecond timers, which should be
adequate in most situations.
5. Implementation status
The University of Oslo is currently working on an implementation of
this in the Chromium browser.
6. Acknowledgements
This work was part-funded by the European Community under its Seventh
Framework Programme through the Reducing Internet Transport Latency
(RITE) project (ICT-317700). The views expressed are solely those of
the authors.
7. IANA Considerations
This memo includes no request to IANA.
8. Security Considerations
The security considerations of RFC 3550 [RFC3550], RFC 4585
[RFC4585], and RFC 5124 [RFC5124] are expected to apply.
Non-authenticated RTCP packets carrying shared bottleneck indications
and summary statistics could allow attackers to alter the bottleneck
sharing characteristics for private gain or disruption of other
parties communication.
9. Change history
Changes made to this document:
WG-03->WG-04 : Add M to terminology table, suggest skew_est based
on previous T and no freq_est in clock skew
section, feedback requirements as a separate sub
section.
WG-02->WG-03 : Correct misspelled author
WG-01->WG-02 : Removed ambiguity associated with the term
"congestion". Expanded the description of
initialisation messages. Removed PDV metric.
Added description of incremental weighted metric
calculations for skew_est. Various clarifications
based on implementation work. Fixed typos and
tuned parameters.
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WG-00->WG-01 : Moved unbiased skew section to replace skew
estimate, more robust variability estimator, the
term variance replaced with variability, clock
drift term corrected to clock skew, revision to
clock skew section with a place holder, description
of parameters.
02->WG-00 : Fixed missing 0.5 in 3.3.2 and missing brace in
3.3.3
01->02 : New section describing improvements to the key
metric calculations that help to remove noise,
bias, and reduce lag. Some revisions to the
notation to make it clearer. Some tightening of
the thresholds.
00->01 : Revisions to terminology for clarity
10. References
10.1. Normative References
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119,
DOI 10.17487/RFC2119, March 1997,
.
10.2. Informative References
[Hayes-LCN14]
Hayes, D., Ferlin, S., and M. Welzl, "Practical Passive
Shared Bottleneck Detection using Shape Summary
Statistics", Proc. the IEEE Local Computer Networks
(LCN) pp150-158, September 2014,
.
[I-D.ietf-rmcat-coupled-cc]
Islam, S., Welzl, M., and S. Gjessing, "Coupled congestion
control for RTP media", draft-ietf-rmcat-coupled-cc-00
(work in progress), September 2015.
[RFC3550] Schulzrinne, H., Casner, S., Frederick, R., and V.
Jacobson, "RTP: A Transport Protocol for Real-Time
Applications", STD 64, RFC 3550, DOI 10.17487/RFC3550,
July 2003, .
Hayes, et al. Expires September 22, 2016 [Page 21]
Internet-Draft SBD for CCC with RTP Media March 2016
[RFC4585] Ott, J., Wenger, S., Sato, N., Burmeister, C., and J. Rey,
"Extended RTP Profile for Real-time Transport Control
Protocol (RTCP)-Based Feedback (RTP/AVPF)", RFC 4585,
DOI 10.17487/RFC4585, July 2006,
.
[RFC5124] Ott, J. and E. Carrara, "Extended Secure RTP Profile for
Real-time Transport Control Protocol (RTCP)-Based Feedback
(RTP/SAVPF)", RFC 5124, DOI 10.17487/RFC5124, February
2008, .
[RFC6817] Shalunov, S., Hazel, G., Iyengar, J., and M. Kuehlewind,
"Low Extra Delay Background Transport (LEDBAT)", RFC 6817,
DOI 10.17487/RFC6817, December 2012,
.
[Zhang-Infocom02]
Zhang, L., Liu, Z., and H. Xia, "Clock synchronization
algorithms for network measurements", Proc. the IEEE
International Conference on Computer Communications
(INFOCOM) pp160-169, September 2002,
.
Authors' Addresses
David Hayes (editor)
University of Oslo
PO Box 1080 Blindern
Oslo N-0316
Norway
Phone: +47 2284 5566
Email: davihay@ifi.uio.no
Simone Ferlin
Simula Research Laboratory
P.O.Box 134
Lysaker 1325
Norway
Phone: +47 4072 0702
Email: ferlin@simula.no
Hayes, et al. Expires September 22, 2016 [Page 22]
Internet-Draft SBD for CCC with RTP Media March 2016
Michael Welzl
University of Oslo
PO Box 1080 Blindern
Oslo N-0316
Norway
Phone: +47 2285 2420
Email: michawe@ifi.uio.no
Kristian Hiorth
University of Oslo
PO Box 1080 Blindern
Oslo N-0316
Norway
Email: kristahi@ifi.uio.no
Hayes, et al. Expires September 22, 2016 [Page 23]