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Network Working Group                                           M. Menth
Internet-Draft                                              F. Lehrieder
Expires: May 22, 2008                            University of Wuerzburg
                                                       November 19, 2007


             Performance Evaluation of PCN-Based Algorithms
                     draft-menth-pcn-performance-01

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Abstract

   This document presents a summary of performance studies for PCN-based
   admission control and flow termination.  The numerical results were
   obtained by simulation or mathematical analysis.


Table of Contents

   1.  Introduction . . . . . . . . . . . . . . . . . . . . . . . . .  4
   2.  Terminology  . . . . . . . . . . . . . . . . . . . . . . . . .  5
   3.  Comparison of Marking Algorithms for PCN-Based Admission
       Control  . . . . . . . . . . . . . . . . . . . . . . . . . . .  6
     3.1.  Definition of Simulated Entities and Simulation Setup  . .  6
       3.1.1.  Metering and Marking Mechanisms  . . . . . . . . . . .  6
       3.1.2.  Congestion Level Estimator . . . . . . . . . . . . . .  6
       3.1.3.  Simulation Setup . . . . . . . . . . . . . . . . . . .  7
     3.2.  Impact of the Marking Threshold T and the Queue Size S . .  8
     3.3.  Two Marking Strategies with Different Admission
           Control Policies . . . . . . . . . . . . . . . . . . . . .  8
       3.3.1.  Marking with Clear Decisions (MCD) . . . . . . . . . .  8
       3.3.2.  Marking with Early Warning (MEW) . . . . . . . . . . .  8
     3.4.  Impact of Ramp Marking . . . . . . . . . . . . . . . . . .  8
     3.5.  Impact of the Memory M of the Congestion Level
           Estimator  . . . . . . . . . . . . . . . . . . . . . . . .  9
     3.6.  Impact of Traffic Characteristics  . . . . . . . . . . . .  9
     3.7.  Response Time of the Marking to Sudden Overload  . . . . . 10
     3.8.  Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 10
   4.  Performance Evaluation of Admission Control with
       Single-Marking . . . . . . . . . . . . . . . . . . . . . . . . 12
     4.1.  Impact on Probing  . . . . . . . . . . . . . . . . . . . . 12
   5.  Performance Evaluation of Measured Rate Termination (MRT)  . . 14
     5.1.  Two Options for MRT  . . . . . . . . . . . . . . . . . . . 14
       5.1.1.  Direct MRT . . . . . . . . . . . . . . . . . . . . . . 14
       5.1.2.  Indirect MRT . . . . . . . . . . . . . . . . . . . . . 14
     5.2.  Impact of Packet Loss  . . . . . . . . . . . . . . . . . . 15
       5.2.1.  Direct MRT under Lose & Mark . . . . . . . . . . . . . 15
       5.2.2.  Indirect MRT under Lose & Mark . . . . . . . . . . . . 15
       5.2.3.  Direct MRT under Mark & Lose . . . . . . . . . . . . . 15
       5.2.4.  Indirect MRT under Mark & Lose . . . . . . . . . . . . 16
       5.2.5.  Summary  . . . . . . . . . . . . . . . . . . . . . . . 16
     5.3.  Unintended Traffic Termination with Indirect MRT
           through Badly Aligned Measurement Intervals  . . . . . . . 16
       5.3.1.  Experiments with Almost CBR Traffic  . . . . . . . . . 17
       5.3.2.  Experiments with VBR Traffic . . . . . . . . . . . . . 17
       5.3.3.  Experiments with On/Off Traffic  . . . . . . . . . . . 17
       5.3.4.  Experiments with Rerouted Traffic  . . . . . . . . . . 18
       5.3.5.  Summary  . . . . . . . . . . . . . . . . . . . . . . . 18



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   6.  Performance Evaluation of Marked Flow Termination on a
       Single Link  . . . . . . . . . . . . . . . . . . . . . . . . . 19
     6.1.  Relative Termination Aggressiveness g_rel  . . . . . . . . 19
     6.2.  Impact of System Parameters  . . . . . . . . . . . . . . . 19
     6.3.  Improvements to the Metering and Marking Algorithm . . . . 20
   7.  Performance Evaluation of Marked Flow Termination (MFT)
       with Multiple Bottleneck Links . . . . . . . . . . . . . . . . 22
     7.1.  Several Serial Links Carrying Only a Common Aggregate  . . 22
     7.2.  Two Serial Links Carrying a Common Aggregate with
           Cross Traffic on the Second Link . . . . . . . . . . . . . 23
     7.3.  Two Serial Links Carrying a Common Aggregate with
           Cross Traffic on the First Link  . . . . . . . . . . . . . 23
     7.4.  Two Serial Links Carrying a Common Aggregate with
           Cross Traffic on Both Links  . . . . . . . . . . . . . . . 24
     7.5.  Summary  . . . . . . . . . . . . . . . . . . . . . . . . . 25
   8.  Changes from Previous Revisions  . . . . . . . . . . . . . . . 26
     8.1.  Changes from Version -00 to Version -01  . . . . . . . . . 26
   9.  References . . . . . . . . . . . . . . . . . . . . . . . . . . 27
     9.1.  Normative References . . . . . . . . . . . . . . . . . . . 27
     9.2.  Informative References . . . . . . . . . . . . . . . . . . 27
     9.3.  Other References . . . . . . . . . . . . . . . . . . . . . 27
   Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 28
   Intellectual Property and Copyright Statements . . . . . . . . . . 29




























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1.  Introduction

   Pre-congestion notification (PCN) is based on the idea of marking
   packets when a certain load threshold on a link is exceeded by PCN
   traffic.  Then, the marking of a packet at the PCN egress node
   provides information whether the rate threshold of at least one link
   of the path over which the packet was carried was exceeded by PCN
   traffic.  This information can be used for admission control and flow
   termination.  Several approaches such as Single-Marking (SM)
   [I-D.charny-pcn-single-marking], CL
   [I-D.briscoe-tsvwg-cl-architecture], 3SM [I-D.babiarz-pcn-3sm] have
   been proposed for that purpose.  An overview of the basic concept is
   given in [I-D.ietf-pcn-architecture].

   The University of Wuerzburg is conducting performance studies to
   understand basic mechanisms and to compare different approaches.
   This document is intended to collect and present summaries of
   performance results documented in more detail in technical papers
   that are available online.  Currently, it covers the following
   studies.

   o  A summary of the results of [TR437] is presented in Section 3.
      [TR437] studies the impact of virtual queue (token bucket)
      parameters on marking results for threshold and ramp marking and
      gives a comparison.

   o  A summary of the results in [Menth07] regarding "Performance
      Evaluation of Admission Control with Single-Marking" is presented
      in Section 4.

   o  A summary of the results in [Menth07] regarding "Performance
      Evaluation of Measured Rate Termination (MRT)" is presented in
      Section 5.

   o  A summary of the results in [Menth07] regarding "Performance
      Evaluation of Marked Flow Termination (MFT) on a Single Link" is
      presented in Section 6.

   o  A summary of the results in [Menth07] regarding "Performance
      Evaluation of Marked Flow Termination (MFT) with Multiple
      Bottleneck Links" is presented in Section 7.

   The next section clarifies some terminology issues.








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2.  Terminology

   The terminology used in this document conforms to the topology of
   [I-D.ietf-pcn-architecture].

   We use the following exceptions for better readability and provide
   the synonyms defined in [I-D.ietf-pcn-architecture].

   o  Admissible rate: PCN-lower-rate

   o  Supportable rate: PCN-upper-rate

   o  Admission-stop marking: first encoding or PCN-lower-rate-marking

   o  Excess-traffic marking: second encoding or PCN-upper-rate-marking




































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3.  Comparison of Marking Algorithms for PCN-Based Admission Control

   The following presents a short summary of [TR437] without the graphs
   and exact numerical results that are provided in the technical
   report.  The interested reader is referred to that document.

3.1.  Definition of Simulated Entities and Simulation Setup

   In this study, we investigate the behaviour of different metering and
   marking algorithms under different configuration and use a congestion
   level estimator to observe the packet markings.

3.1.1.  Metering and Marking Mechanisms

   PCN requires metering and marking algorithms in the interior nodes.
   [TR437] defines

   o  threshold marking and

   o  ramp marking

   based on a virtual queue (VQ), but there are equivalent descriptions
   based on token buckets.

   The parameters are

   o  the size S of the VQ,

   o  the rate R of the VQ,

   o  the marking threshold T for threshold marking, which is also the
      upper threshold for ramp marking,

   o  the marking threshold T_ramp, which is the lower threshold for
      ramp marking

3.1.2.  Congestion Level Estimator

   Furthermore, a congestion level estimator is defined that calculates
   a congestion level estimate (CLE) at the PCN egress node based on an
   exponentially weighted moving average (EWMA).  Marked packets count 1
   and unmarked packets count 0.  The CLE is computed as

   CLE = w o CLE + (1 - w) o X

   where X is the observed packet marking and w<1 is the weight
   parameter.  If w is large, CLE has a long memory M, if it is low, CLE
   has a short memory M. The time between CLE updates also influences



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   the memory M. A formal definition of the memory M is given in 3.4.2
   of [TR437].  The CLE is used to observe the packet markings of the
   simulations.

3.1.3.  Simulation Setup

   We simulate a single link scenario.  Packets from n independent,
   homogeneous traffic sources are multiplexed onto a single link with
   infinite bandwidth and pass a meter and marker.  The markings are
   evaluated by a subsequent congestion level estimator.

   If not mentioned differently, we simulate around n = 100 homogeneous
   flows for sufficiently long time to obtain reliable results.
   However, we omit confidence intervals in all our graphs for the sake
   of clarity.  We choose a Gamma distribution to generate the inter-
   arrival times A between consecutive packets within a flow with a mean
   of E[A] = 20 ms and a coefficient of variation of cvar[A] = 0.1.  The
   packet sizes B are independent and distributed according to a
   deterministic phase of 30 bytes plus a negative binomial
   distribution.  Their overall mean is E[B] = 60 bytes and their
   coefficient of variation is cvar[B] = 0.5.  The values for E[A] and
   E[B] are motivated by typical voice connections that periodically
   send every 20 ms a packet with 20 bytes payload using a 40 bytes IP/
   UDP/RTP header.  However, our flow model is not periodic and has
   variable packet sizes.  We use it for two reasons.  The simulation of
   multiplexed, strictly periodic traffic requires special care due to
   the non-ergodicity of the system and is very time consuming.
   Therefore, we relax cvar[A] = 0.0 to cvar[A] = 0.1.  Furthermore, we
   use cvar[B] = 0.5 instead of cvar[B] = 0.0 because realtime traffic
   consists of packets from different applications with and without
   compression which leads to different packet sizes.

   However, our findings are general and do not depend on special
   parameter settings.  The rate of the virtual queue is R = 2.4 Mbit/s
   such that at most 100 flows can pass unmarked.  The congestion level
   estimator implements an exponentially weighted moving average (EWMA)
   and counts packets with admission-stop marks as 1 and those without
   as 0.  As mentioned previously, its memory M depends on the packet
   rate and the weight parameter w such that w needs to be adapted to
   the desired M and the packet frequency in the experiment for which we
   take the maximum packet rate that can pass unmarked.  Thus, we set
   the weight parameter to w = 0.998 which corresponds to a memory of
   0.1 s when 100 default flows are active.  If the packet rate changes
   due to more bursty traffic, we adapt the weight parameter w to
   achieve the same memory.






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3.2.  Impact of the Marking Threshold T and the Queue Size S

   We measure the percentage of marked packets depending on the PCN rate
   (number of flows n) and the queue parameters size S and marking
   threshold T. The ideal marker marks

   1.  no packets if the PCN rate is below the VQ rate R and

   2.  all packets if it is above.

   We found out that

   1.  is increasingly achieved with increasing threshold T and

   2.  is increasingly achieved with increasing remaining queue size
       S-T.

3.3.  Two Marking Strategies with Different Admission Control Policies

   We construct threshold markers with two different CLE characteristics
   (=function describing the percentage of marked packets depending on
   PCN rate).

3.3.1.  Marking with Clear Decisions (MCD)

   Marking with clear decisions (MCD) means that the above objectives
   (1) and (2) are well achieved.  This can be obtained for threshold
   marking with a large marking threshold T and a large remaining queue
   size S - T. Then, hardly any fluctuations in marking are observed.

3.3.2.  Marking with Early Warning (MEW)

   Marking with early warning (MEW) means that (3) the percentage of
   marked packets already increases when the PCN rate approaches the VQ
   rate and (4) is 100% when the PCN rate is above the VQ rate.  This
   can be obtained for threshold marking with a small marking threshold
   T and a large remaining queue size S - T.

3.4.  Impact of Ramp Marking

   Ramp marking already marks packets probabilistically if the virtual
   queue length is below the marking threshold T. Therefore, it marks
   more packets than threshold marking with the same marking threshold T
   and queue size S. In our study we always set the lower marking
   threshold to T_ramp = 0.  We found out that ramp marking with this
   configuration cannot achieve MCD because it marks a small percentage
   of packets when the PCN rate is below the VQ rate, but it can well
   achieve MEW.  MEW can be achieved both with threshold and ramp



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   marking, but threshold marking requires a smaller threshold parameter
   T to get the same marking results as with ramp marking.

3.5.  Impact of the Memory M of the Congestion Level Estimator

   The memory M of the congestion level estimator does not have an
   impact on the percentage of marked packets that were observed over
   the simulation time, but it impacts the degree to which the CLE
   fluctuates.  If the memory is long, the fluctuation of CLE is small.
   If the memory M is short, the fluctuation of CLE is large.  When we
   configure the queue for MCD, i.e., the threshold T and the remaining
   queue size S-T were chosen sufficiently large, the CLE is almost 0
   for PCN rates smaller than the VQ rate and it is 1 for PCN rates
   larger than the VQ rate.  This holds even for a very small memory M
   of the congestion level estimator.

3.6.  Impact of Traffic Characteristics

   Traffic characteristics have a significant impact on the marking
   result.

   o  Decreased variance of packet sizes: no impact on the CLE
      characteristics in case of MCD, slightly lower curves in case of
      MEW

   o  Increased variance of packet sizes: little impact on the CLE
      characteristics in case of MCD, significantly higher curves in
      case of MEW and larger fluctuation of CLE

   o  Increased aggregation level: no impact on the CLE characteristics
      in case of MCD, slightly higher curves in case of MEW and less
      fluctuation of CLE

   o  Increased variance of inter-arrival times: little impact on the
      CLE characteristics in case of MCD, slightly higher curves in case
      of MEW and larger fluctuation of CLE

   o  Increased burstiness (fewer but larger packets): little impact on
      the CLE characteristics in case of MCD, significantly higher
      curves in case of MEW and large fluctuations of CLE

   o  On/off traffic instead of continuous flows: large impact on the
      CLE characteristics in case of MCD and MEW, in particular very
      large fluctuations of the CLE







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3.7.  Response Time of the Marking to Sudden Overload

   Large marking thresholds T and remaining queue sizes S-T lead to
   stable marking results for MCD, but large parameters slow down the
   reaction time of the marker when the PCN rate exceeds the VQ rate.

3.8.  Conclusion

   One option for pre-congestion notification (PCN) based admission
   control requires that all packets are marked if the current link rate
   exceeds a pre-configured admissible rate.  This can be achieved by
   virtual queue based marking algorithms such as simple threshold
   marking or more complex ramp marking.

   The objective of [TR437] was to study how marking algorithms can
   support admission control in order to limit the utilization of the
   links of a network.  We did not consider the use of marking
   algorithms to support admission control in order to limit the packet
   delay because we assume that PCN will be used in high-speed networks
   where packet delay caused by queuing is negligible as long as link
   utilizations are moderate.

   We investigated the influence of the parameters of the marking
   algorithms on their marking results which are translated into a
   congestion level estimate (CLE) using EWMA-based averaging.  We
   showed that two different marking strategies can be pursued: marking
   such that the CLE leads to clear decisions (MCD) and marking such
   that the CLE yields early warning (MEW) when the rate of PCN traffic
   on a link approaches its admissible rate.  We provided
   recommendations for the configuration of the marking threshold T and
   the size S of the virtual queue in both cases.  Ramp marking
   increases the level of early warning compared to threshold marking,
   but this can be approximated by smaller marking thresholds for simple
   threshold marking such that there is no obvious need for ramp
   marking.

   The CLE values for MEW fluctuate, therefore, it is difficult to infer
   the exact, current traffic rate from the CLE values which is required
   to take advantage of early warning.  A sensitivity study revealed
   that the average CLE values for MEW depend heavily on the traffic
   characteristics.  This makes the use of early warning difficult:
   either the marking parameters need to be adapted to produce similar
   warnings for different traffic types or the mechanism taking early
   warning into account requires knowledge about the traffic
   characteristics to correctly interpret the CLE level.  In contrast,
   CLE values for MCD show hardly any variation and are robust against
   different traffic types.




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   For the sake of simplicity, we advocate for the use of MCD for PCN
   based admission control instead of MEW because the interpretation of
   early warning is difficult due to its high variation and dependency
   on traffic characteristics.  Furthermore, we think that ramp marking
   is not needed for PCN since similar markings can be obtained by
   appropriately configured threshold marking and we do not see any
   benefit that justifies the implementation complexity of ramp marking.












































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4.  Performance Evaluation of Admission Control with Single-Marking

   When the PCN rate exceeds the admissible rate of a link, all unmarked
   packets are re-marked to "admission-stop" in the CL
   [I-D.briscoe-tsvwg-cl-architecture] and 3sm [I-D.babiarz-pcn-3sm]
   proposal.  This is different with Single-Marking (SM)
   [I-D.charny-pcn-single-marking] since it marks only those packets
   with "admission-stop" that exceed the admissible rate.

4.1.  Impact on Probing

   In SM, the egress node calculates the fraction of marked and all
   packets which is the so-called congestion level estimate (CLE).  If
   the CLE exceeds the admission-stop threshold of about 4 %, the
   ingress node stops the admission of further flows.  If the CLE falls
   below an admission-continue threshold of about 2 %, the ingress node
   continues the admission of further flows.  To support probing, SM
   needs to send several probe messages because if the admissible rate
   of a link is exceeded by the current PCN rate, only a fraction of the
   packets is marked and this fraction is the current CLE value which
   can be interpreted as marking probability.  When n_p probe messages
   are used for probing, the new flow is rejected when at least one
   message returns with an admission-stop mark.  However, an error
   probability remains that can be computed as follows:

   p_err(CLE, n_p) = (1 - CLE)^(n_p)

   This error probability decreases exponentially with an increasing
   number of probe packets and it significantly depends on the CLE
   value.  The question in practice is: how many probes are required to
   achieve a reliable probing method, i.e. the error probability of
   probing is less than p_max^err?  To that end, we find

   n_min(CLE,p_max^err)

   = min_(n_p) ( p_err(CLE, n_p) < p_max^err )

   = ceil(log(p_max^err )/log(1 - CLE)).

   We the following table shows the minimum number of probes
   n_min(CLE,p_max^err) required to achieve a probing reliability of
   p_max^err when the fraction of marked packets is CLE.









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   Table 1: Minimum number of required probe packets depending
   on the CLE and the desired reliability p_max^err.
   +---------------------------------------------------------+
   |CLE      | 0.01 | 0.02 | 0.04 | 0.05 | 0.1 | 0.15 | 0.20 |
   +---------------------------------------------------------+
   | 10%     |  230 |  114 |   57 |   45 |  22 |   15 |   11 |
   | 1%      |  459 |  228 |  113 |   90 |  44 |   29 |   21 |
   | 0.1%    |  688 |  342 |  170 |  135 |  66 |   43 |   31 |
   +---------------------------------------------------------+
   |p_max^err|    minimum number of required probe packets   |
   +---------------------------------------------------------+

   Thus, the number of required probe messages to achieve a reliable
   probing method is rather large.  To get representative probes, the
   messages should not be sent in one shot but rather with exponential
   inter-arrival times [SoBa05] such that the large number of required
   probes causes substantial delay.


































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5.  Performance Evaluation of Measured Rate Termination (MRT)

   Measured rate termination (MRT) assumes that PCN interior nodes mark
   packets with "excess-traffic" (ET) when they exceed the supportable
   rate (SR) of a link with some tolerance.  This marking is explained
   in [I-D.babiarz-pcn-3sm] and used in the CL architecture
   [I-D.briscoe-tsvwg-cl-architecture].  The PCN egress node measures
   the rate of marked and unmarked packets and communicates them to the
   PCN egress node.  Based on this information, the PCN ingress node
   calculates the rate that needs to be terminated and chooses an
   appropriate set of flows for termination.  This is not a trivial task
   since the rate of the flows are possibly unknown, but we do not
   further study this issue.  There are two options for MRT: direct and
   indirect MRT.

5.1.  Two Options for MRT

5.1.1.  Direct MRT

   The PCN egress node measures the rate of ET-marked packets per
   ingress-egress aggregate.  If this excess traffic rate (ETR) is
   larger than zero, the PCN egress node communicates it to the
   corresponding PCN ingress node using a "traffic-reduction" message.
   Then, the PCN ingress node terminates sufficiently many flows to
   achieve a reduction of that rate.  A minimum interval, a so-called
   inter-termination time, is required between consecutive rate-
   reduction messages because it takes some time until the effect of the
   previous termination action becomes visible in the measured rate of
   ET-marked traffic at the PCN egress node.  Direct MRT is used as a
   non-standard option to terminate traffic in the E3Tunnel deployment
   model of 3sm [I-D.babiarz-pcn-3sm].

5.1.2.  Indirect MRT

   The marking is again the same as in the CL architecture.  In contrast
   to direct MRT, with indirect MRT the PCN egress node measures the
   rate of traffic that is not marked with ET (nETR) per ingress-egress-
   aggregate.  This is the so-called sustainable rate and the PCN egress
   node immediately sends it to the PCN ingress node.  The PCN ingress
   node measures the rate of traffic to be transmitted per ingress-
   egress aggregate, the so-called ingress rate (IR).  When the PCN
   ingress node receives the sustainable rate from the PCN egress node,
   it calculates the difference between the timely corresponding ingress
   rate and sustainable rate.  This difference is positive if traffic
   had been ET-marked because then the ingress rate is larger than the
   sustainable rate.  If the difference is positive, it is used as an
   estimate for the traffic that should be terminated.  Indirect MRT is
   used as the preferred option in [I-D.briscoe-tsvwg-cl-architecture].



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5.2.  Impact of Packet Loss

   Packet loss has an impact on the rate of marked and unmarked packets
   received by the PCN egress node.  In addition, the fraction of marked
   and unmarked packets depends on whether packets are first lost or
   marked.  We illustrate this issue on a link with 8 Mbit/s and its
   supportable rate being set to 4 Mbit/s.  Due to a reroute or some
   other reason, the link is suddenly confronted with a traffic rate of
   16 Mbit/s.  We consider the behaviour of direct and indirect MRT
   under the conditions that traffic is first lost and then marked (L&M)
   or first marked and then lost (M&R).

5.2.1.  Direct MRT under Lose & Mark

   Under L&M, 8 Mbit/s are lost. 4 Mibt/s out of the remaining 8 Mbit/s
   are AS-marked and the remaining 4 Mbit/s are ET-marked.  As a
   consequence, 4 Mbit/s are terminated such that 12 Mbit/s will remain
   for the next round.  Then, 4 Mbit/s are lost. 4 Mibt/s out of the
   remaining 8 Mbit/s are AS-marked and the remaining 4 Mbit/s are ET-
   marked.  As a consequence, 4 Mbit/s are terminated such that 8 Mbit/s
   will remain for the next round.  Then, no traffic is lost anymore,
   but out of the 8 Mbit/s 4 Mbit/s are AS-marked and the remaining 4
   Mbit/s are ET-marked.  When these 4 Mbit/s have been terminated,
   there is no overload anymore.

5.2.2.  Indirect MRT under Lose & Mark

   Under L&M, 8 Mbit/s are lost. 4 Mibt/s out of the remaining 8 Mbit/s
   are AS-marked and the remaining 4 Mbit/s are ET-marked.  As a
   consequence, there is a sustainable rate of 4 Mbit/s such that 12
   Mbit/s are terminated.  Thus, the overload is already removed after a
   single termination step.

5.2.3.  Direct MRT under Mark & Lose

   Under M&L, 4 Mbit/s out of the initial 16 Mbit/s are AS-marked and
   the remaining 12 Mbit/s are ET-marked.  Then, 8/16 of the traffic is
   lost such that 6 Mbit/s arrive with ET-marks.  After 6 Mbit/s are
   terminated, the system is still confronted with a load of 10Mbit/s
   out of which 4Mbit/s are AS-marked and the remaining 6 Mbit/s are ET-
   marked.  Then, 2/10 of the traffic is lost such that 5.2 Mbit/s
   arrive with ET-marks.  After 5.2 Mbit/s are terminated, the system is
   confronted with a load of 4.8 Mbit/s out of which 4 Mibt/s are AS-
   marked and the remaining 0.8 Mbit/s are ET-marked.  As no loss occurs
   anymore, these 0.8 Mbit/s are terminated such that there is no
   overload anymore.





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5.2.4.  Indirect MRT under Mark & Lose

   Under M&L, 4 Mbit/s out of the initial 16 Mbit/s are AS-marked and
   the remaining 12 Mbit/s are ET-marked.  Then, 8/16 of the traffic is
   lost such that 6 Mbit/s arrive with ET-marks.  As a consequence,
   there is a sustainable rate of 2 Mbit/s such that 14 Mbit/s are
   terminated.  Thus, the overload is already removed after a single
   termination step, but with a substantial amount of overtermination.

5.2.5.  Summary

   Table 2 summarizes the termination behavior of direct and indirectMRT
   under L&M and M&L conditions.  With indirectMRT, sudden SR-overload
   is removed after a single termination step while for direct MRT, the
   removal of SR-overload requires several termination steps.  When
   packet loss occurs before packets are marked by the meter and marker,
   indirect MRT works well.  However, when packets are metered and
   marked before they are lost, then indirectMRT can lead to substantial
   overtermination.

   Table 2: Impact of the order of packet marking and loss on the
   termination behavior with direct and indirect MRT.
   +-----------------------------------------------------------------+
   |       Time      | Lose&Mark | Lose&Mark | Mark&Lose | Mark&Lose |
   |                 | Direct MRT| Ind. MRT  | Direct MRT| Ind. MRT  |
   +-----------------------------------------------------------------+
   |Start of overload|16.0 Mbit/s|16.0 Mbit/s|16.0 Mbit/s|16.0 Mbit/s|
   |After 1st term.  |12.0 Mbit/s| 4.0 Mbit/s|10.0 Mbit/s| 2.0 Mbit/s|
   |After 2nd term.  | 8.0 Mbit/s| 4.0 Mbit/s| 5.2 Mbit/s| 2.0 Mbit/s|
   |After 3rd term.  | 4.0 Mbit/s| 4.0 Mbit/s| 4.0 Mbit/s| 2.0 Mbit/s|
   +-----------------------------------------------------------------+

5.3.  Unintended Traffic Termination with Indirect MRT through Badly
      Aligned Measurement Intervals

   Indirect MRT compares the rate of non-ET marked traffic (nETR) at the
   egress node and compares it with the rate of the PCN traffic at the
   ingress node (IR).  This implies that the same packets are measured
   in the corresponding measurement intervals which is hard to achieve.
   When the delay between PCN ingress and egress node is some fixed
   transmission delay X, the measurement interval at the PCN egress node
   needs to start X time later than the corresponding one at the PCN
   ingress node and it must have the same length to observe the same set
   of packets.  However, X is not exactly fixed due to queuing and other
   effects.  Therefore, exact alignment cannot be achieved.  This
   possibly leads to wrong rate differences when results from badly
   aligned measurement intervals are compared.  In this section, we
   investigate its impact as it can lead to unintended traffic



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   termination.

   We use a measurement interval length of 100 ms and the misalignment
   is 50 ms such that the first packet in the measurement interval a the
   PCN egress is contained in the measurement interval at the PCN
   ingress.

5.3.1.  Experiments with Almost CBR Traffic

   First, we use exactly periodic constant bit rate (CBR) traffic and
   several variants of almost periodic or almost CBR traffic.  Those are
   CBR traffic with at most 1 ms uniformly distributed packet arrival
   delays and constant packet sizes, exactly periodic traffic with
   little variation in packet sizes (coefficient of variation cvar[B] =
   0.1), and almost periodic traffic with little variation in packet
   inter-arrival times (coefficient of variation cvar[A] = 0.1) and
   constant packet sizes.  We consider n = 200 flows and the supportable
   rate is set to infinity such that no packet is marked.  Experiments
   show that in case of exact periodicity and equal packet sizes, no
   flows are terminated.  This is different, when little variation is
   introduced where flows are continuously terminated without any packet
   being lost or ET-marked.

   To repair this, we enhance the indirect MRT method by the side
   condition, that flows are only terminated if a tolerance of Tf is
   exceeded.  This tolerance is usually given as a rate, but we think of
   it as a number of flows as we deal only with equal rate flows in this
   section.  Experiments show that a tolerance of T_f = 1 flow removes
   the unintended flow termination effect.

5.3.2.  Experiments with VBR Traffic

   We now conduct the same experiment with more variable traffic and
   study the impact of different tolerance values T_f on unintended
   traffic termination.  We performed experiments for exactly periodic
   flows having packet sizes with the same mean E[B] = 200 bytes but a
   coefficient of variation of cvar[B] = 0.5 and experiments for flows
   with constant packet sizes but inter-arrival times with the same mean
   E[A] = 20 ms but a coefficient of variation of cvar[A] = 0.5.  In
   both cases, a tolerance value of T_f = 1 flow cannot avoid unintended
   flow termination and even a tolerance of T_f = 5 flows cannot fully
   remove it.

5.3.3.  Experiments with On/Off Traffic

   We now look at on/off traffic, i.e. traffic sources have
   exponentially distributed on and off phases during which they send
   CBR traffic or are silent.  We performed experiments for mean phase



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   durations of 0.5 s and 5 s, respectively.  Again, we see substantial
   unintended flow termination that is mitigated by an increasing
   tolerance value T_f.

5.3.4.  Experiments with Rerouted Traffic

   In the presence of network failures, large amounts of traffic are
   rerouted, i.e. shifted to other links.  The PCN ingress and egress
   nodes perform rate measurement using intervals of length of 100 ms
   starting at a global time of 0 s.  We simulate what happens in such a
   scenario at the PCN ingress node.  At time 50 ms a reroute of 8Mbit/s
   occurs at the PCN ingress node and after another 50 ms the traffic
   arrives at the PCN egress node.  At that time, the PCN egress node
   measures a sustainable rate of 0 Mbit/s for its first measurement
   interval and sends this value to the PCN ingress node.  At time 150
   ms this value arrives there and the PCN ingress node compares the
   ingress rate of 4 Mbit/s measured in the first measurement interval
   with the sustainable rate of 0 Mbit/s.  As a consequence, it
   terminates 4 Mbit/s.

5.3.5.  Summary

   The disadvantage of indirect MRT is that the measurement intervals at
   the PCN ingress and egress nodes require some timely alignment.
   Otherwise, unintended small positive differences can occur without
   any traffic being ET-marked or lost which results in unintended
   traffic termination.  Therefore, the traffic rate to be terminated
   needs to exceed a tolerance threshold $T_f$ before traffic is really
   terminated.  However, it turns out that the value of that threshold
   should increase with increasing traffic variability.  Moreover, in
   case of sudden extra traffic as it can occur with reroutes, a
   substantial fraction of the traffic can be terminated without any
   packets being ET-marked.


















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6.  Performance Evaluation of Marked Flow Termination on a Single Link

   Marked flow termination (MFT) is used in 3sm [I-D.babiarz-pcn-3sm].
   In contrast to measured rate termination (MRT) it requires that the
   metering and marking algorithms in interior nodes mark only some of
   the traffic that exceeds the supportable rate.  This is done by
   adding a slowdown factor of "S" tokens to the bucket whenever a
   packet is marked with ET.  This is called marking frequency reduction
   (MFR).

6.1.  Relative Termination Aggressiveness g_rel

   Given the average flow rate r_f, the flow termination time D_T, and
   the slowdown factor S, we can define the relative termination
   aggressiveness

   g_rel = r_f * D_T / S.

   The termination behaviour of an MFT system is the function describing
   the time-dependent rate from the beginning of the overload until
   termination of further flows stops.  Most interesting is the time to
   remove the SR-overload and the overtermination which is the
   percentage of traffic relative to the supportable rate that was
   unintentionally terminated.

6.2.  Impact of System Parameters

   Adapting the slowdown factor S for different flow rates r_avg caused
   by different inter-arrival times or packet sizes produces can achieve
   the same relative termination aggressiveness.  This produces the same
   termination behaviour.

   We performed experiments showing

   o  an increasing aggressiveness leads to shorter time to remove the
      overload, but to more overtermination

   o  a decreasing aggressivenss leads to longer time to remove the
      overload, but to less overtermination

   A relative termination aggressiveness of g_rel=0.5 leads to short
   time to remove overload and avoids overtermination.

   Different degrees of SR-overload and different aggregation levels
   (n=10, 100, 1000 flows) lead to different curves but to similar time
   to remove the overload and to the same overtermination.

   On/off traffic leads to the same termination behaviour if the on/off



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   phases are sufficiently long (10 ms), in case of short phase
   durations the time to reduce overload is longer, but it also works
   well.

   Increasing flow termination delay D_T extends the time to remove
   overload linearly, but it has no influence on the overtermination.
   Flows with different termination delays see the same termination
   probability.

   Modifying the inter-arrival time or the packet size changes the
   average flow rates.  Keeping the slowdown factor constant also
   changes the relative termination aggressiveness such that the time to
   reduce overload and the overtermination differs significantly.  Flows
   with larger packets or more frequent packets face a larger flow
   blocking probability.

6.3.  Improvements to the Metering and Marking Algorithm

   The objective is to make the termination behaviour insensitive to
   different packet sizes.  To that end, two different improvements are
   introduced.

   o  Packet size independent marking (PSIM) marks a packet already if
      the token bucket has less tokens than the maximum transfer unit
      (MTU) instead of the actual packet size.

   o  Proportional marking frequency reduction (PMFR) adds packet.size/
      MTU*S tokens to the bucket whenever a packet is marked.

   Both improvements are documented in [I-D.babiarz-pcn-3sm].  PSIM
   achieves that the termination probability of a flows is independent
   of its packet size.  PMFR achieves that the termination behaviour of
   the same for different aggregates irrespective of the average packet
   size.  Both options are simple to implement and their combination
   achieves that the relative termination aggressiveness becomes
   independent of packet sizes.  It can be calculated by

   g_rel = MTU * D_T / S / E[A].

   Thus the termination behaviour only depends on the average inter-
   arrival time E[A].  This has also a rather strong effect on the
   relative termination aggressiveness, but given the fact that most
   real-time applications have E[A] between 10 ms and 40 ms allows the
   following robust configuration.  Setting S such that a relative
   aggressiveness of g_rel=0.5 is achieved for E[A]=20 ms, leads to at
   most 10% overtermination for E[A]=10 ms and to a time to remove
   overload of not more than 10*D_T. Different tradeoffs can be chosen.
   This analysis shows that marking frequency reduction (MFT) can be



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   well controlled when the marking algorithm implements PMFR with PSIM.


















































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7.  Performance Evaluation of Marked Flow Termination (MFT) with
    Multiple Bottleneck Links

   In the presence of several bottleneck links, flows can be ET-marked
   by different interior nodes.  As a consequence, an overloaded link
   loses flows whose packets were ET-marked by itself, but it also loses
   flows whose packets were ET-marked by another overloaded link.  This
   impacts the termination speed and possibly leads to unintended
   overtermination.  To avoid this effect, we propose to remove S bytes
   from the virtual queue for each ET-marked packet sent over the
   corresponding link (general MFR) and not only for each packet that
   has been ET-marked by that link itself (local MFR).  We illustrate
   the impact of this change to the metering algorithm.

7.1.  Several Serial Links Carrying Only a Common Aggregate

   We start with a single aggregate crossing several links as shown in
   Figure 1.  All links have a supportable rate of 4Mbit/s such that 125
   flows can be supported.  However, the observed aggregate initially
   carries 8 Mbit/s.  Simulation results show that with local MFR, the
   aggregate rate is reduced to 3.0 Mbit/s, 2.15 Mbit/s, and to 1.6
   Mbit/s in case of 2, 3, and 4 consecutive links.  In contrast, with
   global MFR, the aggregate rate decreases only to 3.9 Mbit/s in all
   studied scenarios.  Thus, we observe a significant degree of
   overtermination for local MFR while with global MFR the reduction of
   the traffic rate meets the expected value quite well and
   independently of the number of serial bottlenecks.

                    +-----------+   +-----------+   +-----------+
   Aggregate a0  ---|           |---|           |---|           |---
                    +-----------+   +-----------+   +-----------+
                       Link l0         Link l1         Link l2

   Several serial links carry only a common aggregate.

                                 Figure 1

   To reconstruct this experiment, it is important to avoid the
   synchronization of the consecutive meters which is achieved when they
   are configured with (a) the same supportable rate (SR) and (b) the
   same supportable burst size (SBS) and (c) the same slowdown factor S,
   and (d) if there is no cross traffic at all.  In our first experiment
   depicted in Figure Figure 1, we have chosen a slightly different SR
   for each link.  In the other experiments that are depicted in
   Figure 2- Figure 4, the links carry cross traffic such that
   precondition (d) for the synchronization effect is violated anyway.





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7.2.  Two Serial Links Carrying a Common Aggregate with Cross Traffic on
      the Second Link

   We consider two serial links carrying an aggregate a0 and the second
   link carrying cross traffic from an aggregate a1 (cf. Figure 2).

       +-----------+   +-----------+
    ---|           |---|           |--- Aggregate a0
       +-----------+   |           |--- Aggregate a1
                      /+-----------+
          Link l0    /     Link l1

   Two serial links carrying a common aggregate with cross traffic on
   the second link.

                                 Figure 2

   The first link l0 has SR(l0) = 4 Mbit/s and the second link l1 has
   SR(l1) = 8Mbit/s.  Initially, there is an SR-overload of 100% since
   both aggregates carry 8 Mbit/s.  Simulation results show that the
   rate of aggregate a0 decreases from 8 Mbit/s to 2.9 Mibt/s with local
   MFR and to 3.0 Mbit/s with global MFR.  The rate of aggregate a1
   (cross traffic) is reduced from 8 Mibt/s to 4.4 Mbit/s with local MFR
   and to 4.8 Mbit/s with global MFR.  As a consequence, the remaining
   rate on the second link l1 is 7.3Mbit/s with localMFR and 7.8Mbit/s
   with globalMFR.  Thus, global MFT leads to visibly less terminated
   traffic in this experiment.

7.3.  Two Serial Links Carrying a Common Aggregate with Cross Traffic on
      the First Link

   We consider two serial links carrying an aggregate a0 and the first
   link carrying cross traffic from an aggregate a1 (cf. Figure 3).

                   +-----------+   +-----------+
   Aggregate a0 ---|           |---|           |---
                   |           |   +-----------+
                  /+-----------+\
   Aggregate a1  /    Link l0    \    Link l1

   Two serial links carrying a common aggregate with cross traffic on
   the first link.

                                 Figure 3

   We consider two serial links carrying an aggregate a0 and the first
   link carrying cross traffic from an aggregate a1 (cf. Figure 3).  The
   first link l0 has SR(l0) = 8 Mbit/s and the second link l1 has SR(l1)



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   = 4 Mbit/s.  Initially, there is an SR-overload of 100% since both
   aggregates carry 8 Mbit/s.  Initially, there is an SR-overload of
   100% since both aggregates carry 8 Mbit/s.  Simulation results show
   that the rate of aggregate a0 decreases from 8 Mbit/s to 2.8 Mibt/s
   with local MFR and to 3.8 Mbit/s with global MFR.  The rate of
   aggregate a1 (cross traffic) is reduced from 8 Mibt/s to 4.5 Mbit/s
   with local MFR and to 4.0 Mbit/s with global MFR.  As a consequence,
   the remaining rate on the second link l0 is 7.3 Mbit/s with local MFR
   and 7.8 Mbit/s with global MFR.  Thus, global MFT leads to visibly
   less terminated traffic in this experiment and to a fairer treatment
   of flows crossing a different numbers of bottlenecks.

7.4.  Two Serial Links Carrying a Common Aggregate with Cross Traffic on
      Both Links

   We consider two serial links carrying a common aggregate with cross
   traffic on both links (cf. Figure 4).

                   +-----------+     +-----------+
   Aggregate a0 ---|           |-----|           |---
   Aggregate a1 ---|           |     |           |--- Aggregate a2
                   +-----------+\   /+-----------+
                      Link l0    \ /    Link l1

   Two serial links carrying a common aggregate with cross traffic on
   both links.

                                 Figure 4

   We consider two serial links carrying an aggregate a0.  The first
   link carries cross traffic from aggregate a1 and the second link
   carries cross traffic from aggregate a2 (cf. Figure 4).  Both links
   have a supportable rate of 8 Mbit/s.  Initially, there is an SR-
   overload of 100% since all three aggregates carry 8 Mbit/s.
   Simulation results show that the rate of aggregate a0 decreases from
   8 Mbit/s to 2.6 Mibt/s with local MFR and to 2.7 Mbit/s with global
   MFR.  The rate of aggregate a1 (cross traffic on link l0) is reduced
   from 8 Mibt/s to 4.5 Mbit/s with local MFR and to 4.3 Mbit/s with
   global MFR and the one of aggregate a2 (cross traffic on link l1) is
   reduced from 8 Mibt/s to 4.3 Mbit/s with local MFR and to 5.1 Mbit/s
   with global MFR.  As a consequence, the remaining rate on the first
   link l0 is 7.2 Mbit/s with local MFR and 7.8 Mbit/s with global MFR
   and the one on the second link l1 is 7.2 Mbit/s with local MFR and
   7.1 Mbit/s with global MFR.  Thus, global MFT leads to visibly less
   terminated cross traffic on the second link in this experiment.






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7.5.  Summary

   Global MFR leads in all studied experiments to less terminated
   traffic than local MFR.  Especially in case of several serial links
   carrying only a single aggregate the degree of overtermination is
   tremendous with local MFR while global MFR does not lead to
   overtermination in that scenario.  In other experiments with cross
   traffic the difference between local and global MFR is still visible
   but less dramatic.  Nevertheless, global MFR is clearly better than
   localMFR.  However, multiple simultaneous bottleneck links are rather
   unlikely and, in particular, the situation with several serial
   bottleneck links where tremendous overtermination with local MFR
   occurs is rather pathologic.  Therefore, local MFR may still be used
   instead of global MFR if it reduces implementation complexity.





































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8.  Changes from Previous Revisions

8.1.  Changes from Version -00 to Version -01

   o  Added section on "Performance Evaluation of Admission Control with
      Single-Marking"

   o  Added section on "Performance Evaluation of Measured Rate
      Termination (MRT)"

   o  Added section on "Performance Evaluation of Marked Flow
      Termination on a Single Link"

   o  Added section on "Performance Evaluation of Marked Flow
      Termination with Multiple Bottleneck Links"




































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9.  References

9.1.  Normative References

9.2.  Informative References

   [I-D.babiarz-pcn-3sm]
              Babiarz, J., "Three State PCN Marking",
              draft-babiarz-pcn-3sm-00 (work in progress), July 2007.

   [I-D.briscoe-tsvwg-cl-architecture]
              Briscoe, B., "An edge-to-edge Deployment Model for Pre-
              Congestion Notification: Admission  Control over a
              DiffServ Region", draft-briscoe-tsvwg-cl-architecture-04
              (work in progress), October 2006.

   [I-D.charny-pcn-single-marking]
              Charny, A., "Pre-Congestion Notification Using Single
              Marking for Admission and  Termination",
              draft-charny-pcn-single-marking-02 (work in progress),
              July 2007.

   [I-D.ietf-pcn-architecture]
              Eardley, P., "Pre-Congestion Notification Architecture",
              draft-ietf-pcn-architecture-01 (work in progress),
              October 2007.

9.3.  Other References

   [Menth07]  Menth, M. and F. Lehrieder, "Performance Evaluation of
              PCN-Based Admission Control and  Flow Termination (work in
              progress)", November 2007, <http://
              www3.informatik.uni-wuerzburg.de/staff/menth/Publications/
              Menth07-PCN-Eval.pdf>.

   [SoBa05]   Sommers, J., Barford, P., , N., and A. Ron, "Improving
              Accuracy in End-to-End Packet Loss Measurement. In: ACM
              SIGCOMM", 2005.

   [TR437]    Menth, M. and F. Lehrieder, "Comparison of Marking
              Algorithms for PCN-Based Admission Control, Technical
              Report No. 437", October 2007, <http://
              www-info3.informatik.uni-wuerzburg.de/TR/tr437.pdf>.








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Authors' Addresses

   Michael Menth
   University of Wuerzburg
   Am Hubland
   Wuerzburg  D-97074
   Germany

   Phone: +49-931-888-6644
   Email: menth@informatik.uni-wuerzburg.de


   Frank Lehrieder
   University of Wuerzburg
   Am Hubland
   Wuerzburg  D-97074
   Germany

   Phone: +49-931-888-6634
   Email: lehrieder@informatik.uni-wuerzburg.de































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Full Copyright Statement

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