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Versions: 00 RFC 3247

    Internet Draft                                       Anna Charny, ed.
                                                           Cisco Systems

                                                              Fred Baker
                                                           Cisco Systems

                                                             Jon Bennett
                                                     Riverdelta Networks

                                                             Kent Benson
                                                                 Tellabs

                                                     Jean-Yves Le Boudec
                                                                    EPFL

                                                             Angela Chiu
                                                               AT&T Labs

                                                        William Courtney
                                                                     TRW

                                                             Bruce Davie
                                                           Cisco Systems

                                                          Shahram Davari
                                                              PMC-Sierra

                                                           Victor Firoiu
                                                         Nortel Networks

                                                        Charles Kalmanek
                                                           AT&T Research

                                                       K.K. Ramakrishnan
                                                      TeraOptic Networks

                                                     Dimitrios Stiliadis
                                                     Lucent Technologies


   Expires August, 2001
   draft-ietf-diffserv-ef-supplemental-00.txt February 2001


         Supplemental Information for the New Definition of the EF PHB

   Status of this Memo

   This document is an Internet Draft and is in full conformance with
   all provisions of Section 10 of RFC2026. Internet Drafts are working
   documents of the Internet Engineering Task Force (IETF), its Areas, and
   its Working Groups.  Note that other groups may also distribute
   working documents as Internet Drafts.

   Internet Drafts are draft documents valid for a maximum of six
   months. Internet Drafts may be updated, replaced, or obsoleted by

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   other documents at any time.  It is not appropriate to use Internet
   Drafts as reference material or to cite them other than as a
   "working draft" or "work in progress."

   The list of current Internet-Drafts can be accessed at
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   To learn the current status of any Internet-Draft, please check the
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   Rim).

   This document is a product of the Diffserv working group of the
   Internet Engineering Task Force. This document was written during the
   process of clarification of RFC2598 [10] that led to the publication
   of [6]. It is published as part of the historical record of the IETF's
   Differentiated Services working group. Please address comments to the
   group's mailing list at diffserv@ietf.org, with a copy to the
   authors.


   Copyright (C) The Internet Society (1999).  All Rights
   Reserved.



   Abstract

   This document is intended to supplement [6]. Its primary motivation is
   providing additional explanation to the revised EF definition and its
   properties. The document also provides additional implementation examples
   and gives some guidance for computation of the numerical parameters of the new
   definition for several well known schedulers and router architectures.


Contents

1.  Introduction .............................................3
2.  Definition of EF PHB .....................................3
2.1 The formal definition ....................................4
2.2 The case of an ideal output-buffered device with an
    EF FIFO at the output ....................................6
2.3 The General case .........................................7
2.3.1 The colorblind definition ..............................7
2.3.2 Packet reordering with the colorblind definition .......8
2.4 The packet-identity-aware definition .....................8
3 Per Packet delay ...........................................9
3.1 Single hop delay bound ...................................9
3.2 Multi-hop worst case delay ...............................9

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4 Packet loss ...............................................10
5 Implementation considerations .............................11
5.1 The output buffered model with aggregate queuing
    at the output............................................12
5.1.1 Strict Non-preemptive Priority Queue ..................12
5.1.2 WF2Q ..................................................12
5.1.3 Deficit Round Robin (DRR)..............................12
5.1.4 Start-Time Fair Queuing (SFQ) and Self-Clocked
      Fair Queuing ..........................................12
5.2 A Router with Variable Internal Delay and Aggregate
      Scheduling at the output...............................12
6 Security Considerations ...................................13
7 References.................................................13
8 Appendix. Difficulties with the RFC 2598 Definition .......14
8.1 Perfectly-Clocked Forwarding.............................15
8.2 Router Internal Delay ...................................15
8.3 Maximum Configurable Rate and Provisioning Efficiency....16
8.4 The Non-trivial Nature of the Difficulties ..............17
9 Authors'addresses .........................................18
10 Full Copyright ...........................................20

Specification of Requirements

   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 [3].

   1 Introduction

   The Expedited Forwarding (EF) Per-Hop Behavior (PHB) was designed to
   be used to build a low-loss, low-latency, low-jitter, assured
   bandwidth service. The potential benefits of this service, and
   therefore the EF PHB, are enormous. Because of the great value of
   this PHB, it is critical that the forwarding behavior required of
   and delivered by an EF-compliant node be specific, quantifiable, and
   unambiguous.

   Unfortunately, the definition of EF PHB in the original RFC2598 [10] was
   not sufficiently precise (see Appendix and [4]). A more precise definition
   is given in [6]. This document is intended to aid in the understanding of
   the properties of the new definition and provide supplemental information
   not included in the text of [6] for sake of brevity.

   The document is outlined as follows. In section 2, we briefly restate the
   definition for EF PHB of [6]. We then provide some additional discussion
   of this definition and describe some of its properties.  We discuss the
   issues associated with per-packet delay and loss in sections 3 and 4. In
   section 5 we discuss the impact of known scheduling architectures on the
   critical parameters of the new definition. We also discuss the impact of
   deviation of real devices from the ideal output-buffered model on the
   magnitude of the critical parameters in the definition.

2 Definition of EF PHB


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2.1 The formal definition

   An intuitive explanation of the new EF definition is described in
   [6]. Here we restate the formal definition from [6] verbatim.

   A node that supports EF on an interface I at some configured rate R
   MUST satisfy the following equations:


         d_j <= f_j + E_a (eq_1)

   where f_j is defined iteratively by

         f_0 = 0, d_0 = 0

         f_j = max(a_j, min(d_j-1, f_j-1)) + l_j/R, for all j > 0 (eq_2)


   In this definition:

      - d_j is the time that the last bit of the j-th EF packet to
      depart actually leaves the node from the interface I.

      - f_j is the target departure time for the j-th EF packet to
      depart from I, the "ideal" time at or before which the last bit of
      that packet should leave the node.

      - a_j is the time that the last bit of the j-th EF packet destined
      to the output I to arrive actually arrives at the node.

      - l_j is the size (bits) of the j-th EF packet to depart from I.
      l_j is measured on the IP datagram (IP header plus payload) and
      does not include any lower layer (e.g. MAC layer) overhead.

      - R is the EF configured rate at output I (in bits/second).

      - E_a is the error term for the treatment of the EF aggregate.
      Note that E_a represents the worst case deviation between actual
      departure time of an EF packet and ideal departure time of the
      same packet, i.e. E_a provides an upper bound on (d_j - f_j) for
      all j.

      - d_0 and f_0 do not refer to a real packet departure but are used
      purely for the purposes of the recursion. The time origin should
      be chosen such that no EF packets are in the system at time 0.


   An EF-compliant node MUST be able to be characterized by the range of
   possible R values that it can support on each of its interfaces while
   conforming to these equations, and the value of E_a that can be met
   on each interface. R may be line rate or less. E_a MAY be specified
   as a worst-case value for all possible R values or MAY be expressed
   as a function of R.


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   Note also that, since a node may have multiple inputs and complex
   internal scheduling, the jth packet to arrive may not be the jth

   packet to depart. It is in this sense that eq_1 and eq_2 are
   colorblind with regard to packet identity.

   In addition, a node that supports EF on an interface I at some
   configured rate R MUST satisfy the following equations:


      D_j <= F_j + E_p (eq_3)

   where F_j is defined iteratively by

      F_0 = 0, D_0 = 0

      F_j = max(A_j, min(D_j-1, F_j-1)) + L_j/R, for all j > 0 (eq_4)


   In this definition:

      - D_j is actual the departure time of the individual EF packet
      that arrived at time A_j, i.e., given a packet which was the j-th
      EF packet destined for I to arrive at the node via any input, D_j
      is the time at which the last bit of that individual packet
      actually leaves the node from the interface I.

      - F_j is the target departure time for the individual EF packet
      which arrived at time A_j.

      - A_j is the time that the last bit of the j-th EF packet destined
      to the output I to arrive actually arrives at the node.

      - L_j is the size (bits) of the j-th EF packet to arrive at the
      node that is destined to output I. L_j is measured on the IP
      datagram (IP header plus payload) and does not include any lower
      layer (e.g. MAC layer) overhead.

      - R is the EF configured rate at output I (in bits/second).

      - E_p is the error term for the treatment of individual EF
      packets. Note that E_p represents the worst case deviation between
      actual departure time of an EF packet and ideal departure time of
      the same packet, i.e. E_p provides an upper bound on (D_j - F_j)
      for all j.

      - D_0 and F_0 do not refer to a real packet departure but are used
      purely for the purposes of the recursion. The time origin should
      be chosen such that no EF packets are in the system at time 0.
   It is the fact that D_j and F_j refer to departure times for the jth
   packet to arrive that makes eq_3 and eq_4 aware of packet identity.
   This is the critical distinction between the last two equations and
   the first two.

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   An EF-compliant node SHOULD be able to be characterized by the range
   of possible R values that it can support on each of its interfaces
   while conforming to these equations, and the value of E_p that can be
   met on each interface. E_p MAY be specified as a worst-case value for
   all possible R values or MAY be expressed as a function of R. An E_p
   value of "undefined" MAY be specified.

2.2 The case of an ideal output-buffered device with an EF FIFO at the
   output

   For an ideal output-buffered device with a FIFO for EF packets at the
   output and no internal delay, the i-th packet to arrive to the device is
   also the i-th packet to depart from the device. Therefore, in this ideal
   model the colorblind and packet-identity-aware characteristics are
   identical, and E_a = E_p.  In this section we therefore omit the subscript
   and refer to the latency term simply as E.

   It could be shown that for such an ideal device the definition of
   section 2 is stronger than the well-known rate-latency curve [2] in the
   sense that if a scheduler satisfies the EF definition it also satisfies
   the rate-latency curve. As a result, all the properties known for the
   rate-latency curve also apply to the modified EF definition.  However, we
   argue below that the definition of section 2.1 is more suitable to reflect
   the intent of EF PHB than the rate-latency curve.

   It is shown in [2] that the rate-latency curve is equivalent to
   the following definition:

   Definition of Rate Latency Curve (RLC):

   D(j) <= F'(j) + E (eq_5)

   where

   F'(0)=0,
   F'(j)=max(a(j), F'(j-1))+ L(j)/R for all j>0 (eq_6)

   It can be easily verified that the EF definition of section 2.1 is
   stronger than RLC by noticing that for all j, F'(j) >= F(j).

   It is easy to see that F'(j) in the definition RLC corresponds to
   the time the j-th departure should have occurred should the EF
   aggregate be constantly served exactly at its configured rate R.
   Following the common convention, we refer to F'(j) as the "fluid
   finish time" of the j-th packet to depart.

   The intuitive meaning of the rate-latency curve of RLC is that any
   packet is served at most time E later than this packet would finish
   service in the fluid model.

   For RLC (and hence for the stronger EF definition) it
   holds that in any interval (0,t) the EF aggregate gets close to the
   desired service rate R (as long as there is enough traffic to

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   sustain this rate). The discrepancy between the ideal and the actual
   service in this interval depends on the latency term E, which in
   turn depends on the scheduling implementation. The smaller E, the
   smaller the difference between the configured rate and the actual
   rate achieved by the
   scheduler.

   While RLC guarantees the desired rate to the EF aggregate in all
   intervals (0,t) to within a specified error, it may nevertheless
   result in large gaps in service.  For example, suppose that (a large
   number) N of identical EF packets of length L arrived from different
   interfaces to the EF queue in the absence of any non-EF traffic.
   Then any work-conserving scheduler will serve all N packets at link
   speed. When the last packet is sent at time NL/C, where C is the
   capacity of output link, F(N) will be equal to NL/R. That is, the
   scheduler is running ahead of ideal, since NL/C < NL/R for R < C.
   Suppose now that at time NL/C a large number of non-EF packets
   arrive, followed by a single EF packet.  Then the scheduler can
   legitimately delay starting to send the EF packet until time
   F(N+1)=(N+1)L/R + E - L/C.  This means that the EF aggregate will
   have no service at all in the interval (NL/C, (N+1)L/R + E - L/C).
   This interval can be  quite large if R is substantially smaller
   than C.  In essence, the EF aggregate can be "punished" by a gap in
   service for receiving faster service than its configured rate at the
   beginning.

   The new EF definition alleviates this problem by introducing the term
   min(D(j-1), F(j-1)) in the recursion.  Essentially, this means
   that the fluid finishing time is "reset" if that packet is sent before
   its "ideal" departure time. As a consequence of that, for the case
   where the EF aggregate is served in the FIFO order, suppose a packet
   arrives at time t to a server satisfying the EF definition. The packet
   will be transmitted no later than time t + Q(t)/R + E, where Q(t) is
   the EF queue size at time t (including the packet under discussion).
   This statement is proved in  [4].

2.3 The General case

   In a more general case, where either the output scheduler does not
   serve the EF packets in a FIFO order, or the variable internal delay in
   the device reorders packets while delivering them to the output (or
   both), the i-th packet destined to a given output interface to arrive
   to the device may no longer be the i-th packet to depart from that
   interface.  In that case the packet-identity-aware and the colorblind
   definitions are no longer identical.

 2.3.1 The colorblind definition

   The colorblind definition can be viewed as a truly aggregate
   characteristic of the service provided to EF packets. For an analogy
   consider a dark reservoir to which all arriving packets are placed.  A
   scheduler is allowed to pick a packet from the reservoir in a random
   order, without any knowledge of the order of packet arrivals.  The
   colorblind part of the definition measures the accuracy of the output

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   rate provided to the EF aggregate as a whole. The smaller E_a, the
   more accurate is the assurance that the reservoir is drained at least
   at the configured rate.

2.3.2 Packet reordering with the colorblind definition

   Note that in this reservoir analogy packets of EF aggregate may be
   arbitrarily reordered. However, the definition of EF PHB given in [6]
   explicitly requires that no packet reordering occur within a
   microflow. This requirement restricts the scheduling implementations,
   or, in the reservoir analogy, the order of pulling packets out of the
   reservoir to make sure that packets within a microflow are not
   reordered, but it still allows reordering at the aggregate
   level.

   Note that reordering within the aggregate, as long as there is no
   flow-level reordering, does not necessarily reflect a "bad"
   service. Consider for example a scheduler that arbitrates among 10
   different EF "flows" with diverse rates.  A scheduler that is aware of
   the rate requirements may choose to send a packet of the faster flow
   before a packet of the slower flow to maintain lower jitter at the
   flow level. In particular, an ideal "flow"-aware WFQ scheduler will
   cause reordering within the aggregate, while maintaining packet
   ordering and small jitter at the flow level.

   It is intuitively clear that for such a scheduler, as well as for a
   simpler FIFO scheduler, the "accuracy" of the service rate is crucial
   for minimizing "flow"-level jitter. The packet-identity-aware
   definition quantifies this accuracy of the service rate.  A small
   value of E_a is a necessary (although not sufficient) condition for
   maintaining small per-flow jitter.

   However, the small value of E_a does not give any assurances about the
   absolute value of per-packet delay. In fact, if the input rate exceeds
   the configured rate, the colorblind definition may result in
   arbitrarily large delay of a subset of packets.  This is the primary
   motivation for the packet-identity-aware definition.

2.4 The packet-identity-aware definition

   The primary goal of the packet-aware characterization of the EF
   implementation is that, unlike the colorblind characterization, it
   provides a way to find a per-packet delay bound as a function of input
   traffic parameters.

   While the colorblind definition characterizes the accuracy of the
   service rate of the entire EF aggregate, the packet-identity-aware
   part of the definition characterizes the deviation of the device from
   an ideal server that serves the EF aggregate in FIFO order at least at
   the configured rate.

   The value of E_p in the packet-identity-aware definition is therefore
   affected by two factors: the accuracy of the aggregate rate service
   and the degree of packet reordering within the EF aggregate (under the

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   constraint that packets within the same microflow are not
   reordered). Therefore, a sub-aggregate aware device that provides an
   ideal service rate to the aggregate, and also provides an ideal rate
   service for each of the sub-aggregates, may nevertheless have a very
   large value of E_p (in this case E_p must be at least equal to the
   ratio of the maximum packet size divided by the smallest rate of any
   sub aggregate).  As a result, a large value of E_p does not
   necessarily mean that the service provided to EF aggregate is bad -
   rather it may be an indication that the service is good, but non-FIFO.
   On the other hand, a large value of E_p may also mean that the
   aggregate service is very inaccurate (bursty), and hence in this case
   the large value of E_p reflects a poor quality of implementation.

   As a result, a large number of E_p does not necessarily provide any
   guidance on the quality of the EF implementation.  However, a small
   value of E_p does indicate a high quality FIFO implementation.

   Since E_p and E_a relate to different aspects of the EF
   implementation, they should be considered together to determine the
   quality of the implementation.

3. Per Packet delay

   The primary motivation for the packet-identity-aware definition is
   that it allows to quantify the per-packet delay bound. This section
   discusses the issues with computing per-packet delay

3.1 Single hop delay bound

   If the total traffic arriving to an output port I from all inputs is
   constrained by a leaky bucket with parameters (R, B), where R is the
   configured rate at I, and B is the bucket depth (burst), then the
   delay of any packet departing from I is bounded by D_p, given by

   D_p = B/R + E_p (eq_7)

   Because the delay bound depends on the configured rate R and the input
   burstiness B, it is desirable for both of these parameters to be
   visible to a user of the device.  A PDB desiring a particular delay
   bound may need to limit the range of configured rates and allowed
   burstiness that it can support in order to deliver such
   bound. Equation (eq_7) provides a means for determining an acceptable
   operating region for the device with a given E_p. It may also be
   useful to limit the total offered load to a given output to some rate
   R_1 < R (e.g. to obtain end-to-end delay bounds [5]). It is important
   to realize that, while R_1 may also be a configurable parameter of the
   device, the delay bound in (eq_7) does not depend on it. It may be
   possible to get better bounds explicitly using the bound on the input
   rate, but the bound (eq_7) does not take advantage of this information.

3.2 Multi-hop worst case delay

   Although the PHB defines inherently local behavior, in this section we
   briefly discuss the issue of per-packet delay as the packet traverses

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   several hops implementing EF PHB.  Given a delay bound (eq_7) at a
   single hop, it is tempting to conclude that per-packet bound across h
   hops is simply h times the bound (eq_7).  However, this is not
   necessarily the case, unless B represents the worst case input
   burstiness across all nodes in the network.

   However, obtaining such a worst case value of B is not trivial.  If EF
   PHB is implemented using aggregate class-based scheduling where all EF
   packets share a single FIFO, the so-called effect of jitter
   accumulation may result in an increase in burstiness from hop to
   hop. In particular, it can be shown that unless severe restrictions on
   EF utilization are imposed, even if all EF flows are ideally shaped at
   the ingress, then for any value of delay D it is possible to construct
   a network where EF utilization on any link is bounded not to exceed a
   given factor, no flow traverses more than a specified number of hops,
   but there exists a packet that experiences a delay more than D [5].
   This result implies that the ability to limit the worst case
   burstiness and the resulting end-to-end delay across several hops may
   require not only limiting EF utilization on all links, but also
   constraining the global network topology. Such topology constraints
   would need to be specified in the definition of any PDB built on top
   of EF PHB, if such PDB requires a strict worst case delay bound.

4. Packet loss

   Any device with finite buffering may need to drop packets if the input
   burstiness becomes sufficiently high. To meet the low loss objective
   of EF, a node may be characterized by the operating region in which
   loss of EF due to  congestion will not occur. This may be specified
   as a token bucket of  rate r <= R and burst size B that can be
   offered from all inputs to a  given output interface without loss.

   However, as discussed in the previous section, the phenomenon of
   jitter accumulation makes it generally difficult to guarantee that the
   input burstiness never exceeds the specified operating region. A
   no-loss guarantee across multiple hops may require specification of
   constraints on network topology which are outside the scope of
   inherently local definition of a PHB.  Thus, it must be possible to
   establish whether a device conforms to the EF definition even when
   some packets are lost.

   This can be done by performing an "off-line" test of conformance to
   equations (eq_1)- (eq_4). After observing a sequence of packets
   entering and leaving the node, the packets which did not leave are
   assumed lost and are notionally removed from the input stream. The
   remaining packets now constitute the arrival stream and the packets
   which left the node constitute the departure stream. Conformance to
   the equations can thus be verified by  considering only those packets
   that successfully passed through the node..

   Note that in the event that loss does occur, the specification of
   which packets are lost is beyond the scope of the definition of EF
   PHB. However, those packets that were not lost must conform to the
   equations definition of EF PHB in section 2.1.

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5. Implementation considerations

   A packet passing through a router will experience delay for a number
   of reasons.  Two familiar components of this delay are the time the
   packet sits in a buffer at an outgoing link waiting for the
   scheduler to select it and the time it takes to actually transmit
   the packet on the outgoing line.

   There may be other components of a packet's delay through a router,
   however.  A router might have to do some amount of header processing
   before the packet can be given to the correct output scheduler, for
   example.  In another case a router may have a FIFO buffer (called a
   transmission queue in [7]) where the packet sits after being
   selected by the output scheduler but before it is transmitted.  In
   cases such as these, the extra delay a packet may experience can be
   accounted for by absorbing it into the latency terms E_a and E_p.

   Implementing EF on a router with a multi-stage switch fabric
   requires special attention. A packet may experience additional
   delays due to the fact that it must compete with other traffic for
   forwarding resources at multiple contention points in the switch
   core. The delay an EF packet may experience before it even reaches the
   output-link scheduler should be included in the latency
   term. Input-buffered and input/output-buffered routers based on
   crossbar design may also require modification of their latency
   terms. The factors such as the speedup factor and the choice of
   crossbar arbitration algorithms may affect the latency terms
   substantially.

   Delay in the switch core comes from two sources, both of which must be
   considered.  The first part of this delay is the fixed delay a packet
   experiences regardless of the other traffic.  This component of the
   delay includes the time it takes for things such as packet segmentation
   and reassembly in cell based cores, enqueueing and dequeueing at each
   stage, and transmission between stages.  The second part of the switch
   core delay is variable and depends on the type and amount of other
   traffic traversing the core.  This delay comes about if the stages in
   the core mix traffic flowing between different input/output port pairs.
   Thus, EF packets must compete against other traffic for forwarding
   resources in the core.  Some of this  competing traffic may even be EF
   traffic from other aggregates. This introduces extra delay, that can
   also be absorbed by the latency term in the definition.


   To capture these considerations, in this section we will consider two
   simplified implementation examples. The first is an ideal output
   buffered node where packets entering the device from an input
   interface are immediately delivered to the output scheduler. In this
   model the properties of the output scheduler fully define the values
   of the parameters E_a and E_p. We will consider the case where the
   output scheduler implements aggregate class-based queueing, so that
   all EF packets share a single queue. We will discuss the values of E_a
   and E_p for a variety of class-based schedulers widely considered

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   acceptable for EF implementations.

   The second example will consider a router modeled as a black box with
   a known bound on the variable delay a packet can experience from the
   time it arrives to an input to the time it is delivered to its
   destination output. The output scheduler in isolation is assumed to be
   an aggregate scheduler with a known value of E_a(S)=E_p(S)=E(S). This
   model provides a reasonable abstraction to a large class of router
   implementations.

5.1. The output buffered model with aggregate queuing at the output.

   As has been mentioned earlier, in this model E_a = E_p, so we shall
   omit the subscript and refer to both terms as latency E.  The
   remainder of this subsection discusses E for a number of scheduling
   implementations.

5.1.1 Strict Non-preemptive Priority Queue

   A Strict Priority scheduler in which all EF packets share a single
   FIFO queue which is served at strict non-preemptive priority over other
   queues satisfies the EF definition with the latency term E = MTU/C
   where MTU is the maximum packet size and C is the speed of output link.

5.1.2 WF2Q

   Another scheduler that satisfies the EF definition with a small
   latency term is WF2Q described in [1]. A class-based WF2Q scheduler,
   in which  all EF traffic shares a single queue with the weight
   corresponding to the configured rate of the EF aggregate satisfies the
   EF definition with the latency term E = MTU/C+MTU/R.

5.1.3.Deficit Round Robin (DRR)

   For DRR [12], both E can be shown to grow linearly with
   N*(r_max/r_min)*MTU, where r_min and r_max denote the smallest and
   the largest rate among the rate assignments of all queues in the
   scheduler, and N is the number of queues in the scheduler

5.1.4. Start-Time Fair Queuing (SFQ) and Self-Clocked Fair Queuing
   (SCFQ)

   For SFQ [9] and SCFQ [8] E can be shown to grow
   linearly with the number of queues in the scheduler.

5.2. A Router with Variable Internal Delay and Aggregate Scheduling at the
output.

   In this section we consider a router which is modeled as follows. A
   packet entering the router may experience a variable delay D_v with a
   known upper bound D. That is, 0<=D_v<D.  At the output all EF packets
   share a single class queue.  Class queues are scheduled by a scheduler
   with a known value E(S) (where E(S) corresponds to the model where
   this scheduler is implemented in an ideal output buffered device).

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   In this case, it can be easily shown that E_a = E(S) + D.

   The computation of E_p is more complicated.  For such device, E_p =
   E(S)+  min((D+B/R), D*C_inp/R), where (B, R) are the input token
   bucket parameters of the EF aggregate at the given input, and C_inp is
   the total capacity of all input links from which EF traffic destined
   to the given  output can arrive.

   Intuitively, this can be understood as follows. The term min((D+B/R),
   D*C_inp/R) is the time to it takes to drain (at rate R) the maximum
   number of EF packets that can arrive in the interval of length D to
   the output from all inputs. Consider an EF packet arriving at the
   input at time t. The ideal departure time d of this packet in the
   packet-identity-aware definition would be determined by the number of
   packets which arrived to the router before this packet.  However, due
   to variable delay, some packets that arrive later than this packet to
   the input of the device may end up arriving before this packet to the
   output. The number of bits in all such packets is bounded by min(DR+B,
   D*C_inp).  If the EF queue is served at the configured rate R, then
   the chosen packet may be delayed additionally by min((D+B/R),
   D*C_inp/R).

   Recall from the discussion of section 3 that bounding input burstiness
   B may not be easy in a general topology. In the absence of the
   knowledge of a bound on B one can bound E_p as E_p = E(S) +
   D*C_inp/R.

   Note also that the bounds in this section are derived using only the
   bound on the variable portion of the interval delay and the error
   bound of the output scheduler.  If more details about the architecture
   of a device are available, it may be possible to compute better
   bounds.

6. Security Considerations

   This informational draft provides additional information to aid in
   understanding of the EF PHB described in [6].  It adds no new
   functions to it. As a result, it adds no security issues to those
   described in that specification.

7. References

   [1] J.C.R. Bennett and H. Zhang, ``WF2Q: Worst-case
   Fair Weighted Fair Queuing'', INFOCOM'96, Mar, 1996

   [2] J.-Y. Le Boudec, "Application of Network Calculus To
   Guaranteed Service Networks", IEEE Transactions on
   Information theory, (44) 3, May 1998

   [3] S. Bradner, "Key Words for Use in RFCs to Indicate
   Requirement Levels", BCP 14, RFC 2119, March 1997.

   [4] J. Bennett, K. Benson, A. Charny, W. Courney, J.Y. Le Boudec,

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   "Delay Jitter Bounds and Packet Scale Rate Guarantee for Expedited
   Forwarding", Proc. Infocom 2001, April 2001.

   [5] A. Charny, J.-Y. Le Boudec "Delay Bounds in a
   Network with Aggregate Scheduling". Proc. of QoFIS'2000, September
   25-26, 2000, Berlin, Germany.

   [6] B. Davie, ed. et al, "An Expedited Forwarding PHB",
   draft-ietf-diffserv-rfc2598bis-00.txt, work in progress, February
   2001.

   [7] T. Ferrari and P. F. Chimento, "A Measurement-
   Based Analysis of Expedited Forwarding PHB
   Mechanisms," Eighth International Workshop on Quality
   of Service, Pittsburgh, PA, June 2000,


   [8] S.J. Golestani. "A Self-clocked Fair Queuing
   Scheme for Broad-band Applications". In Proceedings of
   IEEE INFOCOM'94, pages 636-646, Toronto, CA, April
   1994.

   [9] P. Goyal, H.M. Vin, and H. Chen. "Start-time
   Fair Queuing: A Scheduling Algorithm for Integrated
   Services". In Proceedings of the ACM-SIGCOMM 96, pages
   157-168, Palo Alto, CA, August 1996.

   [10] V. Jacobson, K. Nichols, K. Poduri, "An Expedited
   Forwarding PHB", RFC 2598, June 1999

   [11] V. Jacobson, K. Nichols, K. Poduri,
   "The 'Virtual Wire' Behavior Aggregate,"
   (draft-ietf-diffserv-ba-vw-00.txt), March 2000.

   [12] M. Shreedhar and G. Varghese. "Efficient Fair Queueing


   Using Deficit Round Robin". In Proceedings of
   SIGCOMM'95, pages 231-243, Boston, MA, September 1995.


   8. Appendix. Difficulties with the RFC 2598 EF PHB Definition

   The definition of the EF PHB as given in [10] states:

   "The EF PHB is defined as a forwarding treatment for a particular
   diffserv aggregate where the departure rate of the aggregate's
   packets from any diffserv node must equal or exceed a configurable
   rate.  The EF traffic SHOULD receive this rate independent of the
   intensity of any other traffic attempting to transit the node.
   It [the EF PHB departure rate] SHOULD average at least the
   configured rate when measured over any time interval equal
   to or longer than the time it takes to send an output link
   MTU sized packet at the configured rate."

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   A literal interpretation of the definition would consider the
   behaviors given in the next two subsections as non-compliant. The
   definition also unnecessarily constrains the maximum configurable
   rate of an EF aggregate.

   8.1 Perfectly-Clocked Forwarding

   Consider the following stream forwarded from a router with EF-
   configured rate R=C/2, where C is the output line rate. In the
   illustration, E is an MTU-sized EF packet while x is a non-EF packet
   or unused capacity, also of size MTU.

        ... E x E x E x E x E x E x...
                 |-----|

   The interval between the vertical bars is 3*MTU/C, which is greater
   than MTU/(C/2), and so is subject to the EF PHB definition. During
   this interval, 3*MTU/2 bits of the EF aggregate should be forwarded,
   but only MTU bits are forwarded.  Therefore, while this forwarding
   pattern should be considered compliant under any reasonable
   interpretation of the EF PHB, it actually does not formally comply
   with the definition of RFC 2598.

   Note that this forwarding pattern can occur in any work-conserving
   scheduler in an ideal output-buffered architecture where EF packets
   arrive in a perfectly clocked manner according to the above pattern
   and are forwarded according to exactly the same pattern in the
   absence of any non-EF traffic.

   Trivial as this example may be, it reveals the lack of mathematical
   precision in the formal definition. The fact that no work-conserving
   scheduler can formally comply with the definition is unfortunate,
   and appears to warrant some changes to the definition that would
   correct this problem.

   The underlying reason for the problem described here is quite simple
   - one can only expect that the EF aggregate is served at configured
   rate in some interval where there is enough backlog of EF packets to
   sustain that rate. In the example above the packets come in exactly
   at the rate at which they are served, and so there is no persistent
   backlog.  Certainly, if the input rate is even smaller than the
   configured rate of the EF aggregate, there will be no backlog as
   well, and a similar formal difficulty will occur.

   A seemingly simple solution to this difficulty might be to require
   that the EF aggregate is served at its configured rate only when the
   queue is backlogged.  However, as we show in the remainder of this
   section, this solution does not suffice.

   8.2 Router Internal Delay

   We now argue that the example considered in the previous section is
   not as trivial as it may seem at first glance.

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   Consider a router with EF configured rate R = C/2 as in the previous
   example, but with an internal delay of 3T (where T = MTU/C) between
   the time that a packet arrives at the router and the time that it is
   first eligible for forwarding at the output link. Such things as
   header processing, route look-up, and delay in switching through a
   multi-layer fabric could cause this delay. Now suppose that EF
   traffic arrives regularly at a rate of (2/3)R = C/3. The router will
   perform as shown below.

         EF Packet Number 1 2 3 4 5 6 ...
         Arrival (at router) 0 3T 6T 9T 12T 15T ...
         Arrival (at scheduler) 3T 6T 9T 12T 15T 18T ...
         Departure 4T 7T 10T 13T 16T 19T ...


   Again, the output does not satisfy the RFC 2598 definition of EF
   PHB. As in the previous example, the underlying reason for this
   problem is that the scheduler cannot forward EF traffic faster than
   it arrives. However, it can be easily seen that the existence of
   internal delay causes one packet to be inside the router at all
   times. An external observer will rightfully conclude that the number
   of EF packets that arrived to the router is always at least one
   greater than the number of EF packets that left the router, and
   therefore the EF aggregate is constantly backlogged. However, while
   the EF aggregate is continuously backlogged, the observed output
   rate is nevertheless strictly less that the configured rate.

   This example indicates that the simple addition of the condition
   that EF aggregate must receive its configured rate only when the EF
   aggregate is backlogged does not suffice in this case.

   Yet, the problem described here is of fundamental importance in
   practice.  Most routers have a certain amount of internal delay.  A
   vendor declaring EF compliance is not expected to simultaneously
   declare the details of the internals of the router.  Therefore, the
   existence of internal delay may cause a perfectly reasonable EF
   implementation to display seemingly non-conformant behavior, which
   is clearly undesirable.

   8.3 Maximum Configurable Rate and Provisioning Efficiency

   It is well understood that with any non-preemptive scheduler, the
   compliant configurable rate for an EF aggregate cannot exceed C/2
   [11]. This is because an MTU-sized EF packet may arrive to an
   empty queue at time t just as an MTU-sized non-EF packet begins
   service. The maximum number of EF bits that could be forwarded
   during the interval [t, t + 2*MTU/C] is MTU. But if configured rate
   R > C/2, then this interval would be of length greater than MTU/R,
   and more than MTU EF bits would have to be served during this
   interval for the router to be compliant. Thus, R must be no greater
   than C/2.

   It can be shown that for schedulers other than PQ, such as various

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   implementations of WFQ, the maximum compliant configured rate may be
   much smaller than 50%. For example, for SCFQ [8] the maximum
   configured rate cannot exceed C/N, where N is the number of queues
   in the scheduler. For WRR, mentioned as compliant in section 2.2 of
   RFC 2598, this limitation is even more severe. This is because in
   these schedulers a packet arriving to an empty EF queue may be
   forced to wait until one packet from each other queue (in the case
   of SCFQ) or until several packets from each other queue (in the case
   of WRR) are served before it will finally be forwarded.

   While it is frequently assumed that the configured rate of EF
   traffic will be substantially smaller than the link bandwidth, the
   requirement that this rate should never exceed 50% of the link
   bandwidth appears unnecessarily limiting.  For example, in a fully
   connected mesh network, where any flow traverses a single link on
   its way from source to its destination there seems no compelling
   reason to limit the amount of EF traffic to 50% (or an even smaller
   percentage for some schedulers) of the link bandwidth.

   Another, perhaps even more striking example is the fact that even a
   TDM circuit with dedicated slots cannot be configured to forward EF
   packets at more than 50% of the link speed without violating RFC
   2598 (unless the entire link is configured for EF). If the
   configured rate of EF traffic is greater than 50% (but less than the
   link speed), there will always exist an interval longer than MTU/R
   in which less than the configured rate is achieved. For example,
   suppose the configured rate of the EF aggregate is 2C/3. Then the
   forwarding pattern of the TDM circuit might be

   E E x E E x E E x ...
      |---|

   where only one packet is served in the marked interval of length 2T
   = 2MTU/C. But at least 4/3 MTU would have to be served during this
   interval by a router in compliance with the definition in RFC 2598.
   The fact that even a TDM line cannot be booked over 50% by EF
   traffic indicates that the restriction is artificial and
   unnecessary.

   8.4 The Non-trivial Nature of the Difficulties

   One possibility to correct the problems discussed in the previous
   sections might be to attempt to clarify the definition of the
   intervals to which the definition applied or by averaging over
   multiple intervals. However, an attempt to do so meets with
   considerable analytical and implementation difficulties. For
   example, attempting to align interval start times with some epochs
   of the forwarded stream appears to require a certain degree of
   global clock synchronization and is fraught with the risk of
   misinterpretation and mistake in practice.

   Another approach might be to allow averaging of the rates over some
   larger time scale. However, it is unclear exactly what finite time
   scale would suffice in all reasonable cases. Furthermore, this

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   approach would compromise the notion of very short-term time scale
   guarantees that are the essence of EF PHB.

   We also explored a combination of two simple fixes. The first is the
   addition of the condition that the only intervals subject to the
   definition are those that fall inside a period during which the EF
   aggregate is continuously backlogged in the router (i.e., when an EF
   packet is in the router). The second is the addition of an error
   (latency) term that could serve as a figure-of-merit in the
   advertising of EF services.


   With the addition of these two changes the candidate definition
   becomes as follows:

   In any interval of time (t1, t2) in which EF traffic is
   continuously backlogged, at least R(t2 - t1 - E) bits of EF
   traffic must be served, where R is the configured rate for the
   EF aggregate and E is an implementation-specific latency term.

   The "continuously backlogged" condition eliminates the insufficient-
   packets-to-forward difficulty while the addition of the latency term
   of size MTU/C resolves the perfectly-clocked forwarding example
   (section 1.2.1), and also removes the limitation on EF configured
   rate.

   However, neither fix (nor the two of them together) resolves the
   example of section 1.2.2. To see this, recall that in the example of
   section 1.2.2 the EF aggregate is continuously backlogged, but the
   service rate of the EF aggregate is consistently smaller than the
   configured rate, and therefore no finite latency term will suffice
   to bring the example into conformance.

9. Authors' addresses

   Anna Charny, ed.
   Cisco Systems
   300 Apollo Drive
   Chelmsford, MA 01824
   acharny@cisco.edu

   Fred Baker
   Cisco Systems
   170 West Tasman Dr.
   San Jose, CA 95134
   fred@cisco.com

   Jon Bennett
   RiverDelta Networks
   3 Highwood Drive East
   Tewksbury, MA 01876
   jcrb@riverdelta.com

   Kent Benson

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   Tellabs Research Center
   3740 Edison Lake Parkway #101
   Mishawaka, IN 46545
   Kent.Benson@tellabs.com

   Jean-Yves Le Boudec
   ICA-EPFL, INN
   Ecublens, CH-1015
   Lausanne-EPFL, Switzerland
   leboudec@epfl.c

   Angela Chiu
   AT&T Labs
   100 Schulz Dr. Rm 4-204
   Red Bank, NJ 07701
   alchiu@att.com

   Bill Courtney
   TRW
   Bldg. 201/3702
   One Space Park
   Redondo Beach, CA 90278

   bill.courtney@trw.com

   Shahram Davari
   PMC-Sierra Inc
   555 Legget drive
   Suit 834, Tower B
   Ottawa, ON K2K 2X3, Canada
   shahram_davari@pmc-sierra.com

   Bruce Davie
   Cisco Systems
   300 Apollo Drive
   Chelmsford, MA 01824
   bsd@cisco.com

   Victor Firoiu
   Nortel Networks
   600 Tech Park
   Billerica, MA 01821
   vfirou@nortelnetworks.com

   Charles Kalmanek
   AT&T Labs-Research
   180 Park Avenue, Room A113,
   Florham Park NJ
   crk@research.att.com.

   K.K. Ramakrishnan
   AT&T Labs-Research
   Rm. A155, 180 Park Ave,
   Florham Park, NJ 07932

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   kkrama@research.att.com

   Dimitrios Stiliadis
   Lucent Technologies
   1380 Rodick Road
   Markham, Ontario, L3R-4G5, Canada
   stiliadi@bell-labs.com

   10. Full Copyright

   Copyright (C) The Internet Society 1999.  All Rights Reserved.

   This document and translations of it may be copied and furnished to
   others, and derivative works that comment on or otherwise explain it
   or assist in its implementation may be prepared, copied, published
   and distributed, in whole or in part, without restriction of any
   kind, provided that the above copyright notice and this paragraph
   are included on all such copies and derivative works.  However, this
   document itself may not be modified in any way, such as by removing
   the copyright notice or references to the Internet Society or other
   Internet organizations, except as needed for the purpose ofdeveloping
   Internet standards in which case the procedures for
   copyrights defined in the Internet Standards process must be
   followed, or as required to translate it into languages other than
   English.

   The limited permissions granted above are perpetual and will not be
   revoked by the Internet Society or its successors or assigns.

   This document and the information contained herein is provided on an
   "AS IS" basis and THE INTERNET SOCIETY AND THE INTERNET ENGINEERING
   TASK FORCE DISCLAIMS ALL WARRANTIES, EXPRESS OR IMPLIED, INCLUDING
   BUT NOT LIMITED TO ANY WARRANTY THAT THE USE OF THE INFORMATION
   HEREIN WILL NOT INFRINGE ANY RIGHTS OR ANY IMPLIED WARRANTIES OF
   MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.




















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