Effective capacity: a wireless link model for support of quality of service

TLDR: This paper proposes and develops a link-layer channel model termed effective capacity (EC), which first model a wireless link by two EC functions, namely, the probability of nonempty buffer, and the QoS exponent of a connection, and proposes a simple and efficient algorithm to estimate these EC functions.

Abstract: To facilitate the efficient support of quality of service (QoS) in next-generation wireless networks, it is essential to model a wireless channel in terms of connection-level QoS metrics such as data rate, delay, and delay-violation probability. However, the existing wireless channel models, i.e., physical-layer channel models, do not explicitly characterize a wireless channel in terms of these QoS metrics. In this paper, we propose and develop a link-layer channel model termed effective capacity (EC). In this approach, we first model a wireless link by two EC functions, namely, the probability of nonempty buffer, and the QoS exponent of a connection. Then, we propose a simple and efficient algorithm to estimate these EC functions. The physical-layer analogs of these two link-layer EC functions are the marginal distribution (e.g., Rayleigh-Ricean distribution) and the Doppler spectrum, respectively. The key advantages of the EC link-layer modeling and estimation are: 1) ease of translation into QoS guarantees, such as delay bounds; 2) simplicity of implementation; and 3) accuracy, and hence, efficiency in admission control and resource reservation. We illustrate the advantage of our approach with a set of simulation experiments, which show that the actual QoS metric is closely approximated by the QoS metric predicted by the EC link-layer model, under a wide range of conditions.

Figures

Figure 3: TraÆc and service characterization.

Figure 5: Relation between service curve and delay-bound violation.

Figure 8: Estimated function ̂( ) vs. source rate .

Figure 7: Estimated function ̂( ) vs. source rate .

Figure 9: Marginal CDF and ( ) vs. source rate .

Figure 1: A packet-based wireless communication system.

Full text

Eective Capacity: A Wireless Link Mo del
for Supp ort of Quality of Service
Dap eng Wu Rohit Negi

Abstract
To facilitate the eÆcient support of quality of service (QoS) in next-generation wireless networks, it
is essential to mo del a wireless channel in terms of connection-level QoS metrics such as data rate, delay
and delay-violation probability. However, the existing wireless channel models,
i.e.
, physical-layer channel
models, do not explicitly characterize a wireless channel in terms of these QoS metrics. In this paper,
we propose and develop a link-layer channel mo del termed
eective capacity
(EC). In this approach, we
rst model a wireless link bytwo EC functions, namely, the probability of non-empty buer, and the QoS
exponent of a connection. Then, we propose a simple and eÆcient algorithm to estimate these EC func-
tions. The physical-layer analogs of these two link-layer EC functions are the marginal distribution (
e.g.
,
Rayleigh/Ricean distribution) and the Doppler sp ectrum, resp ectively. The key advantages of the EC link-
layer mo deling and estimation are (1) ease of translation into QoS guarantees, such as delay b ounds, (2)
simplicity of implementation, (3) accuracy, and hence, eÆciency in admission control and resource reserva-
tion. We illustrate the advantage of our approach with a set of simulation experiments, which show that the
actual QoS metric is closely approximated by the QoS metric predicted by the EC link-layer mo del, under
a wide range of conditions.
Key Words:
Wireless channel mo del, QoS, delay, Doppler sp ectrum, fading, queueing theory.

This work was supp orted in part by the National Science Foundation under the grant ANI-0111818. Any opinions,
ndings, and conclusions or recommendations expressed in this paper are those of the authors and do not necessarily
reect the views of the National Science Foundation. Please direct all corresp ondence to Dapeng Wu, Carnegie Mellon
University, Dept. of Electrical & Computer Engineering, 5000 Forbes Avenue, Pittsburgh, PA 15213, USA. Email:
dpwu@cs.cmu.edu. URL: http://www.cs.cmu.edu/~dpwu. Rohit Negi is with Carnegie Mellon University, Dept. of
Electrical & Computer Engineering, 5000 Forbes Avenue, Pittsburgh, PA 15213, USA. Email: negi@ece.cmu.edu.
URL: http://www.ece.cmu.edu/~negi.

1 Intro duction
The next-generation wireless networks such as the third generation (3G) and the fourth generation
(4G) wireless systems are targeted at supporting diverse quality of service (QoS) requirements and
traÆc characteristics [9]. The success in the deploymentofsuch networks will critically dep end up on
how eÆciently the wireless networks can supp ort traÆc ows with QoS guarantees [10]. Toachieve
this goal, mechanisms for guaranteeing QoS (
e.g.
, admission control and resource reservation) need
to b e eÆcient and practical [6].
EÆcient and practical mechanisms for QoS supp ort require accurate and simple channel models
[10]. Towards this end, it is essential to model a wireless channel in terms of QoS metrics such
as data rate, delay and delay-violation probability. However, the existing channel mo dels (
e.g.
,
Rayleigh fading mo del with a sp ecied Doppler spectrum) do not explicitly characterize a wireless
channel in terms of these QoS metrics. To use the existing channel mo dels for QoS supp ort, we
rst need to estimate the parameters for the channel model, and then extract QoS metrics from the
mo del. This two-step approachisobviously complex, and may lead to inaccuracies due to possible
approximations in extracting QoS metrics from the mo dels.
To address this issue, we prop ose and develop a link-layer channel mo del termed the
eective
capacity
(EC) mo del. In this approach, we rst mo del a wireless link bytwo EC functions, namely,
the probability of non-empty buer, and the QoS exp onent of the connection. Then, we prop ose a
simple and eÆcient algorithm to estimate these EC functions. The physical-layer analogs of these
two link-layer EC functions are the marginal distribution (
e.g.
,Rayleigh/Ricean distribution) and
the Doppler sp ectrum, resp ectively. The key advantages of EC link-layer mo deling and estimation
are (1) ease of translation into QoS guarantees, such as delay b ounds, (2) simplicity of implementa-
tion, (3) accuracy, and hence, eÆciency in admission control and resource reservation. Simulation
results show that the actual QoS metric is closely approximated by the estimated QoS metric ob-
tained from our channel estimation algorithm, under a wide range of conditions. This demonstrates
the eectiveness of the EC link-layer model, in guaranteeing QoS.
Conventional channel mo dels directly characterize the uctuations in the amplitude of a radio
signal. We call these mo dels
physical-layer channel
mo dels, to distinguish them from the
link-
layer channel
mo del we prop ose. In this pap er, we consider small-scale fading mo del [12] for the
physical-layer channel. Small-scale fading mo dels describe the characteristics of generic radio paths
in a statistical fashion. Small-scale fading refers to the dramatic changes in signal amplitude and
phase that can be exp erienced as a result of small changes (as small as a half-wavelength) in
the spatial separation between a receiver and a transmitter. Small-scale fading can be slow or
fast, dep ending on the Doppler spread. The statistical time-varying nature of the envelop e of a
at-fading signal is characterized by distributions suchasRayleigh, Ricean, Nakagami, etc. [12].
Physical-layer channel models provide a quick estimate of the physical-layer p erformance of
wireless communications systems (
e.g.
, symbol error rate vs. signal-to-noise ratio (SNR)). However,
physical-layer channel mo dels cannot b e easily translated into complex link-layer QoS guarantees
for a connection, such as b ounds on delay. The reason is that, these complex QoS requirements
1

Wireless
channel
Data
source
decoder
Channel
Modulator
encoder
Receiver
Data
sink
Demodulator
Channel
access device
Network
Network
Transmitter
Link-layer channel
SNR
Received
Instantanteous channel capacity
log(1+SNR)
access device
Physical-layer channel
Figure 1: A packet-based wireless communication system.
need an analysis of the queueing b ehavior of the connection, which is hard to extract from physical-
layer mo dels. Thus it is hard to use physical-layer mo dels in QoS supp ort mechanisms, such as
admission control and resource reservation.
Recognizing that the limitation of physical-layer channel mo dels in QoS support, is the diÆculty
in analyzing queues using them, we prop ose moving the channel mo del up the protocol stack, from
the physical-layer to the link-layer. We call the resulting mo del an
eective capacity
link mo del,
b ecause it captures a generalized link-level capacity notion of the fading channel. Figure 1 illustrates
the dierence between the conventional physical-layer and our prop osed link-layer mo del.
1
For
simplicity,weinterchange \physical-layer channel" with \physical channel" and interchange \link-
layer channel" with \link" in the rest of the paper.
To summarize, the eective capacity link mo del that we prop ose, aims to characterize wireless
channels in terms of functions that can be easily mapped to link-level QoS metrics, such as delay-
b ound violation probability. Furthermore, we prop ose a novel channel estimation algorithm that
allows practical and accurate measurements of the eective capacity mo del functions.
The remainder of this pap er is organized as follows. In Section 2, we elaborate on the QoS
guarantees that motivate us to search for a link-layer mo del. We describ e usage parameter control
(UPC) traÆc characterization, and its dual, the service curve (SC) network service characteriza-
tion. We show that these concepts, b orrowed from networking literature, lead us to consider the
eective capacity mo del of wireless channels. In Section 3, we formally dene the eective capacity
1
In Figure 1, we use Shannon's channel capacity to represent the instantaneous channel capacity. In practical
situations, the instantaneous channel capacity is log (1 +
SN R=

link
), where 
link
is determined by the modulation
scheme and the channel co de used.
2

link mo del, in terms of two functions, probability of non-empty buer and QoS exp onent. We
then describ e an estimation algorithm, which accurately estimates these functions, with very low
complexity. Section 4 shows simulation results that demonstrate the advantage of using the EC link
mo del to accurately predict QoS, under a variety of conditions. This leads to eÆcient admission
control and resource reservation. Section 5 concludes this pap er and p oints out future research
directions. Table 1 lists the notations used in this pap er.
2 Motivation for Using Link-layer Channel Mo dels
Physical-layer channel mo dels have b een extremely successful in wireless transmitter/receiver de-
sign, since they can b e used to predict physical-layer p erformance characteristics such as bit/frame
error rates as a function of SNR. These are very useful for circuit switched applications, such as
cellular telephony. However, future wireless systems will need to handle increasingly diverse multi-
media traÆc, which are exp ected to b e primarily packet switched. For example, the new Wideband
Co de Division Multiple Access (W-CDMA) sp ecications make explicit provisions for 3G networks
to evolveover time, from circuit switching to packet switching. The key dierence b etween circuit
switching and packet switching, from a link-layer design viewpoint, is that packet switching requires
queueing
analysis of the link. Thus, it b ecomes imp ortant to characterize the eect of the data
traÆc pattern, as well as the channel b ehavior, on the performance of the communication system.
QoS guarantees have b een heavily researched in the
wired
networks (
e.g.
, Asynchronous Transfer
Mo de (ATM) and Internet Proto col (IP) networks). These guarantees rely on the queueing mo del
shown in Figure 2. This gure shows that the source traÆc and the network service are matched
using a First-In-First-Out (FIFO) buer (queue). Thus, the queue prevents loss of packets that
could o ccur when the source rate is more than the service rate, at the exp ense of increasing the
delay. Queueing analysis, which is needed to design appropriate admission control and resource
reservation algorithms [1, 13 ], requires source
traÆc characterization
and
service characterization
.
The most widely used approach for traÆc characterization, is to require that the amount of data
(
i.e.
, bits as a function of time
t
) pro duced by a source conform to an upp er b ound, called the
traÆc
envelope
(
t
). The service characterization for guaranteed service is a guarantee of a minimum
service (
i.e.
, bits communicated as a function of time) level, sp ecied by a
service curve
(
t
) [7].
Functions (
t
) and (
t
) are sp ecied in terms of certain traÆc and service parameters resp ectively.
Examples include the UPC parameters used in ATM [1] for traÆc characterization, and the traÆc
sp ecication T-SPEC and the service sp ecication R-SPEC elds used with the resource reservation
proto col (RSVP) [2 , 7 ] in IP networks.
To elaborate on this point, a traÆc envelop e (
t
) characterizes the source behavior in the
following manner: over any window of size
t
, the amount of actual source traÆc
A
(
t
) do es not
exceed (
t
) (see Figure 3). For example, the UPC parameters sp ecify (
t
)by,
(
t
) = min
f

(
s
)
p
t; 
(
s
)
s
t
+

(
s
)
g
(1)
where

(
s
)
p
is the p eak data rate,

(
s
)
s
the sustainable rate, and

(
s
)
the leaky-bucket size [7 ]. As
3

Table 1: Notations.
Pr
fg
: probability of the event
fg
.
(
t
) : a traÆc envelop e.
(
t
) : a network service curve.
A
(
t
) : the amount of source data over the time interval [0,
t
).
S
(
t
) : the actual service of a channel in bits, over the time interval [0,
t
).
r
(
t
) : the instantaneous capacityofachannel at time
t
.
~
S
(
t
) : the service provided byachannel,
i.e.
,
S
(
t
)=
R
t
0
r
(

)d

.

(
s
)
p
: the peak rate of a source.

(
s
)
s
: the sustainable rate of a source.

(
s
)
: the leaky-bucket size for the source mo del.

(
c
)
s
: the channel sustainable rate.

(
c
) : the maximum fade duration of a channel.
r
: the service rate of a queue.
B
: the buer size of a queue.
(
u
) : the asymptotic log-moment generating function of a sto chastic pro cess.

(
u
) : the eective bandwidth of a source.

(
c
)
(
u
) : the eective capacityofachannel.
Q
(
t
) : the length of a queue at time
t
.
D
(
t
) : the delay experienced by a packet arriving at time
t
.
D
max
: the delay b ound required by a connection.
"
: the target QoS violation probability for a connection.

: the QoS exp onent of a connection.

: probability of the event that a queue is non-empty.
S
(
f
) : the Doppler sp ectrum (p ower spectral density) of a channel.
f
m
: the maximum Doppler frequency for a mobile terminal.
f
c
: the carrier frequency.
det
(
:
) : the determinant of a matrix.
x
n
: the
n
th channel gain (normalized by the noise variance).
r
awgn
: the capacity of an additive white Gaussian noise (AWGN) channel.
source
Data
B
S(t)
Rate
Q(t)
Queue
Channel
µ
Capacity
r
A(t)
Figure 2: A queueing system mo del.
4

Frequently asked questions

Q1. What have the authors contributed in "E ective capacity: a wireless link model for support of quality of service" ?

In this paper, the authors propose and develop a link-layer channel model termed e ective capacity ( EC ). Then, the authors propose a simple and eÆcient algorithm to estimate these EC functions. The authors illustrate the advantage of their approach with a set of simulation experiments, which show that the actual QoS metric is closely approximated by the QoS metric predicted by the EC link-layer model, under a wide range of conditions. 

Q2. What have the authors stated for future works in "E ective capacity: a wireless link model for support of quality of service" ?

Therefore, the authors believe that the EC link model, which was speci cally constructed keeping in mind this QoS metric, will nd wide applicability in future wireless networks that need QoS provisioning. In addition, their link model provides a general framework, under which physical-layer fading channels such as AWGN, Rayleigh fading, and Ricean fading channels can be studied. The authors show that the f ( c ) ( ) ; ( c ) ( ) g functions that specify their e ective capacity link model, can be easily used to obtain the service curve speci cation ( t ) = f ( c ) ; ( c ) s g. 

Q3. What is the definition of small-scale fading?

Small-scale fading refers to the dramatic changes in signal amplitude and phase that can be experienced as a result of small changes (as small as a half-wavelength) in the spatial separation between a receiver and a transmitter. 

Q4. How many samples of Rayleigh/Ricean were generated for each 1000-second run?

Since the channel sample rate is 1000 samples/sec, 1,000,000 samples of Rayleigh/Ricean at fading xn were generated for each 1000- second run, using a rst-order auto-regressive (AR) model. 

Q5. What is the way to analyze the performance of the link layer?

With the multi-state Markov chain model, the performance of the link layer can be analyzed, but only at expense of enormous complexity. 

Q6. What is the rst order of the packets?

Generated packets are rst sent to the (in nite) bu er at the transmitter, whose queue length is Qn, where n refers to the n th sample-interval. 

Q7. What are the main features of the EC link model?

In summary, their EC link model has the following features: simplicity of implementation, eÆciency in admission control, and exibility in allocating bandwidth and delay for connections. 

Q8. What is the service characterization for guaranteed service?

The service characterization for guaranteed service is a guarantee of a minimum service (i.e., bits communicated as a function of time) level, speci ed by a service curve (t) [7]. 

Q9. what is the probability of a connection being non-empty?

Q(t) : the length of a queue at time t. D(t) : the delay experienced by a packet arriving at time t. Dmax : the delay bound required by a connection. " : the target QoS violation probability for a connection. : the QoS exponent of a connection. : probability of the event that a queue is non-empty. 

Q10. What is the probability of the source being nonempty?

For a given source rate , (c)( ) = PrfQ(t) 0g is again the probability that the bu er is nonempty at a randomly chosen time t, while the QoS exponent (c)( ) is de ned as ( ) = 1( ), where 1( ) is the inverse function of (c)(u). 

Q11. What is the e ective capacity of a wireless channel?

Figure 4(b) shows that the e ective capacity (c)(u) decreases with increasing QoS exponent u; that is, as the QoS requirement becomes more stringent, the source rate that a wireless channel can support with this QoS guarantee, decreases. 

Q12. Why does higher SNR result in smaller probability of a packet being fading?

This is because higher SNR results in larger channel capacity, which leads to smaller probability that a packet will be bu ered, i.e., smaller ̂( ). 

Q13. Why is the probability of non-empty bu er larger than the outage probability?

The reason is that the probability of non-empty bu er takes into account the e ect of packet accumulation in the bu er, while the outage probability does not (i.e., an arrival packet will be immediately discarded if the SNR falls below a threshold). 

Q14. What is the definition of a deterministic service curve?

recognizing that the time-varying wireless channel cannot deterministically guarantee a useful service curve, the authors propose to use a statistical service curve f (t); "g.As mentioned earlier, it is hard to extract a statistical service curve using the existing physicallayer channel models. 

Q15. How do the authors plot the marginal CDF of the Rayleigh channel?

Solving (42) for SNRth, the authors obtainSNRth = (1 + SNRavg) rawgn 1 (43)Using (41) and (43), the authors plot the marginal CDF of the Rayleigh channel, as a function of source rate .