Traffic Descriptors for VBR Video Teleconferencing Over ATM Networks

IE.EWACM TRANSAC”IIONS ON NETWORKING,

VOL 3. NO 3, JUNE 1995

Traffic Descriptors for VBR Video Teleconferencing Over ATM Networks Amy

R. Reibman

and Arthur

Ab.Watt-This paper examines the problem of video transport over ATM networks using knowledge of both video system design and broadband net works. The following issues are addressed: video system delay caused by internal buffering, traffic descriptors (TD) for video, and call admission. We find that while different video sequences require different TD parameters, the following trends hold for all sequences examined. Fkst, increasing the delay in the video system decreases the neeessary peak rate and significantly increases the number of calls that can be carried by the network. Second, as an operational traffic descriptor for video, the leaky-bucket algorithm appears to be superior to the sliding-window algorithm. And finally, with a delay in the video system, the statistical multiplexing gain from VBR over CBR video is upper bounded by roughly a factor of four, and to obtain a gain of about 2.0 can require the operational traffic descriptor to have a window or bucket size on the order of a thousand cells. We briefly discuss how increasing the complexity of the video system may enable the size of the bucket or window to be reduced.

1,

E ENVIS1ON video

w

Network

(B-ISDN)

(ATM).

video

terminal

descriptor.

to initiate and

of service.

the negotiated

traffic

traffic

over

ATM

design

using

broadband

that

may

be

provides this paper

Manuscript

appears

received

approved by IEEE/ACM

the

resources,

and terminal

may andhr

is cstabl i shed. the network

[o ensure

that it does comply of the above scenario

the problem

knowledge

familiar

some important

to the

to that traffic

for the truftic descriptor

networks.

and broadband-network

to submit

descriptor.

We view

networks

and

material

system.

the de-

if it can provide

In this paper, we describe the influence on the video

Transfer

does not have available

If the call

a

Digital

uses a traffic

to a call conforming

parameters

the submitted

carrying

a call,

it intends

the call

reject tbe call, or the nctw(mk

altema[ive

the quality monitors

of service

If the netw(wk

it may simply negotiate

accepts

for

Services

on Asynchronous

the network the traffic

network

quality

scenario

Integrated

tbe user decides

contacts

The

desired

with

thut is based

When

to characterize

network.

following

the

call in a Broadband

Mode

scriptor

INTROI){JCTION

While to

this

either

researchers, insights.

of video

of both

the

transport

video paper

system contains

video

researchers

unified

perspective

An abbreviated

version

of

in I I],

September

18, 1992; revised

September

15. 1993:

TRA~SW_TK)W ON NHIVORKiNG Editor D. Raychaud.

huri. The authors we with AT&T Bell Iidmratories, IEEE Log Number 9410804.

Holmdel, NJ 07733 USA.

1063V6692/95$04.00

W. Berger

We examine

the impact that the presence of a network

monitor

(or Lfsage Parameter

system.

We argue that this monitor

to apply meets

rate control

the negotiated

to ensure traffic

traffic

(UPC)) has on the video

Control

will

force the video ~ystem

its submitted

traffic

indeed

descriptors.

We are interested in the traffic descriptor for a video call in a B-ISDN using ATM. Viewing a traffic descriptor as a means for specifying

user traffic

levels that will place demands

on

resources,

there

shared

different

approaches

and 2) an The theory,

network

that can be taken

operutiotrul approach,

statistical

approach

average

may be motivated

two

fundamentally approach.

see [2].

is [he more conventional

and focuses on statistical

long-term

are

I ) a .sfatisficu/

traffic parameters,

rate and burst duration. by the apparent

in traffic such as the

Such an approach

availability

of methodolo-

for predicting performance of a network stressed by traffic with given statistical parameters. However, associated with a statistical framework for traffic is the difficult task of verifying a set of statistical traffic parameters. By the very nature of their definitions, statistical traffic parameters may require a lengthy observation interval for verification. making real-time traffic-compliance-testing nearly impossible. Sec 13I or [4] for examples of such difficulties. With the operational approach, little heed is given to traffic at levels well within compliance with traffic contracts; rather focus is placed on traffic that is either just compliant or not compliant. This is achieved by implementing an opgies

erational

traffic

descriptor

as a parametrized

compliance-

testing algorithm intended to discriminate “excessive” traffic from “nonexcessive” traffic. Thus, by focusing on trafficcompliance-testing itself, we immediately resolve the issue of real-time traffic-compliance-testing at the terminal. Currently. the International Telecommunication Union (ITU, formerly CCITT) has on] y specified a traffic descriptor for the peak rate. though additional parameters arc expected to be specified in the future [5]. Tbe definition of the peak rate is operational. though the specifics of the definition are not of importance for the present paper. 1 Herein,

we begin the investigation

of suitable

traffic descrip-

for teleconference cal Is by comparing two potential TD’s: One consisting of a peak rate and a sliding-window algorithm, and the other consisting of a peak rate and a leakytors (TD’s)

1[n [5] the peak mte of a virtual chwrnel crmnectinn and of a ~irtual path connection is defined to he the reciprocal nf the minimum time between requests tu send an ATM Protocol Data Unit (a cell) to the Physic~l Layer Service Access Point in an ‘“equivalent” termimd, where the [utter is a gcmrd model for end-user equipment. (3 1995 IEEE

330

IEEWACM TRANSACTIONS

bucket algorithm. (These algorithms are reviewed in Section V; for more details, see, e.g., [4] and references therein.) Note that herein the sliding-window and leaky-bucket algorithms are not attempting to approximate the peak rate but rather are an additional element of the TD. Also, the algorithms do not attempt to approximate the average rate of the call (number of bits transmitted divided by the duration of the call). The algorithms do determine, though, a rate at which the source could continuously submit compliant traffic; we call this rate the “negotiated average rate.” Last, recall that these operational TDs are not intended to be a model that fully characterizes the source traffic; for such models see, e.g., [6]–[9]. For sample teleconference sequences, we determine the parameter values of the leaky bucket and sliding window so that the given video sequence is compliant with the traffic descriptor. Our results not only illustrate the magnitude of the parameter values that would be needed, but also provide a comparison of the two algorithms. Note that herein we determine the parameters afrer the video sequence has taken place, which, of course, can not be done in a real video call. Since TD parameters must be chosen prior to video compression in a real video call, it is impossible to guarantee that the chosen parameters will allow the VBR stream to pass without constraint. This leads to the question of how can a video terminal emit traffic that is compliant with the traffic descriptor negotiated at call setup. This question is addressed in [ 10], where Reibman and Haskell presented a joint encoderlchannel rate control algorithm. Voeten et al. [ 1I ] considered a preventive policing mechanism for a video terminal that also addresses this question. Section II briefly describes the video used for the experimental results in this paper. It also describes some important characteristics of a generic packet video system. In Section III, we describe the notions of traffic descriptors and Usage Parameter Control used in this paper, and illustrate their importance for video systems. In Section IV, we discuss comparisons between CBR and VBR video. Section V presents traffic descriptor parameter values for video. We show that the delay has a significant impact on the peak rate of the video call and consequently on the number of calls that can be carried by the network. Section VI briefly discusses call admission and possible multiplexing gains given the actual video data. Section VII concludes the paper with some discussions about how this information can be applied to the design of real systems. Throughout this paper, we describe the problem using the frame period as the discrete time unit; however, smaller sampling intervals are possible.

II. VIDEO A. Experimental

video

sequences

The video used in these examples was recorded at an actual meeting. The output of a CCD camera was digitized and recorded on a D I tape machine, in order to create repeatable digital source material. The CCIR601 format video was converted into common intermediate format (CIF) (240

ON NETWORKING,

I

tlLAvLT

i

A

ENCCOER BUFFER 1

I

R,

I wDEO ENCODER

VOL. 3, NO. 3, JUNE 1995

I I

CHANNEL 14TERFACl

NETWORK

UXODER SUFFER

Vlmo DECDCIER

A

U---F+= Fig. 1.

A generic packet video system.

lines) using the MPEG-SM filter[ 14]. The video was coded using a one-layer codec that has syntax compatible with H.261 [12]. The codec uses exhaustive motion estimation with +15 search range, a constant quantizer step-size of 8, and intra/inter/motion-compensation decisions for each macrobbck as in Reference Model 8 [13]. The first frame is coded intraframe, and all remaining frames are coded predictively. Within each frame, 3 macroblocks are transmitted intraframe. Eight sequences are used here. Sequence A is 10 min long and consists of a person listening and interspersing occasional comments and questions. Sequences B–F are both 5 min long, and each contains one active participant. In sequence B, the subject is constantly moving, while in sequences C–F, the subject moves only occasionally. Sequence G and H are 3 min 40 s. Sequence G contains one person listening, and sequence H contains two people. Detailed results are presented for only sequences A-C to conserve space. In all the sequences, intervals with high activity do not necessarily imply that the subject is speaking. Often, a high activity region corresponds to a period in which the subject is silent but moving, and a low activity region corresponds to when they speak. B. A Generic Packet Video System The system we consider is shown in Fig. 1. A video signal is applied to the video encoder, which produces an encoded video bit-stream. The number of encoded bits produced by frame i is Ei. The encoded bit-stream is stored in the encoder buffer before being transmitted via the channel interface to the network. The rate control device selects Ri, the number of bits transmitted on the channel during frame period i, such that no video buffer constraints will be violated and no traffic that exceeds the negotiated TD parameters is submitted to the network [10]. In addition, the rate control device also selects the quantizer step-size used by the encoder. After being transmitted across the network, the video bit-stream is stored in the decoder buffer. It is then input to the video decoder, which outputs a video signal. For a CBR video system, everything is identical except the traffic descriptor specifies a constant bit rate. A delay may be necessary in the video system to guarantee that the decoder will have access to all the bits corresponding to frame i by the time that frame needs to be displayed. The

RI-.IBMAN

delay

AND

is dc[ined

rcceivcs

by the interval

between

the time (he decoder

the lirst bit a[ the start of the call

decoder

to decode.

begins

every

until

the

time

the

commences,

a frame 1/;10 seconds. Thus, the

Once decoding

must then be displayed

‘1’ =

vulue of (he delay. given by I.’f ’ seconds where

/, is a non-

negative

at both

real

encoder

number.

must

be known

Moreover.

and the decoder.

c:ill, since the video bit-stream in the encoder delay

buffer

twtwctm

buffer.

so that a Iramc

delay

frame

fr{ml

delay

buffer

ou[put

delay

the video

Therefore,

is encoded

every

the encoder

is constan(

variable

there

to ensure

in the decoder

the

during the course of’ the

may experience

can be decoded

fw a variahlc

(J prim-i.

and in the network,

[hc time

al the decoder

7

and equal

is a variable

causes the video

system

to be

with

that

compliant

this control

or adjustment

part of the ~rqfic

network triiffic

will

seconds,

there

However,

tageous

both

statistical more

for

the

input

to 1,7

to the decoder plus the realized

is expected

network

multiplexing.

and

for

the network

There pared

not shape

are three

to CBR

VBR

the user is expected

video

than CBR

the same average However,

form

multiplexing.

neously.

In

this

user.

either

could

conservative

is necessary,

along

wilh

and

network,

understands

two

things

transport

\ti//

any tmffic

traffic set from

titited traffic

descriptor.

the network

has the option

infornlation

traffic The

enforces

policing

network tioning

and

simply

of service

terminal

some

and the user controls

115 ]. The

contract.

cell-loss

to the decoder

due

Hence.

by user

First.

with

the nego-

control

other

(UPC) The

users The

from

UPC

malicious

and a control The

traffic

as low-priority

certain

limits.

For

to be performed

control

excessive

loss of a high-priority

can be allowed

to happen.

that all high-priority with

action

The

algorithm

that is applied

by varying

exceed

simplifying

still be necessary,

comparable

delay,

and VBR

systems

is difficult

systems

varies

constant

have

variable

quality

A typical generate

method

rate of the CBR

of VBR quality

VBR

codec codec

will

will

vary

while

CBR

cell nor its possible

later loss therefore

system

submitted

must

to the network

descriptor.

Thus.

the

of the UPC for the present work is that its existence

will

one may seem better

and VBR

VBR video bit-stream

later.

video

is to

and to set the

to be equal to the peak rate of the VBR

so, the CBR

the

step-size

may be true a few seconds

quantizer rate. However,

neither

video tbe two

CBR

is within

that

and CBR between

the

between

action

the

is comparable

The

to compare

video

This

induced

I ) and make

while

Therefore,

an unconstrained

the delay

delay

since the quantizer

the reverse

not

of time.

quality,

with the image content.

it will

video. the quality

as a function

(nearly)

so the VBR unconstrained.

(see Fig.

since the relative

have

momentarily,

we consider

system

stream fills in the valleys

traffic

TD, although

that the network

comparing

step-

high-priority

as for CBR.

in the video

assumption

to obtain;

the feedback

the

will

To obtain

the

variable

the quantizer III.

the negotiated

excessive

the control

be simple

in Section

or to mark

argue

traffic

saw

buffer

within

produces

and disconnect

bit-stream.

video

traffic

the negotiated

the

should

buffer

as frequently

by the buffers

across today’s

a delay

feedback

be either

excessive We

known

protect

induce

could

the sake of this paper, is immaterial.

via

video

the

to make

equivalent.

A feedback

loop

statistical

by most codecs is by nature

codec can not bc completely

be exercised

may be simulta-

and we equate

for transmission

the bit-rate

never

com-

and better

the potential

output of a video

users or malfunc-

action

traffic,

provided

to

a monitoring

traffic drop

descriptor

informally

serves

must

video

quality.

systems and attempt

buffers

VBR

as we

to VBR

by using an encoder-decoder

the encoder

However,

bit-rate

and CBR

The

surface,

remove

However,

excess

traffic

the

for both CBR

MM.Y1m~[ submit

function.

includes

to the

VIDEO

video.

and the rate-control

is submitted. not be

UPC

traffic.

[() immediately

system,

examine

into CBR

feedback.

it. For video.

and should

the negotiated

that the

to conform

better

of VBR

channels

loop that controls size.

the

rate (CLR))

if excess traffic

l(~r the incoming

importance

bit-

of not transporting

to the excessive

is compliant

unconstrained

that is compliant

function.

terminals.

immediate

quality.

example

agreed-to

the video

the usage parameter as the

have

priority.

network

with

systems

and congestion

Second,

is vital

therefore,

as high

switched

video

policy.

the service

(with

the user submits

dropped:

pair

we

video produced

VBR. It is converted

with

the network

for

in tire

uses the same

one of these advantages

of both roughly

circuit

video calls.

a quality

quality

The compressed

to carry

be under-utilized

admission

between

that

that all can be obtained

(SMG)

Through

be able

both

not ensure (w would

call

contract

end-system

some

when

paper,

gain

delay,

Any

in both the VBR

On

connections,

of service

network

even

traffic

advantages

shorter

but it is unlikely

advan-

to obtain better quality

if all streams have completely

for established

ensure

the

should

primary

video:

statistical

rate.

ratc, the network to a very

video,

(Note

algorithms

the UPC

the user’s

possible,

the video

to be

VBR video calls than constant bit-rate (CBR)

Alternatively.

system

is not addressed. ) We assume

W. VBR VIDEO VERSUS CBR

must

the per-

111. VBR VIDEO AND NETWORK POLICING video

or both.

and sliding-window

and

video

descriptor.

delay (VBR)

step-size,

traffic

descriptor

in the

de.wripfor-whether

algorithms

priority)

traffic

buffering

of quantizer

multiplexing

bit-rate

necessitates

this paper the leaky-bucket

or different

the (high

negotiated

and it arrives

Imnsmissi{m.

Variable

to control the

bits are available

buffer.

buffer

delay

ATM cell that carries the first bits of the video

of the

73!

TRAF’E’IC DESCRIPTORS FOR VBR VIDEO TELECONFERENCING

H[:R(;ER:

is illustrated

in Fig. 3 where

the CBR

bit-

VBR peaks by reducing the step-size and thus increasing the instantaneous bit-

have superior given

by doing quality.

the presence

However.

given

of delay

rate. In the appendix,

VBR bit-stream

video

the delay will in the CBR

that we are imposing

we can use the buffer a

Also,

in the VBR we present

codec

will

undoubtedly

not be comparable, codec. comparable to reduce

an algorithm

delays, the peak

that generates

with minimum peak rate by making use of

IEEEJACM TRANSACTIONS

332

TABLE I

a

46 ,

STATISTICSFOR EJGRT SEQUENCES

r

1

\lean ,,1,

Seq.m.e(kb/s)

II

I

‘

B

II

239.6

I

o

I

I

20

30

1

I

50

60

2561

I,XA

4

849.9

ON NETWORKING, VOL. 3, NO. 3, JUNE 1995

s

,7. 33,. 2113 1617

o 1 2

,

..0,1. . , 2.49 1.90

II

.,7

z rn x

(u

c?

-

c

3’”

D

351,1

E

320.1

,

1.1?7, G H

I Q 3

j! 2240 994 I

0 3 .

23 8

... . ,1: .

..

[

,:, 6.66 263 I

0 54 137

024

7.31 2.s4

54 154

216,4

0 3

26644 924 9-

12.22 4.26

48 138

214.2

0 3

4004 ] 1054 I

18.69 ] 4.921

31 120

I

available buffering and delay. Throughout the following, we refer to the resulting constrained VBR bit-stream as the VBR bit-stream with delay. By using the algorithm in the appendix, the peak rate of the VBR bit-stream with delay is significantly smaller than the peak rate of the VBR stream without delay. Table I illustrates the reduction in the peak rate as the deIay increases, for all eight sequences. Ideally, to find the appropriate rate for the CBR video such that the quality is roughly equal to that of the VBR video, subjective tests for many choices of the CBR rate may be necessary [16]. Since this is quite difficult and tedious, in this paper we make the simple choice of setting the rate of the CBR to be equal to the peak rate of the VBR bit stream with delay. As our choice is somewhat arbitrary, we compare the resulting quality via plots of the peak signal-to-noise ratio (PSNR)2 and via subjective tests. In comparing the PSNR’S of CBR and VBR encoded bit streams from multiple example sequences, we find that the PSNR for VBR is nearly constant, while the CBR PSNR fluctuates wildly. Typically, there are alternating intervals of varying length where the PSNR from the CBR video is greater than that from the VBR video and where the PSNRS are roughly equal. Fig. 2 shows a typical example for sequence B, where the rate for the CBR was chosen as discussed above. The two sequences have identical PSNRS for several 10 s intervals, which may be long enough to be the determining factor in a viewer’s subjective evaluation. For a more direct examination of the relative quality in the context of the present study, we conducted subjective tests for three example sequences using both expert and nonexpert viewers. When the CBR video rate is the peak rate of the VBR bit-stream with delay, the quality of the CBR video is generally somewhat better than the VBR video in 2The PSNR is an objective measure for video quality. It provides a measure of the closeness of a coded frame to its original uncoded version. In general, larger values imply better quality. However, larger values of PSNR may

not translate into improvedsubjectivequality. Furthermore,the PSNR only measuresquality for a given frame, and does not provide a measure of the temporal quality.

40

Time (seconds)

EE2E3

.354

10

Fig. 2. Quality comparison between CBR and VBR,

Time Fig.

3.

Bit

rate

comparison

between

CBR and VBR.

the subjective tests. However, typically, the preference for the CBR video was not strong. Undoubtedly, the quality is closer to being equivalent than when the CBR rate is the peak rate of unconstrained VBR. For the present work, we will consider the quality of the CBR and VBR video as roughly equivalent. Heuristically, this rough equivalence has the “same level of accuracy” as the approximate model we use to estimate the SMG, see Section VI, and thus is a reasonable assumption to make for the present study. In a more detailed study, to obtain quality that is more equivalent, the CBR rate should be chosen lower than was done herein, though how much lower requires further study. As an interesting side note, Tan et al. [16] did a subjective evaluation of CBR and VBR and found that a CBR source with rate 1.84 times the VBR mean rate had comparable quality to an unbuffered VBR source with peak-to-mean ratio of 4. As shown in Table I, we found the same statistical parameters for sequence B with a delay of L = 3 frames. V. TRAFFIC DESCRIPTOR

PARAMETER

SELECTION

As mentioned in the introduction, we compare two potential traffic descriptors for a video call: One consisting of a peak rate and a sliding-window algorithm, and the other consisting of a peak rate and a leaky-bucket algorithm. We define the peak rate to be R,.a. = maxi Ri. Furthermore, for the simplicity of the mathematical descriptions below. we assume the size units are measured in bits and

RFMIMAN AND 13 ER(WR: TRA1-l-’K-EX-ZSCRIPTORS

FOR

VIIR

VIDEO TELECONFERENCING

m

RATE Window slze=6

=25

=> R

‘sequence average rate :

I 1, ,,

m v Window sbze= 5 => R

avg

.24

111111111111 0 5

Fly 4.

the

Example 01’ diding

TIME

Fig. 5.

window

(itme-in(crvid units are measured

can he easily time

converted

\ ‘--0 ---–-’-‘L =’-L- -=J 4 0 500 1000 1500200025003000 Negotiated average rate (kb/s)

in frame periods. These

into size units of bytes or cells,

and

units of seconds.

i o 3500

TD parameters. \equencc A.

if we ignore the finite capacity of the bucket. Thus, the traffic would be in compliance if we choose the bucket capacity N ,,,ax such that .’V, s N,,,,,TVI.

A. Sliding Window

C. Examples

A sliding window specifies that no more than a given number of bits (or cells) can be emitted in a time interval of a specified length, where the time interval can begin at any epoch, The sliding window can be described by two parameters. the time duration S,,,,,,, and the maximum number of bits that can be transmitted in that time window, W,,laJ. An alternate description could usc ti ‘n,(,r and the negotiated average bit-rate, R = It-,,,,,,, /,!!’l,,,,,, Mathematically, the constraint on the channel rate that is imposed by the sliding window is

We present examples both with and without delay in the video system. Without delay, the number of transmitted bits per frame period is equal to the number of encoded bits in that frame period, R, = Ei. With delay, the R, are obtained using the smoothing algorithm in the appendix. Table I shows the peak rate Rw,az and mean rate for 8 teleconferencing the

capacity

lSDN/ATM STS-3C)

k+.sr, ,f

(1)

for all A.

a given sequence of R,, it is a simple matter to determine the size of the sliding window parameters necessary to pass a given bit-stream without violation by computing the maximum number of bits in any window for each window length of interi~~. The negotiated average mte does not necessarily decrease monotonically as the window size increases. Fig. 4 shows an example in which the negotiated average rate increases as the window size increases from 5 to 6. Therefore, using a larger window size may actually decrease the transmission efficiency. For

sequences. of

the

a physical

provides

In

slowest

max{(),N-,

+

R; – R}.

(2)

the

the transmission

C

denotes

connection.

layer of 155.52Mb/sec

notation

layer.

capacity

In

(e.g.

B-

SONET

of 149.760Mb/sec

l.r]

in the last column

than or equal video

We assume that the video

connections connections

Likewise,

the largest

integer

less

equals the number of VBR

that can be earned

peak rate allocation. video

means

Thus, l~j

to r.

on the link,

l~j

assuming

is the number

that can be carried,

assuming

a

of CBR

the encoder

R,,,~X. Table I shows how increasing the delay in the video codecs

controls

the bit rate to be

decreases

the Wak

connections

that

rate

and increases

can be carried.

For

the number example,

for

of video sequence

A, if the delay is increased from zero to three frames, then the number of CBR connections that can be carried on a link three

fold

from

49 to 150.

Figs. 5–7 show the parameter

.V, =

last column, in

ATM Adaptation Layer (AAL) uses three bytes, and given the five bytes of ATM header in the 53 byte cell, the bit rate available for the video information, C, is 149.760 x 45/53 = 127. 155Mb/s. The

to the ATM

increases

A leaky bucket is a counter that increments by one for each cell emitted, up to a maximum value, and decrements at a given rate to as low as zerka cell can be emitted if the counter is less than the maximum value minus one. The leaky bucket can be considered as an imaginary FIFO buffer of size ,V,r,,,., bits with constant drain rate R bits per frame period. Let N, be the bucket fullness (in bits) at the end of frame period i. Since R, bits arrive in frame period i,

the

link

and the leaky bucket

values of the sliding

that guarantee

the sequences

ant to the traffic

descriptor

for sequences

average

is plotted

as a function

TD.”

rate

Herein,

to Wmax leaky

A-C.

we use the phrase the “size

for the sliding window

bucket

bucket

R

algorithm.

and the sliding

algorithm

The negotiated

of the

“size

of the

of the TD”

to refer

and N,,,.,

for the

(To show the parameters window

window

are compli-

of the leaky

on the same plot, we describe

of tbe window size, W,,,.,, and the negotiated average rate kir,,,~~/S’,,.,,,. To obtain the window length, .9,,.,,1, simply divide W,,,a, by tbe negotiated

the

sliding

window

in

terms

IEEWACMTRANSACTIONSON NETWORKING,VOL. 3, NO. 3, JUNE 1995

334

K :“

SW, no delay — - SW, withdelay

‘1

800 600

—

@

–– - LB,

II:1

no delay -- LB, with delay

I

;,

1389

[

01 0

1

(

500

1000

‘, \ ,——

~

——

o

15002000250030003500

Negotiated average Fig. 6.

__

c

1

!’

S1,d,= w,ndow with delay 143,771

(400,000)

127,621 (.255,000) 16,338 (45,WO) 127,617 (355,0W) 72,860 (202,0613) 11,135 (31,DGQ) 72,882 (202,000)

THE NEGOTIATEDAVERAGE RATE, fi, IS TWICETHE ALTL.IALAVERAGE RATE. (FOR SEQUENCEB WiTH DELAY, THE ENTRIESAREA DASH BECAUSETHEPEAK RATE M LESS THAN TWICETHE ACTLIALMEAN RATE)

rate (I&/s)

kaky bucket sequence without delay A 1,217 (3,381) 59 (164) s) c 751 (2,086)

SW, no delay — - SW, with dela~ —-- LB, no delay -----

with delay

LB,

\l sequence

average

rate

‘;,1 I

1 500

k ~Y b.