Sep 18, 1992 - for teleconference cal Is by comparing two potential. TD's: One consisting of a ... algorithms do determine, though, a rate at which the source.
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.