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Versions: (draft-mercankosk-diffserv-pdb-vw) 00

Internet Engineering Task Force                         Van Jacobson
Differentiated Services Working Group                   Kathleen Nichols
                                                        Packet Design, Inc.
Internet Draft                                          Kedar Poduri
Expires Jan., 2001                                      Cisco Systems, Inc.
draft-ietf-diffserv-pdb-vw-00.txt                       July, 2000



        The `Virtual Wire' Per-Domain Behavior
        <draft-ietf-diffserv-pdb-vw-00.txt>

  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),
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Internet-Drafts are draft documents valid for a maximum of six
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The list of current Internet-Drafts can be accessed at http://
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shadow.html. Distribution of this memo is unlimited.

  Abstract

This document describes an edge-to-edge behavior, in diffserv
terminology a per-domain behavior, called `Virtual Wire' (VW)
that can be constructed in any domain supporting the diffserv EF
PHB plus appropriate domain ingress policers. The VW behavior is
essentially indistinguishable from a dedicated circuit and can be
used anywhere it is desired to replace dedicated circuits with IP
transport. Although one attribute of VW is the delivery of a peak
rate, in VW this is explicitly coupled with a bounded jitter
attribute.

The document is a edited version of the earlier draft-ietf-diff-
serv-ba-vw-00.txt with a new name to reflect a change in Diffserv
WG terminology.

A pdf version of this document is available at ftp://ftp.packet-
design.com/ietf/vw_pdb_0.pdf

1.0  Introduction

[RFC2598] describes a diffserv PHB called expedited forwarding
(EF) intended for use in building a scalable, low loss, low
latency, low jitter, assured bandwidth, end-to-end service that
appears to the endpoints like an unshared, point-to-point connec-

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tion or `virtual wire.' For scalability, a diffserv domain sup-
plying this service must be completely unaware of the individual
endpoints using it and sees instead only the aggregate EF marked
traffic entering and transiting the domain. This document pro-
vides the specifications necessary on that aggregated traffic (in
diffserv terminology, a per-domain behavior or PDB) in order to
meet these requirements and thus defines a new pdb, the Virtual
Wire per-domain behavior or VW PDB. Despite the lack of per-flow
state, if the aggregate input rates are appropriately policed and
the EF service rates on interior links are appropriately config-
ured, the edge-to-edge service supplied by the domain will be
indistinguishable from that supplied by dedicated wires between
the endpoints. This note gives a quantitative definition of what
is meant by `appropriately policed and configured'.

Network hardware has become sufficiently reliable that the over-
whelming majority of network loss, latency and jitter are due to
the queues traffic experiences while transiting the network.
Therefore providing low loss, latency and jitter to a traffic
aggregate means ensuring that the packets of the aggregate see no
(or very small) queues. Queues arise when short-term traffic
arrival rate exceeds departure rate at some node(s). Thus ensur-
ing no queues for a particular traffic aggregate is equivalent to
bounding rates such that, at every transit node, the aggregate's
maximum arrival rate is less than that aggregate's minimum depar-
ture rate. These attributes can be ensured for a traffic aggregate
by using the VW PDB.

Creating the VW PDB has two parts:

        1.      Configuring individual nodes so that the aggregate has a
well-defined minimum departure rate. (`Well-defined' means
independent of the dynamic state of the node. In particular,
independent of the intensity of other traffic at the node.)

        2.      Conditioning the entire DS domain's aggregate (via policing
and shaping) so that its arrival rate at any node is always
less than that node's configured minimum departure rate.

[RFC2598] provides the first part. This document describes how
one configures the EF PHBs in the collection of nodes that make up
a DS domain and the domain's boundary traffic conditioners
(described in [RFC2475]) to provide the second part. This
description results in a diffserv per-domain behavior, as
described in [PDBDEF].

This document introduces and describes VW informally via pictures
and examples rather than by derivation and formal proof. The
intended audience is ISPs and router builders and the authors feel
this community is best served by aids to developing a strong intu-
ition for how and why VW works. However, VW has a simple, formal
description and its properties can and have been derived quite
rigorously. Such papers may prove interesting, but are outside

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the intent of this document.

The VW PDB has two major attributes: an assured peak rate and a
bounded jitter. It is possible to define a different PDB with only
the first of these, a "constant bit-rate" PDB, but this is not the
objective of this document.

The next sections describe the VW PDB in detail and give examples
of how it might be implemented. The keywords "MUST", "MUST NOT",
"REQUIRED", "SHOULD", "SHOULD NOT", and "MAY" that appear in this
document are to be interpreted as described in [RFC2119].

2.0  Description of the Virtual Wire PDB

2.1  Applicability

A Virtual Wire (VW) PDB is intended to send "circuit replacement"
traffic across a diffserv network. That is, this PDB is intended
to mimic, from the point of view of the originating and terminat-
ing nodes, the behavior of a hard-wired circuit of some fixed
capacity. It does this in a scalable (aggregatable) way that
doesn't require `per-circuit' state to exist anywhere but the
ingress router adjacent to the originator. This PDB should be
suitable for any packetizable traffic that currently uses fixed
circuits (e.g., telephony, telephone trunking, broadcast video
distribution, leased data lines) and packet traffic that has sim-
ilar delivery requirements (e.g., IP telephony or video confer-
encing). Thus the conceptual model of the VW PDB is as shown in
Figure 1: some portion (possibly all) of a physical wire between a
sender and receiver is replaced by a (higher bandwidth) DS domain
implementing VW in a way that is invisible to S, R or the circuit
infrastructure outside of the cloud.

Figure 1: VW conceptual model

2.2  Rules

The VW PDB uses the EF PHB to implement a transit behavior with
the required attributes. Each node in the domain MUST implement
the EF PHB as described in section 2 of [RFC2598] but with the
SHOULDs of that section taken as MUSTs. Specifically, RFC2598
states "The EF PHB is defined as a forwarding treatment for a par-
ticular diffserv aggregate where the departure rate of the aggre-
gate's packets from any diffserv node must equal or exceed a
configurable rate." The EF traffic SHOULD receive this rate inde-
pendent of the intensity of any other traffic attempting to tran-
sit the node. It 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." This leads to an "EF bound" on the delay that EF-marked
packets can experience at each node that is inversely propor-
tional to the configured EF rate for that link.


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The bandwidth limit of each output interface SHOULD be configured
as described in Section 2.4 of this document. In addition, each
domain boundary input interface that can be the ingress for EF
marked traffic MUST strictly police that traffic as described in
Section 2.4. Each domain boundary output interface that can be the
egress for EF marked traffic MUST strictly shape that traffic as
described in Section 2.4.

2.3  Attributes

Colloquially, "the same as a wire." That is, as long as packets
are sourced at a rate <= the virtual wire's configured rate, they
will be delivered with a high degree of assurance and with almost
no distortion of the interpacket timing imposed by the source.
However, any packets sourced at a rate greater than the VW config-
ured rate, measured over any time scale longer than a packet time
at that rate, will be unconditionally discarded.

2.4  Parameters

This section develops a parameterization of VW in terms of measur-
able properties of the traffic (i.e., the packet size and physical
wire bandwidth) and domain (the link bandwidths and EF transit
bound of each of the domain's routers). We will show that:

        1.      There is a simple formula relating the circuit bandwidth,
domain link bandwidths, packet size and maximum tolerable `jit-
ter' across the domain, and this jitter bound holds for each
packet individually - there is no interpacket dependence.

        2.      This formula and the EF bound described in [RFC2598] deter-
mine the maximum VW bandwidth that can be allocated between
some ingress and egress of the domain. (This is because the EF
bound is essentially a bound on the worst-case jitter that will
be seen by EF marked packets transiting some router and the
formula says that any three parameters from the set <jitter,
circuit bandwidth, link bandwidth, MTU> determine the fourth.)

        3.      When the ingress VW flows are allocated and policed so as to
ensure that this maximum VW bandwidth is not exceeded at any
node of the domain, the EF BA on a link exiting a node can con-
sist of an arbitrary aggregate of VW flows (i.e., no per-flow
state is needed) because there is no perturbation of the aggre-
gate's service order that will cause any of the constituent
flows to exceed its domain transit jitter bound.

2.4.1  The Jitter bound and `Jitter Window' for a single VW
circuit (flow)



Figure 2: Time structure of packets of a CBR stream at a high to
low bandwidth transition

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Figure 2 shows a CBR stream of size S packets being sourced at
rate R. At the domain egress border router, the packets arrive on
a link of bandwidth B (= nR) and depart to their destination on a
link of bandwidth R.

Figure 3: Details of arrival / departure relationships

Figure 3 shows the detailed timing of events at the router. At
time T0 the last bit of packet 0 arrives so output is started on
the egress link. It will take until time  for packet 0
to be completely output. As long as the last bit of packet 1
arrives at the border router before , the destination node will
find the traffic indistinguishable from a stream carried the
entire way on a dedicated wire of bandwidth R. This means that
packets can be jittered or displaced in time (due to queue waits)
as they cross the domain and that there is a jitter window at the
border router of duration

(EQ 1)

that must bound the sum of all the queue waits seen be a packet as
it transits the domain. As long as this sum is less than , the
destination will see service identical to a dedicated wire. Note
that the jitter window is (implicitly) computed relative to the
first packet of the flight of packets departing the boundary
router and, thus, can only include variable delays. Any transit
delay experienced by all the packets, be it propagation time,
router forwarding latency, or even average queue waits, is
removed by the relative measure so the sum described in this para-
graph is not sensitive to delay but only to delay variation. Also
note that when packets enter the domain they are already separated
by  so, effectively, everything is pushed to the left edge of
the jitter window and there's no slack time to absorb delay vari-
ation in the domain. However by simply delaying the output of the
first packet to arrive at E by one packet time (S/R), the phase
reference for all the traffic is reset so that all subsequent
packets enter at the right of their jitter window and have maximum
slack time during transit.

Figure 4: Packet timing structure edge-to-edge

Figure 4 shows the edge-to-edge path from the source to the desti-
nation. The links from S to I and E to D run at the virtual wire
rate R (or the traffic is shaped to rate R if the links run at a
higher rate). The solid rectangles on these links indicate the
packet time S/R. The dotted lines carry the packet times across
the domain since the time boundaries of these virtual packets form
the jitter window boundaries of the actual packets (whose dura-
tion and spacing are shown by the solid rectangles below the
intra-domain link). Note that each packet's jitter is indepen-
dent. E.g., even though the two packets about to arrive at E have
been displaced in opposite directions so that the total time

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between them is almost , neither has gone out of its jitter win-
dow so the output from E to D will be smooth and continuous.

The preceding derives the jitter window in terms of the bandwidths
of the ingress circuit and intra-domain links. In practice, the
`givens' are more likely to be the intradomain link bandwidths and
the jitter window (which can be no less than the EF bound associ-
ated with each output link that might be traversed by some VW
flow(s)). Rearranging Equation 1 based on this gives R, the maxi-
mum amount of bandwidth that can be allocated to the aggregate of
all VW circuits, as a function of the EF bound (= jitter window =
):

(EQ 2)

Note that the upper bound on VW traffic that can be handled by any
output link is simply the MTU divided by the link's EF bound.

2.4.2  Jitter independence under aggregation



Figure 5: Three VW customers forming an aggregate

This jitter independence is what allows multiple `virtual wires'
to be transparently aggregated into a single VW PDB. Figure 5
shows three independent VW customers, blue, yellow and red,
entering the domain at I. Assume that their traffic has worst-case
phasing, i.e., that one packet from each stream arrives simulta-
neously at I. Even if the output link scheduler makes a random
choice of which packet to send from its EF queue, no packet will
get pushed outside its jitter window. For example, in Figure 5
node I ships a different perturbation of the 3 customer aggregate
in every window yet this has no effect on the edge-to-edge VW
properties).

The jitter independence means that we only have to compare the
jitter window of Equation 1 to the worst case of the total queue
wait that can be seen by a single VW packet as it crosses the
domain. There are three potential sources of queue wait for a VW
packet:

        1.      it can queue behind non-EF packets (if any)

        2.      it can queue behind another VW packet from the same customer

        3.      it can queue behind VW packet(s) from other customers

For case (1), the EF `priority queuing' model says that the VW
traffic will never wait while a non-EF queue is serviced so the
only delay it can experience from non-EF traffic is if it has to
wait for the finish of a packet that was being sent at the time it
arrived. For an output link of bandwidth B, this can impose a

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worst-case delay of S/B. Note that this implies that if the (low
bandwidth) links of a network are carrying both VW and other traf-
fic, then n in Equation 1 must be at least 2 (i.e., the EF bound
can be at most half the link bandwidth) in order to make the jit-
ter window large enough to absorb this delay.

Case (2) can only happen if the previous packet hasn't completely
departed at the time the next packet arrives. Since each ingress
VW stream is strictly shaped to a rate R, any two packets will be
separated by at least time S/R so having leftovers is equivalent
to saying the departure rate on some link is <R over this time
scale. But the EF property is precisely that the departure rate
MUST be >R over any time scale of S/R or longer so this can't hap-
pen for any legal VW/EF configuration. Or, to put it another way,
if case (2) happens, either the VW policer is set too loosely or
some link's EF bound is set too tight.

Case (3) is a simple generalization of (2). If there are a total
of n customers, the worst possible queue occurs if all n arrive
simultaneously at some output link. Since each customer is indi-
vidually shaped to rate R, when this happens then no new packets
from any stream can arrive for at least time S/R. At the end of
this time, there can only be leftover packets in the queue if the
departure rate < nR over this time scale. Conforming to the EF
property (restated in section 2.2) means that any link capable of
handling the aggregate traffic must have a departure rate > nR
over any time scale longer than S/(nR) so, again, this can't hap-
pen in any legal VW/EF configuration.

For case (1), a packet could be displaced by non-EF traffic once
per hop so the edge-to-edge jitter is a function of the path
length. But this isn't true for case (3): The strict ingress
policing implies that a packet from any given VW stream can meet
any other VW stream in a queue at most once. This means the worst
case jitter caused by aggregating VW customers is a linear func-
tion of the number of customers in the aggregate but completely
independent of topology.

2.4.3  Topological effects on allocation

Although the jitter caused by aggregating VW customers is inde-
pendent of topology, the number of customers and/or bandwidth per
customer is very sensitive to topology and the topological
effects may be subtle. Equation 2 gives the aggregate VW that can
traverse any link but if there are n customers, the topology and
their (possible) paths through it determine how this bandwidth
divided among them.

Figure 6: Cumulative jitter from spatially distinct flows

The first thought is to simply divide the aggregate bandwidth by
the customer in-degree at some link. E.g., in Figure 5 there are
three customers aggregated into the I>E link so each should get a

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third of the available VW bandwidth. But Figure 6 shows that this
is too optimistic. Note that the yellow flow (I>E) gets jittered
one packet time when it meets the blue flow (I>2) then an addi-
tional packet time when it meets the red flow (3>4). So even
though the maximum in-degree is two and the largest possible
aggregate has only two components, the combined interactions
require that each customer get at most 1/3 of the available VW
bandwidth rather than 1/2. In general, if nj is the total number
of other customers encountered (or potentially encountered) by
customer j as it traverses the domain, then the bandwidth shares
can be at most .

It is possible to `tune' the topology to trade off total VW band-
width vs. reliability. For example in Figure 7, if the SF>NY VW
traffic is constrained (via route pinning or tunneling) to only
follow the northern path and LA>DC to only follow the southern
path, then each customer gets the entire VW bandwidth on their
path but at the expense of neither being able to use the alternate
path in the event of a link failure. If they want to take advan-
tage of the redundancy, only half the bandwidth can be allocated
to each even though the full bandwidth will be available most of
the time. Mixed strategies are also possible. For example the
SF>NY customer could get an expensive SLA that guaranteed the full
VW bandwidth even under a link failure and LA>DC could get a cheap
SLA that gave full bandwidth unless there was a link failure in
which case it gave nothing.

Figure 7: bandwidth vs. redundancy trade-off

2.4.4  Per-customer bandwidth and/or packet size variation

Figure 8: Aggregating VW flows with different bandwidth shares

In the last example, customers could get different VW shares
because their traffic was engineered to be disjoint. But when cus-
tomers with different shares transit the same link(s), there can
be problems. For example, Figure 8 shows blue and red customers
allocated 1/4 share each while yellow gets a 1/2 share. Since yel-
low's share is larger, its jitter window is smaller (the dotted
yellow line). Since the packets from a customer can appear any-
where in the jitter window, it's perfectly possible for packets
from red, blue and yellow to arrive simultaneously at I. Since I
has no per-customer state, the serving order for the three is ran-
dom and it's entirely possible that blue and red will be served
before yellow. But since yellow's jitter window is only two link
packet times wide, this results in no packets in its first window
and two in its second so its jitter bound is violated. There are
at least three different ways to deal with this:

        1.      Make all customers use the smallest jitter window. This is
equivalent to provisioning based on the number of customers
times the max customer rate rather than on the sum of the cus-
tomer rates. In bandwidth rich regions of the cloud this is

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probably the simplest solution but in bandwidth poor regions it
can result in denying customers that there is capacity to
accept.

        2.      Utilize a set of LU DSCPs to create an EF-like code point per
rate and service them in rate magnitude order. For a small set
of customer rates this makes full use of the capacity at the
expense of additional router queues (one per code point).

        3.      Separate rate and jitter bounds in the SLA. I.e., base the
jitter bound on the packet time of the minimum customer rate
(which is equivalent to making all customers use the largest
jitter window). This effectively treats the larger customers as
if their traffic were an aggregate of min rate flows which may
be the appropriate choice if the flow is indeed an aggregate,
e.g., a trunk containing many voice calls.

2.5  Assumptions

The topology independence of the VW PDB holds only while routing
is relatively stable. Since packets can be duplicated while rout-
ing is converging, and since path lengths can be shorter after a
routing change, it is possible to violate the VW traffic bounds
and thus jitter stream(s) more than their jitter window for a
small time during and just after a routing change.

The derivation in the preceding section assumed that the VW PDB
was the only user of EF in the domain. If this is not true, the
provisioning and allocation calculations must be modified to
account for the other users of EF.

2.6  Example uses

An enterprise could use VW to provision a large scale, internal
VoIP telephony system. Say for example that the internal links are
all Fast Ethernet (100Mb/s) or faster and arranged in a 3 level
hierarchy (switching/aggregation/routing) so the network diameter
is 5 hops. Typical telephone audio codecs deliver a packet every
20ms. At this codec rate, RTP encapsulated G.711 voice is 200 byte
packets & G.729 voice is 60 byte packets.

20ms at 100 Mb/s is 250 Kbytes (~150 MTUs, ~1200 G.711 calls or
~4,000 G.729 calls) which would be the capacity if the net were
carrying only VW telephony traffic.

Worse case jitter from other traffic through a diameter 5
enterprise is 5 MTU times or 0.6 ms leaving between 19 ms
(optimistic) to 10 ms (ultra conservative - see scaling notes in
the appendix) for VW. 10ms at 100Mb/s is 125Kbytes so using the
most conservative assumptions we can admit ~600 G.711 or ~2000
G.729 calls if the ingress can simultaneously police both packet &
bit rate. If the ingress can police only one of these, we can only
admit ~75 calls because each packet might be as long as an MTU.

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2.7  Environmental concerns

Routing instability will generally translate directly into VW
service degradation.

Multipath routing of VW will, in general, increase the jitter and
degrade the service unless either the paths are exactly the same
length (so there is no effect on jitter) and/or the routing deci-
sion is such that it always sends any particular customer down the
same path.

The analysis in Section 2.4 would hold in a world where traffic
policers and link schedulers are perfect and mathematically
exact. When computing parameters for our world, 5-10% fudge fac-
tors should be used.

3.0  Security Considerations

There are no security considerations for the VW PDB other than
those associated with the EF PHB which are described in [RFC2598].

4.0  References

[RFC2119]       "Key words for use in RFCs to Indicate Requirement Lev-
els", S.Bradner, www.ietf.org/rfc/rfc2119

[RFC2474]       "Definition of the Differentiated Services Field (DS
Field) in the IPv4 and IPv6 Headers", K.Nichols, S.
Blake, F. Baker, D. Black, www.ietf.org/rfc/rfc2474.txt

[RFC2475]       "An Architecture for Differentiated Services", S. Blake,
D. Black, M.Carlson,E.Davies,Z.Wang,W.Weiss,
www.ietf.org/rfc/rfc2475.txt

[RFC2597]       "Assured Forwarding PHB Group", F. Baker, J. Heinanen,
W. Weiss, J. Wroclawski, ftp://ftp.isi.edu/in-notes/
rfc2597.txt

[RFC2598]       "An Expedited Forwarding PHB", V.Jacobson, K.Nichols,
K.Poduri, ftp://ftp.isi.edu/in-notes/rfc2598.txt

[RFC2638]       "A Two-bit Differentiated Services Architecture for the
Internet", K. Nichols, V. Jacobson, and L. Zhang,
www.ietf.org/rfc/rfc2638.{txt,ps}

[PDBDEF]        "Definition of Differentiated Services Per-domain Behav-
iors and Rules for their Specification", K.Nichols,
B.Carpenter, draft-ietf-diffserv-pdb-def-00.[txt, pdf]

[CAIDA] The nature of the beast: recent traffic measurements from
an Internet backbone. K Claffy, Greg Miller and Kevin
Thompson. http://www.caida.org/Papers/Inet98/index.html

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[NS2]   The simulator ns-2, available at: http://www-mash.cs.ber-
keley.edu/ns/.

[FBK]   K. Nichols, "Improving Network Simulation with Feedback",
Proceedings of LCN'98, October, 1998.

[RFC2415]       RFC 2415, K. Poduri and K. Nichols, "Simulation Studies
of Increased Initial TCP Window Size", September, 1998.

5.0  Authors' Addresses

Van Jacobson
Packet Design, Inc.
66 Willow Place
Menlo Park, CA 94025
van@packetdesign.com

Kathleen Nichols
Packet Design, Inc.
66 Willow Place
Menlo Park, CA 94025
nichols@packetdesign.com

Kedar Poduri
Cisco Systems, Inc.
170 W. Tasman Drive
San Jose, CA 95134-1706
poduri@cisco.com

6.0  Appendix: On Jitter for the VW PDB

The VW PDB's bounded jitter translates into the generally useful
properties of network bandwidth limits and buffer resource lim-
its. These properties make VW useful for a variety of statically
and dynamically provisioned services, many of which have no
intrinsic need for jitter bounds. IP telephony is an important
application for the VW PDB where expected and worst-case jitter
for rate-controlled streams of packets is of interest; thus this
appendix is primarily focused on voice jitter.

Rather than the "phase jitter" used in the body of this document,
this appendix used "interpacket jitter" for a variety of reasons.
This might be changed in a future version. Note that, as shown in
section 2.4.1, the phase jitter can correct for a larger inter-
packet jitter.

The appendix focuses on jitter for individual flows aggregated in
a VW PDB, derives worst-case bounds on the jitter, and gives sim-
ulation results for jitter.

6.1  Jitter and Delay


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The VW PDB is sufficiently restrictive in its rules to preserve
the required EF per-hop behavior under aggregation. These proper-
ties also make it useful as a basis for Internet telephony, to get
low jitter and delay. Since a VW PDB will have link arrival rates
that do not exceed departure rates over fairly small time scales,
end-to-end delay is based on the transmission time of a packet on
a wire and the handling time of individual network elements and
thus is a function of the number of hops in a path, the bandwidth
of the links, and the properties of the particular piece of equip-
ment used. Unless the end-to-end delay is excessive due to very
slow links or very slow equipment, it is usually the jitter, or
variation of delay, of a voice stream that is more critical than
the delay.

We derive the worst case jitter for a a VW PDB in a DS domain
using it to carry a number of rate-controlled flows. For this we
use inter-packet jitter, defined as the absolute value of the dif-
ference between the arrival time difference of two adjacent pack-
ets and their departure time difference, that is:

(EQ 3)jitter = |(ak-aj) - (dk-dj)|

The maximum jitter will occur if one packet waits for no other
packets at any hop of its path and the adjacent packet waits for
the maximum amount of packets possible. There are two sources of
jitter, one from waiting for other EF packets that may have accu-
mulated in a queue due to simultaneous arrivals of EF packets on
several input lines feeding the same queue and another from wait-
ing for non-EF packets to complete. The first type is strictly
bounded by the properties of the VW PDB and the EF PHB. The second
type is minimized by using a Priority Queuing mechanism to sched-
ule the output link and giving priority to EF packets and this
value can be approached by using a non-bursty weighted round-
robin packet scheduler and giving the EF queue a large weight. The
total jitter is the sum of these two.

Maximum jitter will be given across the domain in terms of T, the
virtual packet time or cycle time. It is important to recall the
analysis of section 2.0 showing that this jitter across the DS
domain is completely invisible to the end-to-end flow using the VW
PDB if it is within the jitter window at the egress router.

6.1.1  Jitter from other VW packets

The jitter from meeting other packets of the VW aggregate comes
from (near) simultaneous arrival of packets at different input
ports all destined for the same output queue that can be com-
pletely rearranged at the next packet arrival to that queue. This
jitter has a strict bound which we will show here.

It will be helpful to remember that, from RFC 2598, a PDB using
the EF PHB will get its configured share of each link at all time
scales above the time to send an MTU at the rate corresponding to

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that share of that link.

Focus on the DS domain of Figure 9. Unless otherwise stated, in
this section assume M Boundary Routers, each having N inputs and
outputs. We assume that each of the BR's ingress ports receives a
flow of EF-marked packets that are being policed to a peak rate R.
If each flow sends a fixed size packet, then it's possible to cal-
culate the fixed time, T, between packets of each of these MxN
flows that enters the DS domain, a quite reasonable assumption for
packets carrying voice. For example, assume a domain traversed by
MxN flows of 68 byte voice packets sent at 20 ms time intervals.
Note we assume all ingress links have some packets that will be
marked for the VW aggregate. Thus the total number of ingress EF-
marked streams to the VW aggregate is I = MxN.

To construct a network where the maximum jitter can occur, a sin-
gle flow traversing the network must be able to meet packets from
all the other flows marked for the EF PHB and it should be possi-
ble to meet them in the worst possible way.

Figure 9: A DS domain

Unless otherwise stated, assume that all the routers of the domain
have N inputs and outputs and that all links have the same band-
width B. Although there are a number of ways that the individual
streams from different egress ports might combine in the interior
of the network, in a properly configured network, the arrival rate
of the VW PDB must not exceed the departure rate at any network
node. Consider a particular flow from A to Z and how to ensure
that packets entering the VW PDB at A meet every other flow enter-
ing the domain from all egress points as they traverse the domain
to Z. Consider three cases: the first is a single bottleneck, the
second makes no assumptions about routing in the network and the
third assumes that the paths of individual flows can be completely
specified.

Assume there are H hops from A to Z and that delay is the minimum
time it takes for a packet to go from A to Z in the absence of
queuing. Both packets experience delay and thus it subtracts in
the jitter calculation. Recall that the packets of the flow are
separated in time by T, then (normalizing to a start time of 0):

(EQ 4)dj = 0

(EQ 5)dk = T

(EQ 6)aj = delay

(EQ 7)ak = time spent waiting behind all other packets +delay+T

Then we can use:

(EQ 8)jitter = time spent waiting behind all other packets

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as we explore calculating worst case jitter for different topolo-
gies. That is, the worst case queueing delay can be used to bound
the jitter.

The next step is to establish some useful relationships between
parameters. First, assume that some fraction, f, of a link's
capacity is allocated to EF-marked packets. Since we are assuming
that all the flows that are admitted into this DS domain's VW
aggregate generate packets at a spacing of T, this can be
expressed in time as fxT. Then the amount of time to send an EF
packet on each link can be written as fxT/(total number of EF-
marked flow crossing the link). Note that f should be less than
0.5 in order that an MTU-sized non-EF packet will not cause the EF
condition to be violated. In the subsequent analysis, we will, in
general, assume that the entire fraction f of EF traffic is
present in order to calculate worst case bounds.

6.1.1.1  Worst case jitter in a network with a dumbbell bottleneck

Consider a DS domain topology shown in Figure 10. In order for a
packet of the (A,Z) flow to wait behind packets of all the other
MxN - 1 flows, packets from each of these flows must be sitting in
the router queue for the bottleneck link L when the (A,Z) packet
arrives. Since N flows arrive on each of the M links, the lowest
bound on the bandwidth B occurs when the N packets arrive in
bursts. In this case, B must be large enough (relative to L) so
that the packets are still sitting in L's queue when our (A,Z)
packet arrives at the end of a burst of N packets, that is B >
NxL. Then the

(EQ 9)jitterworst case = MxNx(time to send an EF packet on L)

Since we expressed the EF aggregate's allocation on L as fxL, the
time to send an EF packet on L is (at most) fxT/(MxN), so

(EQ 10)jitterworst case = fxT



Figure 10: A dumbbell bottleneck

This result shows that the worst case jitter will be less than
half a packet time for any VW-compliant allocation on this topol-
ogy. For the worst case to occur, all N packets must arrive at
each of the M border routers within the time it takes to transmit
them all on B (from above, this is bounded by fxT/N). By assuming
independence, an interested person should be able to get some
insight on the likelihood of this happening. Simulation results
are included in a later section.

6.1.1.2  Worst case jitter in an arbitrary network


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Consider the network of Figure 9 and in this case, one packet of
the (A,Z) flow must arrive at the same time, but be queued behind
a packet from each of the other flows as it passes through the
network. This can happen at any link of the network and even at
the same link. Assume all links have bandwidth B and that we don't
know the path the individual EF packets or flows of the aggregate
will follow. Then the worst case jitter is

(EQ 11)jitterworst case = Ix(fxT/I) = fxT

the same as the bottleneck case. In a somewhat pathological con-
struct where two flows pass through the same link more than once,
but take different paths between those links, we assume the pack-
ets are serialized when they first meet and are not retimed by the
disjoint paths to meet again. Although one could construct a case
where the a particular packet queues behind another multiple
times, a bit of thought should show that this is unlikely in the
realm of applicability of the VW PDB.

If the allocation can have knowledge that not all flows of the
aggregate will take the same path, then one could allocate each
link to a smaller number of flows, but this would also imply that
the number of flows that it's possible to meet and be jittered by
is smaller. Allocation can be kept to under 0.5 times the band-
width of a core link, while the existence of multiple paths offers
both fault tolerance and an expectation that the actual load on
any link will be less than 0.5.

How likely is this case to happen? One packet of the (A,Z) flow
must encounter and queue behind every other individual shaped
flow that makes up the domain's VW aggregate as it crosses the
domain.

6.1.1.3  Maximal jitter in a network with "pinned" paths per flow

Then at each hop the (A,Z) packet has to arrive at the same time
as an EF packet from the (N-1) other inputs and the (A,Z) packet
has to be able to end up anywhere within that burst of N packets.
In particular, for two adjacent packets of the (A,Z) flow, one
must arrive at the front of every hop's burst and the other at the
end of every hop's burst. This clearly requires an unrealistic
form of path pinning or route selection by every individual EF-
marked flow entering the DS domain. This unidirectional path is
shown in Figure 11 where all routers have N inputs and at each of
the H routers on the path from A to Z, N-1 flows are sent to other
output queues, while N-1 of the shaped input flows that have not
yet crossed the A to Z path enter the router at the other input
ports.

Figure 11: Example path for maximal jitter across DS domain from
A to Z

It should be noted that if the number of hops from A to Z is not

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large enough, it won't be possible for one of its packets to meet
all the other shaped flows and if the number of hops is larger
than what's required there won't be any other shaped flows to meet
there. For the flow from A to B to meet every other ingress stream
as it traverses a path of H hops:

(EQ 12) Hx(N-1) = MxN - 1

then compute the maximum jitter as:

(EQ 13)jitter = Hx(N-1)x(time to send an EF packet on each link)

If the total number of ingress streams exceeds Hx(N-1) + 1, then
it's not possible to meet all the other streams and the maximum
jitter is

(EQ 14)jitterworst case = H x (N-1) x fT/(number of ingress-shaped
EF flows on each link)

Otherwise the max jitter is

(EQ 15)jitterworst case = (MxN - 1) x fT/(number of ingress-shaped
EF flows on each link)

Then the maximum jitter depends on the number of hops or the num-
ber of border routers. In this construction, the number of
ingress-shaped EF flows on each link is N, thus:

(EQ 16)jitterworst case < smaller of (HxfT, MxfxT)

 Dividing out T gives jitter in terms of the number of ingress
flow cycle times (or virtual packet times). Then, for the jitter
to exceed the cycle time (or 20 ms for our VoIP example),

(EQ 17)fxH > 1 and fxM > 1

If f were at its maximum of 0.5, then it appears to be easy to
exceed a cycle time of jitter across a domain. However, it's use-
ful to examine what f might typically be. Note that for this con-
struction:

(EQ 18)f= NxR/B

For our example voice flows, a reasonable R is 28-32 Kbps. Then,
for a link of 128 Kbps, f = 0.25xN; for 1.5 Mbps, f = 0.02xN; for
10 Mbps, f = 0.003xN; for 45 Mbps, f = 0.0007xN; and for 100 Mbps,
f = 0.0003xN. Then such a network of DS3 links can handle almost
1500 individual shaped flows at this rate. Another way to look at
this is that the hop count times the number of ingress ports of
each router must exceed the link bandwidth divided by the VoIP
rate in order to have a maximum jitter of a packet time at the
VoIP rate.


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(EQ 19)HxN > B/R

For a network of all T1 links, this becomes HxN > 50 and for
larger bandwidth links, it increases.

Suppose that the ingress flows are not the same rate. If the allo-
cation, f, is at its maximum, then this means the number of
ingress flows must decrease. For example, if the A to Z flow is
10xR, then it will meet 9 fewer packets as it traverses the net-
work. Even though the assumptions behind this case are not realis-
tic, we can see that the jitter can be kept to a reasonable
amount. The rules of the EF PHB and the VW PDB should make it easy
to compute the worst case jitter for any topology and allocation.

6.1.1.4  Achievability of the maximum

Now that we've examined how to compute the worst case jitter, we
look at how likely it is that this worst case happens and how it
relates to the jitter window.

In addition to the topological and allocation assumptions that
were made in order to allow a flow to have the opportunity of
meeting every other flow, events must align so that the meeting
actually happens at each hop. If we could assume independence of
the timing of each flow's arrival within an interval of T, then
that probability is on the order of (fT/N)N For this to happen at
every hop we need the joint probability of this happening at all H
nodes. Further we need the joint probability of that event in com-
bination with an adjacent packet not meeting any other packets.
For each additional hop, the number of ways the packets can com-
bine increases exponentially, thus the probability of that par-
ticular worst case combination decreases.

6.1.1.5  Jitter from non-VW packets

The worst case occurs when one packet of a flow waits for no other
packets to complete and the adjacent packet arrives at every hop
just as an MTU-sized non-EF packet has begun transmission. That
worst case jitter is the sum of the times to send MTU-sized pack-
ets at the link bandwidth of all the hops in the path or, for
equal bandwidth paths,

(EQ 20)jitter = HxMTU/B

Note that if one link has a bandwidth much smaller than the oth-
ers, that term will dominate the jitter.

If we assume that the MTU is on the order of 10-20 times the voice
packet size in our example, then the time to send an MTU on a link
is 10 or 20 times fxT/N so that our jitter bound becomes 20 x H x
fxT/N.

What has to happen in order to achieve the worst case? For jitter

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against the default traffic, one packet waits for no default traf-
fic and the adjacent packet arrives just as an MTU of the default
type begins transmission on the link.

The worst case is linear in the number of hops, but since the
joint probability of an EF packet arriving at each queue precisely
at the start of a non-EF packet on the link decreases in hop
count, measured or simulated jitter will be seen to grow as a neg-
ative exponential of the number of hops in a path, even at very
high percentiles of probability. The reason for this is that the
number of ways that the packets can arrive at the EF queue grows
as pH so the probability is on the order of p-H. When the link
bandwidth is small, it may be necessary to fragment non-EF packet
to control jitter.

How should we relate jitter in terms of source cycle times or vir-
tual packet times to the jitter window defined in section 2.0?
Note that we can write

(EQ 21)jitter window = Sx(1/R - 1/((nxR)/f))

and noting that T = S/R, we get:

(EQ 22)jitter window = Tx(n-f/n)

So that, in many cases, the jitter window can be approximated by
T.

6.2  Quantifying Jitter through Simulation

Section 1 derived and discussed the worst-case jitter for indi-
vidual flows of a diffserv per-domain behavior (PDB) based on the
EF PHB. We showed that the worst case jitter can be bounded and
calculated these theoretical bounds. The worst case bounds repre-
sent possible, but not likely, values. Thus, to get a better feel
for the likely worst jitter values, we used simulation.

We use the ns-2 network simulator; our use of this simulator has
been described in a number of documents [NS2,FBK,RFC2415]. The
following subsections describe the simulation set-up for these
particular experiments.

6.2.1  Topology

Figure 12 shows the topology we used in the simulations. A and Z
are edge routers through which traffic from various customers
enters and exits the Diffserv cloud. We vary the topology within
the Diffserv cloud to explore the worst-case jitter for EF traffic
in various scenarios. Jitter is measured on a flow or set of flows
that transit the network from A to Z. To avoid per hop synchroni-
zations, half the DE traffic at each hop is new to the path while
half of the DE traffic exits the path. For the mixed EF and DE
simulations, half the EF flows go from A to Z while, at each hop,

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the other half of the 10% rate only crosses the path at that hop.
As discussed in section 1, this is an unlikely construction but we
undertake it to give a more pessimistic jitter For the EF-only
simulations, we emulate the case analyzed in section 1.1.3 by mea-
suring jitter on one end to end flow and having (N-1) new EF flows
meet that flow at every hop. Note that N is determined by the max-
imum number of 28 kbps flows that can fit in the EF share of each
link, so N=share x bandwidth/28 kbps.

Figure 12: Simulated topology

6.2.2  Traffic

Traffic is generated to emulate G.729 voice flows with packet size
(B) of 68 Bytes and a 20 ms packetization rate. The resultant
flows have a rate of 27 Kbps. As previously discussed, jitter
experienced by the voice flows has two main components; jitter
caused by meeting others flows in the EF queue, and jitter due to
traffic in other low priority classes. To analyze the first compo-
nent, we vary the multiplexing level of voice flows that are
admitted into the DS domain and for the second, we generate data
traffic for the default or DE PHB. Since we are interested in
exploring the worst case jitter, data traffic is generated as
long-lived TCP connections with 1500 Byte MTU segments. Current
measurements show real Internet traffic consists of a mixture of
packet sizes, over 50% of which are minimum-sized packets of 40
bytes and over 80% of which are much smaller than 1500 Bytes
[CAIDA]. Thus a realistic traffic mix would only improve the jit-
ter that we see in the simulations.

6.2.3  Schedulers and Queues

All the nodes(routers) in the network have the same configura-
tion: a simple Priority Queue (PQ) scheduler with two queues.
Voice traffic is queued in the high priority queue while the data
traffic is queued in the queue with the lower priority. The sched-
uler empties all the packets in the high priority queue before
servicing the data packets in a lower priority queue. However, if
the scheduler is busy servicing a data packet at the time of
arrival of a voice packet, the voice packet is served only after
the data packet is serviced completely, i.e., the scheduler is
non-preemptive. For priority queuing where the low priority queue
is kept congested, simulating two queues is adequate.

Figure 13: Link scheduling in the simulations

6.2.4  Results

In the following simulations, three bandwidth values were used
for the DS domain links: 1.5 Mbps, 10 Mbps, and 45 Mbps. Unless
otherwise stated, the aggregate of EF traffic was allocated 10% of
the link bandwidth. The hops per path was varied from 1 to 24.
Then, the 1.5 Mbps links can carry about 5 voice flows, the 10

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Mbps about 36 voice flows, and 45 Mbps about 160.

6.2.4.1  Jitter due to other voice traffic only

To see the jitter that comes only from meeting other EF-marked
packets, we simulated voice traffic only and found this to be
quite negligible. For example, with a 10 Mbps link and 10% of the
link share assigned to the voice flows, a single bottleneck link
in a dumbbell has a worst case jitter of 2 ms. In simulation the
99.97th percentile jitter for one to 25 hops never exceeds a third
of a millisecond. This source of jitter is quite small, particu-
larly compared to the jitter from traffic in other queue(s) as we
will see in the next section.

6.2.4.2  Jitter in a voice flow where there is a congested default
class

Our traffic model for the DE queue keeps it full with mostly 1500
byte packets. From section 1, the worst case jitter is equal to
the number of hops times the time to transmit a packet at the link
rate. The likelihood of this worst case occurring goes down expo-
nentially in hop count, and the simulations confirm this. Figure
15 shows several percentiles of the jitter for 10 Mbps links where
the time to transmit an MTU at link speed is 1.2 ms.

Figure 14: Various percentile jitter values for 10 Mbps links and
10% allocation

Recall that the period of the voice streams is 20 ms and note
that, the jitter does not even reach half a period. The median
jitter gets quite flat with number of hops. Although the higher
percentile values increase at a somewhat higher rate with number
of hops, it still does not approach the calculated worst case. The
data is also shown normalized by the MTU transmission time at 10
Mbps. Now the vertical axis value is the number of MTU sized pack-
ets of jitter that the flow experiences. This normalization is
presented to make it easier to relate the results to the analysis,
though it obscures the impact (or lack thereof) of the jitter on
the 20 ms flows.

Figure 16 shows the same results for 1.5 Mbps links and Figure 17
for 45 Mbps links.

Figure 15: Various percentiles of jitter for 1.5 Mbps links and
10% share

Notice that the worst case jitter for the 1.5 Mbps link is on the
order of two cycle times while, for 45 Mbps, it is less than 10%
of the cycle time. However, the behavior in terms of number of
MTUs is similar.

Figure 16: Various percentiles of jitter for 45 Mbps links and
10% share

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The jitter in time and thus as a fraction of the virtual packet
time of the flow being measured clearly increases with decreasing
bandwidth. Even the smallest bandwidth, 1.5 Mbps can handle
nearly all jitter with a jitter buffer of 2 packets. The two
higher bandwidths don't even jitter by one virtual packet time,
thus staying within the jitter window. Figures 18, 19, and 20 com-
pare the median, 99th percentile and 99.97th percentile (essen-
tially the worst case). It's also interesting to normalize the
results of each experiment by the MTU transmission time at that
link bandwidth. The normalized values show that all scenarios
experience the same behavior relative to the MTU transmission
time.

Figure 17:  Median jitter for all three bandwidths by time and
normalized

Figure 18: 99th percentile of jitter for the three bandwidths;
absolute time and normalized

Figure 19: 99.97th percentile of jitter; absolute time and
normalized by MTU transmission times

The simulation experiments are not yet complete, but they clearly
show the probability of achieving the worst case jitter decreas-
ing with hop count and show that jitter can be controlled. The
normalization shows that the jitter behavior is the same regard-
less of bandwidth. The absolute times differ by scale factors that
depend on the bandwidth.

6.2.4.3  Jitter with an increased allocation

In the following, the experiments of the last section are
repeated, but using a 20% link share, rather than a 10% link share
Figure 21 shows the jitter percentiles for 10 Mbps links and a 20%
share. The values are also plotted with the 10% share results (on
the right hand side) to show how similar they are.

Figure 20: Jitter percentiles for 10 Mbps links and 20% EF share

Using the previous section, we would believe that the results for
other bandwidths would have the same shape, but be scaled by the
bandwidth difference. Figure 22 shows this to indeed be the case.
Thus it is sufficient to simulated only a single bandwidth.

Figure 21: Jitter for 1.5 Mbps links (on left) and 45 Mbps links
(on right)

In all the experiments, it can be clearly seen that the shape of
the jitter vs. hops curve flattens because the probability of the
worst case occurring at each hop decreases exponentially in hops.
To see if there is an allocation level at which the jitter behav-
ior diverges, we simulated and show results for allocations of 10,

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20, 30, 40, and 50 percent, all for 10 Mbps links in Figure 23.

Figure 22: Median and 99th percentile jitter for various
allocations and 10 Mbps links

What may not be obvious from figure 19 is that the similarity
between the five allocation levels shows that jitter from other EF
traffic is negligible compared to the jitter from waiting for DE
packets to complete. Clearly, the probability of jitter from
other EF traffic goes up with increasing allocation level, but it
is so small compared to the DE-induced jitter that it isn't visi-
ble except for the highest percentiles and the largest hop count.


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