Opportunistic Scheduling: An Illustration of Cross-layer Design
Xin Liu
Computer Science Dept.
Univ. of California, Davis
Ness B. Shroff
Dept. of Electrical & Computer Engineering
Purdue University
Abstract
The
unique
characteristics
of
wireless
communication systems - namely, timing-varying
channel conditions and multiuser diversity - call for
specifically tailored system designs. In this paper, we
overview a cross-layer design method, named
opportunistic scheduling, for exploiting the timevarying nature of the radio environment to increase
the overall performance of the system under certain
QoS/fairness requirements of users. We first discuss
a general system model, and the fairness and QoS
constraints being considered. Then, we present
various optimal index policies and discuss their
properties. We also outline a methodology to
implement these opportunistic scheduling solutions
in practice. Lastly, we discuss the advantages and
costs associated with opportunistic scheduling, and
identify possible future research directions.
1. Introduction and Literature Review
Built upon the success of second generation cellular
services, tremendous amounts of resources have
been invested into 3G systems, especially in Asia, by
companies such as SK Telcom and NTT DoCoMo.
Further, other wireless systems, including WLAN,
ad-hoc networks, and wireless sensor networks, are
rapidly proliferating. In summary, the demand for
wireless data services is skyrocketing and there is a
real need to optimally design and engineer wireless
systems.A major challenge is that wireless communication requires sharing a limited natural
resource: the radio frequency spectrum. The data-rate
capacity that a radio frequency channel can support is
limited by Shannon’s capacity laws. Hence, in the
wireless environment, one has to engineer the
network very carefully so that little, if any, wireless
spectrum is wasted.
Compared with the wired counterpart, wireless
systems have some unique characteristics, namely
scare resource, time-varying and location dependent
channel conditions. The nature of the wireless
medium makes it particularly attractive for crosslayer design. Different layers have been considered,
as illustrated by the following examples. 1)
Application layer and network layer. For instance, a
multimedia server can adjust the coding scheme
based on available bandwidth by tracking packet
losses. 2) Transport layer and network layer, e.g.,
Edwin K. P. Chong
Dept. of Electrical & Computer Engineering
Colorado State University
TCP modifications for energy efficiency. 3) Network
layer and data link layer. For instance, link reliability
information can facilitate routing decisions. 4) MAC
and physical layer, which is the focus of this paper.
The basic idea of “opportunistic scheduling” that will
be overviewed in this paper is allocating resources to
links when they experience good channel conditions
while avoiding allocating resources to links when
they experience poor channel conditions, thus
efficiently utilizing radio resources. This is also
referred as channel-aware scheduling or exploiting
multi-user diversity. We use the term opportunistic
to denote the ability to schedule users based on
favorable channel conditions. On the other hand, the
potential to transmit at higher data rates
opportunistically (i.e., when channel conditions
permit) also introduces an important tradeoff between
wireless resource efficiency and the level of
satisfaction among different users. For example,
allowing only users close to the base station to
transmit at high transmission power may result in
very high throughput, but sacrifice the transmissions
of other users. Such a scheme cannot satisfy the
increasing demand for quality of service (QoS)
provisioning in the emerging high-rate data wireless
networks. To address this problem, we present here a
framework for scheduling users in an opportunistic
way. The objective is to improve wireless resource
efficiency by exploiting time-varying channel
conditions while at the same time controlling the
level of fairness and QoS among users.
1.1 Literature Review
Wireless scheduling schemes have attracted a lot of
recent attention. First, the scheduling policies of
wireline networks are extended wireless networks.
The proposed wireless scheduling schemes provide
various degrees of performance guarantees, including
short-term and long-term fairness, as well as shortterm and long-term throughput bounds. A survey of
these algorithms can be found in [1]. However, these
efforts model a channel as being either “good” or
“bad,” which may be too simple to effectively
characterize realistic wireless channels, especially for
data services.
In [2, 3], the authors present a scheduling scheme for
the Qualcomm/HDR system. Their scheduling
scheme exploits time-varying channel conditions
while maintaining “proportional fairness,” as defined
in [3, 4].
In [5, 6, 7, 8], the authors study scheduling
algorithms for the transmission of data to multiple
users. Both delay and channel conditions are taken
into account. Throughput optimality is defined in [6]
as follows: a scheduling algorithm is throughput
optimal if it is able to keep all queues stable if this is
at all feasible to do with any scheduling algorithm.
Furthermore, the authors of [9] investigate a
scheduling algorithm to maximize the minimum
weighted throughput of users. We discuss these
schemes in more detail later.
In [10, 11], we present a framework for opportunistic
scheduling. In particular, the overall performance of
the system is maximized under certain QoS/fairness
requirements of users.
Opportunistic scheduling exploits the channel
fluctuations of users. Thus a natural question to ask is
what we should do in environments with little
scattering and/or slow fading. In [12], the authors
present a scheme that uses multiple transmission
antennas to “induce” channel fluctuations, and thus
exploit multi-user diversity. Further, such a scheme
can also be used opportunistically to null inter-cell
interference.
In [13], scheduling problems for real-time traffic are
studied. The authors show that the greedy algorithm
is 1/2 competitive against the offline optimal
algorithm. Further, they show that no deterministic
online algorithm can achieve a competitive ratio
higher than 1/2.
Opportunistic scheduling has also been studied under
various scenarios, including distributed systems,
(e.g., [14, 15, 16],) systems with multiple input and
multiple output (MIMO) antenna arrays, (e.g., [17,
18, 12],) multi-carrier systems, (e.g., [19],) sensor
networks, (e.g., [20],) multi-hop wireless systems,
(e.g., [21, 22],) and with power and rate control, (e.g.,
[23, 24, 25]). A cautionary note on cross-layer design
is presented in [26]. A thorough analysis on user –
level performance is given in [27].
1.2 Organization
This paper overviews the concept of opportunistic
scheduling and how it can be used to improve system
efficiency as well as provide adequate QoS. In
Section 2, we provide a general system model, and
the fairness and QoS constraints being considered.
Then, in Section 3, we present various optimal index
policies and discuss their properties. In Section 3, we
also outline a methodology of how to implement
these opportunistic scheduling solutions in practice.
In Section 4 we provide a discussion of various issues
as well as some precautionary notes and possible
future research directions. This is followed by a
conclusion in Section 5. All the results are presented
without proofs. We refer readers to the corresponding
papers for reference.
2. System Model and Constraints
2.1 System Model
We consider a time-slotted system where time is the
resource to be shared among all users. The system
can have more than one channel (frequency band),
but at any given time, only one user can occupy a
given channel within a cell. Here, we focus on the
scheduling problem for a single given channel. Such
a system model includes TDMA systems as well as
time-slotted CDMA systems (an example of the latter
is the IS-856 system, also known as HDR).
Channel conditions in wireless networks are timevarying, and thus users experience time-varying
performance. We use a stochastic model to capture
the time-varying and channel-condition-dependent
performance of each user. Specifically, following the
k
approach of [12], let {U i } be a stochastic process
k
associated with user i , where U i is the level of
performance that would be experienced by user i if
k
it is scheduled to transmit at time k. The value of U i
measures the “worth” or “utility” of time-slot k to the
user i, and is in general a function of its channel
condition. The better the channel condition of user i,
k
the larger the value of U i . Examples of the value of
U ik are throughput, the value of throughput minus
the cost of power consumption, etc. We assume that
U ik is nonnegative and bounded. For simplicity, we
k
assume that {U i } is stationary and ergodic (this
assumption can be removed in some case, e.g., see
[11]). For convenience, we use the notation

U  {U1 , , U N } , where U i is a random
variable representing the performance value of user i
at a generic time-slot. Note that the stationary
assumption does not preclude correlations across
users or across time and moreover this assumption
can be relaxed, as in [11].
Wireless spectrum is a scarce resource, hence
improving the efficiency of spectrum utilization is
important, especially to provide affordable high-ratedata service. However, a scheme designed only to
maximize the overall throughput could be unfairly
biased, especially when there are users with widely
disparate distances from the base station. To address
this
problem,
we
introduce
QoS/fairness
requirements into the framework of opportunistic
scheduling— our goal is to maximize the system
performance (defined later) by exploiting timevarying channel conditions while maintaining certain
user-oriented constraints. Examples of such
constraints include long-term and/or short-term
fairness constraints or (direct) performance
constraints.
Throughput maximization In this case, the only
objective is to maximize the overall system
throughput regardless the performance of each
individual user. In other words, each user is
guaranteed zero percent of the system throughput. In
this case, a small number of users with very good
channel conditions may consume all the resource and
starve other users.
A scheduling policy is a rule that specifies which user
is scheduled at each time-slot. For simplicity of
Max-min fairness The objective of the throughput
max-min fairness is to maximize the minimum
throughput of all users. Let N be the number of users
in the system. Each user is guaranteed 1/N portion of
the system throughput. This objective is “absolutely”
fair. However, when there are users with very poor
channel conditions, to achieve max-min throughput
fairness will cause significant system performance
penalty.

notation, let Q (U ) be the decision of a stationary

policy Q at a general time-slot where U is the
performance value of users. At a generic time-slot, if

a policy Q schedules user i  Q(U )  {1,..., N }
to transmit, then the system receives a “reward” of
U i . Note that E (UQ (U ) ) is the average system
performance value associated with policy Q, and it is
the sum of all users’ average performance values
(where we reap a reward of U i only if user i is
scheduled). The objective is to find a policy Q that
maximizes the average system performance value
E (U Q (U ) ) under the constraints. In this paper, we
focus on stationary policies. Extensions on more
general policies, including non-stationary and noncausal policies, can be found in [11].
We are interested only in policies that satisfy specific
QoS/fairness requirements. We say that a policy Q is
feasible if it satisfies the constraints for all users. Our
goal is to find a feasible policy Q that maximizes the
system performance, which may be defined
differently under different assumptions.
We focus on the downlink of a wireless network. The
base station serves as the scheduling agent. The
scheduling scheme does the following: at the
beginning of a time-slot, the scheduler (i.e., the base
station) decides which user should be assigned the
time-slot based on the performance values of the
users at that time-slot. If a user is assigned a timeslot, then the base station will transmit to the user in
that time-slot. In general, downlink transmission is
more important for data traffic because of the highly
asymmetric nature of the data service.
2.2 Fairness and QoS Constraints
We first summarize the fairness and QoS constraints
discussed in the paper.
Utilitarian fairness: In this case, each
guaranteed a certain portion of the total
throughput. Two extreme cases of utilitarian
is the max-min throughput fairness and
throughput maximization.
user is
system
fairness
system
Proportional fairness: Proportional fairness (PF)
scheduler maximizes the product of the throughput
delivered to all the users. In other words, the set of
throughput achieved by different users is
proportionally fair if increasing the throughput of one
user from the current level by x% requires a
cumulative percentage decrease in all the users of
more than x%. Proportional fairness presents a
tradeoff between the overall throughput and each
user’s throughput.
Temporal resource-sharing fairness: In this case,
each user is guaranteed a certain portion of the
resource, i.e., time-slots. Note that temporal resourcesharing fairness is different from the utilitarian
fairness. In wireline networks, when a certain amount
of resource is assigned to a user, it is equivalent to
granting the user a certain amount of
throughput/performance value. However, the
situation is different in wireless networks, where the
amount of resource and the performance value are
not directly related (though closely correlated). By
limiting the resource of each individual user, a user is
guaranteed a certain throughput (based on its channel
conditions). Resource consumed by a user can be
directly connected with the price the user should pay.
Premium users will obtain better services in a
stochastic sense.
Minimum data-rate constraints: In this case, each
user is guaranteed a minimum data-rate. This type of
QoS constraint is desirable for users, but difficult for
the system where feasibility is a major concern.
3. Optimal Scheduling Policies
A common objective of opportunistic scheduling is to
maximize the system performance given the
fairness/QoS constraints. To maximize the system
performance is formally presented as
max Q E (U Q (U ) ) .

Let Ti (Q)  E(Ui 1{Q(U )  i}) be the throughput
of user i under policy Q where 1{.} is the indicator
function. We have
T (Q)  i 1 Ti (Q)  E (UQ (U ) ).
N
Of course, the values of

Ti (Q ) depends on the
distribution of U , which is ignored in the notation
for simplicity. In this section, we summarize some
results in opportunistic scheduling. It is interesting
that optimal policies turn out to be simple, easily
implementable index policies under various fairness
and QoS constraints.
fairness constraint, and the greater the opportunity to
improve the system performance.
An optimal policy
Q* is defined as follows:

Q* (U )  arg max i (ui*  U i ) ,
*
where the u i s are real parameters satisfying
a) mi n i (ui )  0 ;
*

P{Q* (U )  i}  ri .

*
*
c) for all i, if P{Q (U )  i}  ri then u i =0.
b) for all i,
*
Let us explain the heuristics of the policy Q , which
is helpful to understand the intuition of opportunistic
*
3.1. Temporal Fairness
Because time is the resource shared among users, a
natural fairness criterion is to give each user at least a
certain share of the entire resource, i.e., time. Let ri
denote the minimum time-fraction that should be
assigned to user i, where ri  0 ,

N
r  1 , and
i 1 i
N is the number of users in the cell. Here, we assume
that the ri s are predetermined and serve as prespecified fairness constraints. The value of ri
dictates the minimum fraction of time that a user
should transmit on the channel, which is typically
determined by the user's class, the price the user is
willing to pay for the wireless service, or the user's
current channel conditions.
The scheduling
algorithm then decides which time-slot should be
assigned to which user, given the minimum timefraction requirement. Our goal is to develop a
scheduling policy Q that exploits the time-varying
channel conditions to maximize the total expected
system performance while satisfying the resourcesharing constraint. The problem can be stated
formally as follows:
scheduling. For a proof of the optimality of Q , we
refer readers to [11]. We can think of the parameter
u i* above as an “offset” used to satisfy the fairness
requirement. To elaborate, consider the case where
we want to maximize the overall performance
without any QoS requirements. It is straightforward
to show that we should always choose the “best” user
(i.e., the user with the maximum performance value)
to transmit. In other words,

Q* (U )  arg max i Ui .
However, such a scheme may be unfair to certain
users. Hence, to satisfy the fairness requirement, the
scheduling policy schedules the “relatively-best” user
to transmit. User i is “relatively-best” if
ui*  U i  u*j  U j for all j. If u i* >0, then user i
is an “unfortunate” user, i.e., the channel condition it
experiences is relatively poor. Hence, it has to take
advantage of some other users (e.g., users with
u *j =0) to satisfy its fairness requirement. Thus, to
maximize the overall system performance, we can
only give the “unfortunate” users the amount of
resource equivalent to their minimum requirements.
Last, when

P{Q* (U )  i}  ri for user i, the user
gets more than its minimum requirement---this user
*
max Q E (U Q (U ) )
cannot take advantage of other users, i.e., u i =0. In

subject to P{Q(U )  i}  ri , i  1,2,...N
summary, condition (a) above on
In words, the problem is to find an optimal policy
among all policies such that the total system
throughput is maximized where each user’s resourcesharing requirement is satisfied. Note that
 : i 1 ri  1 is a tuning parameter such that the
smaller the value of  , the less restrictive the
N
u i* is for
normalization and condition (b) is the feasibility
requirement. Condition (c) is important to the
*
optimality of Q . Its heuristic interpretation is that a
good user that gets more than its minimum
requirement cannot take advantage of other users.
This condition can also be explained in terms of
complementary slackness: if the constraint is not
active (i.e., the average performance of user i is
greater than its minimum requirement), then the
*
corresponding u i (which can be interpreted as a
Lagrange multiplier) is zero.
Property:
If
the
performance
values
U i s,
i  1,2,...N , are independent, then

Ti {Q}  P{Q(U )  i}U i  riU i , i  1,2,...N.
This property makes a strong statement about the
individual performance of each user. If users’
performance values are independent, the average
performance of every user in our opportunistic
scheduling scheme will be at least that of any nonopportunistic scheduling scheme. In this sense, the
opportunistic scheduling policy does not sacrifice any
user’s performance to improve the overall system
performance. Of course, different users may
experience different amounts of improvement. This
property can also be explored to provide direct
performance guarantees to users with simple resource
allocation schemes.
The authors of [9] consider a special case of the
above
opportunistic
scheduling
problem.
Specifically, they consider maximizing the minimum
weighted performance of users. This is a special case
of the utilitarian fairness problem defined in this
section.
This problem setting requires fairness in terms of
performance values, which, to some extent, parallels
the concept of weighted fair queueing used in
wireline networks. The difference is that the overall
capacity here is not fixed; it depends on channel
conditions, the values of ai , and the scheduling
policy.
*
The parameter vi can be considered a “scaling” used
to satisfy the utilitarian fairness constraint. The
optimal scheduling policy always chooses the
relatively-best user to transmit. In this case, a user is
relatively-best if
(b  v *j )U j  arg max i (b  vi* )U i .
*
The values of the u i s are determined by the

distribution of U and the values of the ri . In

practice, the distribution of U is unknown, and
*
hence we need to estimate the parameter u i .
Similarly, in the opportunistic scheduling schemes
discussed in other sections, there are also parameters
that need to be estimated. Estimations of the
parameters are discussed in Section 3.5.
3.2. Utilitarian Fairness
The problem formulation of the utilitarian fairness is
presented as
max Q T (Q )
subject to Ti (Q)  aiT (Q), i  1,2,...N ,
where
ai  0, and

N
i 1
ai  1.

Q* (U )  arg max i (b  vi* )Ui
b  1  i 1 ai vi* , and the vi* s are real
N
parameters satisfying
a) mi n i ( vi )  0 ;
*
b) for all i, Ti (Q )  ai T (Q );
*
c) for all i, if Ti (Q )  ai T (Q ); then vi =0.
*
Utilitarian scheduling schemes have certain notable
features. First, the utilitarian fairness constraint
controls the maximum discrepancy of performance
values among users. Second, the constraint given
ensures that a user is given at least a certain share of
the total performance, and is hence more suitable in
some situations than the temporal fairness constraint.
However, there is also a significant disadvantage of a
utilitarian scheduling scheme: a user experiencing
poor channel conditions could have a detrimental
impact on the overall system performance because a
substantial portion of the total time-slots may have to
be allocated to this user in order to meet its fairness
requirement. To alleviate this potential problem, one
can devise an adaptive threshold strategy [11].
Thus far, we have discussed two optimal scheduling
schemes that provide users with different fairness
guarantees. From a user’s viewpoint, a more direct
QoS is defined in terms of minimum-performance
guarantees.
To elaborate, the objective is to
maximize the average system performance subject to
meeting
each
user's
minimum-performance
requirement, formulated as:
max Q T (Q )
*
*
user, and its average performance value equals the
minimum requirement.
3.3 Minimum-performance Guarantee
An optimal policy is defined as follows:
where
*
As before, if vi >0, then the user is an “unfortunate”
*
subject to Ti (Q)  Ci , i  1,2,...N
where

Q* (U )  arg max i i*Ui
Ci is the minimum-throughput requirement of
user i. Consideration of this problem raises two
questions: (i) Is the requirements feasible, i.e., does
there exist a policy such that Ti (Q)  Ci , for all i?
is optimal for many types of scheduling problems.
For example, the optimal utilitarian policy defined
(ii) If it is feasible, which policy maximizes the
overall performance under the given QoS
requirement?
policy maximizes the total system throughput. On the
Compared to fairness requirements, the formulation
here offers users a more “direct” service guarantee.
For example, if the performance measure is defined
as the data-rate, then each user is guaranteed a
minimum data-rate, which may be more important to
a user than knowing that a minimum amount of
resource will be assigned to it. While appealing to
users, providing minimum-performance guarantees
can be quite difficult in practice because of the
feasibility issue---can the system satisfy the
performance requirements for all users? (Note that
feasibility is not a concern in the fairness-based
constraints.) More discussion on feasibility can be
found in [11]. There are, however, some natural
settings where feasibility is not a problem. For
example, the requirements can be set as the average
data rates in a non-opportunistic round-robin
scheduling scheme. Then, it is guaranteed to be
feasible for opportunistic scheduling policies.
An optimal policy is defined as follows:

Q* (U )  arg max i i*Ui
where
 i* s are real parameters satisfying
a) mi n i ( i )  1 ;
*
b) for all i, Ti (Q )  Ci ;
*
c) for all i, if Ti (Q )  Ci , then
*
The parameter
 i*
 i* =0.
“scales” the performance values
of users, and the scheduling policy schedules the
relatively-best user, where a user is relatively-best if
 U j  arg max i  Ui . If the scaling factor for a
*
j
*
i
user is larger than 1, then the user is an “unfortunate”
user, and it is granted only an average performance
value that equals its minimum-performance
requirement. The opportunistic scheduling policy
always provides “no-worse” performance values for
each user relative to that of the non-opportunistic
scheduling policy, assuming that the signaling cost is
negligible. Thus, the opportunistic scheduling policy
dominates non-opportunistic policies.
3.4 Index Policies
It turns out that a scheduling policy of the form of
earlier is in this form. If
other hand, if
 i*  1 for all i ,
 i*  1 / Ti (Q * ) for all i ,
then the
then the
policy is proportional fair [2].
In [5,6], the authors study scheduling algorithms
where both delay and channel conditions are taken
into account. Roughly speaking, the algorithm is:

Q* (U )  arg max i i*UiWi ,
where
Wi is the head-of-the-line packet delay for
queue i, and
 i*
is some constant. The policy is
throughput optimal.
We have presented a framework for opportunistic
scheduling and studied different scheduling
problems. These scheduling problems share a
common goal: to improve the spectrum efficiency
while maintaining certain levels of QoS for each user
using opportunistic scheduling algorithms.
The
solutions to these scheduling problems turn out to be
index policies---all the schemes choose the
“relatively-best” user to transmit. Although
“relatively-best” has a different meaning for each
scheduling policy, the basic idea is to use an offset or
a scaling to satisfy the QoS requirements for users. In
general, the larger the number of users sharing the

same channel, or the larger the variance of U , the
larger the “opportunistic” scheduling gain compared
with
non-opportunistic
scheduling
policies.
Furthermore, the more restrictive the QoS constraint,
the less the flexibility for opportunistic scheduling
decisions, and the lower the system performance
gain.
3.5 Implementation
Figure 1 shows a block diagram of a practical
scheduling procedure that incorporates on-line
parameters estimation. In our scheduling policy, the
base station needs to obtain information of each
user’s performance value at a given time slot to make
the scheduling decision. At a time slot, a user could
measure the received signal power level (from the
user’s base station) and the interference power level.
Based on the estimated SINR, the user can then
obtain its performance value. The information is sent
back to the base station, which can be accomplished
in several ways. For example, each user could
maintain a small signaling channel with the base
station. Alternatively, the required information could
be piggybacked over the user’s acknowledgment
packets. Then the base station makes the scheduling
decision based on the scheduling policy and transmits
to the selected user. Last, parameters used in the
scheduling policy are updated, which is discussed
next.

eik  gik  fi (u k )


 (uik  min j u kj )(1{Q k (U )  i}  P{Q k (U )  i})
which is an unbiased estimate. Hence, we can use a
stochastic approximation algorithm of the form
uik 1  uik   k gik ,
where, e.g.,
Figure 1. Block diagram of the scheduling policy
with on-line parameter estimation.
The opportunistic scheduling policies described in
previous sections all involve some parameters that
need to be estimated online. Such parameters are
determined by the values of the QoS requirements
and the distribution of the utility values. In practice,
such a distribution is a priori unknown, and hence we
need to estimate the parameters. In this section, we
use the temporal fairness scheduling scheme as an
example to describe briefly how to estimate these
parameters efficiently via stochastic approximation
techniques. Similar estimations can be applied for
other scheduling policies.
Recall that the parameters are chosen to satisfy the
following
requirement:
for
all
i,
if

P{Q(U )  i}  ri then u i* =0. Hence, we can write

as a root of the equation f (u )  0 , where the ith
component is given by


fi (u )  (ui  min j u j )( P{Q(U )  i}  ri ) ,
where i=1,2,…N. Next, we use a stochastic
approximation algorithm to generate a sequence of
1  2  3


u * . Each u k defines a policy Q k given by

Q k (U )  arg max i (Ui  uik ) . To construct the
iterates u , u , u , … that represent estimates of
stochastic approximation algorithm, we need an
k
estimate of f (u ) . Although we cannot obtain

f (u k ) directly, we have a noisy observation of its
components:

gik  (uik  min j u kj )(1{Q k (U )  i}  ri ) ,
where i=1,2,…N. The observation error in this case is
 k =1/k.
uik  min j u kj , we also need to ensure that


P{Q k (U )  i}  ri . If P{Q k (U )  i}  ri , then

u k is an infeasible parameter vector, which causes
When
some fairness constraint to be violated. To ensure
*
k
k
that u converges to u , we should project u

onto the feasible set of u s. However, because we do

not have knowledge of the distribution of U , it is
very difficult to find the exact projection. Hence, we
use the following intuitive algorithm as a projection.

It is easy to see that P{Q (U )  i} is an increasing
k
k
function of u i . Hence, if
uik  min j u kj , and

P{Q k (U )  i}  ri , then we increase the value of

u ik to increase the value of P{Q k (U )  i} , as a
projection to the feasible set. Although we do not

know the value of P{Q (U )  i} , we can estimate
k
k
it by a moving average. Let pi be the estimate of

P{Q k (U )  i} . We update pik in each time-slot
as follows:

pik  (1  w) pik 1  w1{Qk (U )  i},
k
where w is a constant, indicating how fast pi tracks

P{Q k (U )  i} .
If pi  ri ,
k
and
u  min j u , then we increase the value of u by
k
a small constant. By doing this, we push u towards

the feasible set of u s. Simulations indicate that this
k
i
k
j
k
i
approach works well.
4. Discussion
Different schemes may be suitable for different
scenarios. For example, if the service provider wants
to build a simple wireless network with pricing, the
temporal fairness scheduling scheme is a reasonable
choice. The temporal fairness scheduling scheme is
simple and flexible without feasibility concerns. The
amount of resource consumed by a user determines
the minimum performance the user gets (with
technical assumptions). The resource consumed by a
user can be connected directly with the price the user
should pay. On the other hand, the minimumperformance guarantee scheme provides users a
direct performance assurance, but involves the
additional complication of feasibility. If the service
provider wants to build a network that provides datarate guarantees, then this scheme is an appropriate
choice. However, in practice, the feasibility issue
may be difficult to handle, especially in a wireless
setting, and providing service performance
guarantees is challenging in both wireless and
wireline networks.
It should be noted that the framework for
opportunistic scheduling that we have described here
can also cover cases where there are different
constraints from different users. For example, some
users may have resource requirements while other
users can have a minimum-data-rate requirement. In
such scenarios, similar optimal solutions can be
provided under this framework using similar
optimization techniques.
4.1 Precautionary Notes
Opportunistic scheduling schemes, as an illustration
of the cross-layer design of wireless systems, exploit
time-varying channel conditions of users with the
objective to improve the system throughput.
However, nothing comes for free. Opportunistic
scheduling also has its own costs and limitations
discussed as follows.
There are signaling costs involved in all opportunistic
scheduling schemes because scheduling decisions
inherently depend on channel. Users need to
constantly estimate their channel conditions and
report to the base station. Hence, the actual
scheduling gain should take into account the
signaling costs.
Because users need to estimate the channel
conditions, estimation errors occur in all scheduling
schemes. There are various sources of estimation
errors: errors of estimations of channels, errors of
estimations of parameters involved in scheduling
schemes, and errors caused by various delays such as
transmission delay, estimation delay, and restriction
of time-slots, etc. In general, if the variation of
channel conditions is relatively slow, then the
estimation is good. We recommend a rigorous study
on this problem, especially in the case of fast fading.
Opportunistic scheduling exploits the fluctuation of
channel conditions, and thus scheduling gain
inherently depends on the amplitude of the variations
of channels. In general, the greater the fluctuation of
channel conditions, the larger the number of users,
the better the performance gain.
Another concern in opportunistic scheduling is the
time scale of fluctuation. The fluctuation of channels
should be slow enough for users to estimate and
exploit it. On the other hand, the fluctuation should
be fast enough, so that users won’t experience
extreme long delays. Though many data users are
delay-tolerant, extreme delays may cause upper-layer
problems such as TCP timeout.
There is a tradeoff between scheduling gain and
short-term performance. In general, the stronger the
time-correlation of channel conditions (i.e., the
slower the channel fluctuation), the worse the shortterm performance, and the greater the improvement
in the short-term performance, the less the scheduling
gain.
In general, scheduling gain increases as the number
of users increases. However, the normalized
scheduling gain (scheduling gain over number of
users) decreases with the increase of the number of
users, while the signaling cost per user remains the
same. Hence, it is a question of practical importance
to decide the number of users sharing the same
channel.
In summary, opportunistic scheduling presents a new
design approach, especially for delay-tolerant data
traffic. It has its own advantages and limitations. It is
thus important that the system designer to take a
holistic view of the cross-layer design in order to
avoid potential negative system-wide impacts.
4.2 Possible Research Directions
Many interesting problems are yet to be resolved in
opportunistic scheduling. We discuss some possible
research problems next.
Short-term Fairness We should note that the
problem formulations, the objectives, and the
constraints are expressed in terms of expectation in
this paper, which is a long-term performance
measure. There is no guarantee of short-term
performance. In [10], an extension is provided to
improve short-term performance. The basic idea is to
increase a user's probability of transmission when it
is behind in its share. There is a need for general
short-term fairness criteria tailored to wireless
networks and dealing with the short-term
performance in depth. We also refer interested
readers to [5-8] where queueing delays are
considered, [13] where real-time scheduling is
discussed, and [27] where user-level performance is
studied.
Delay A problem related to improving short-term
performance is to schedule traffic with deadlines, i.e.,
real-time traffic. Specifically, upon arrival, each realtime packet has a delay deadline, and packets that
cannot be transmitted before their deadlines are
dropped/marked. Research on scheduling with
deadlines in the wireline setting has led to various
approaches. The additional challenge in wireless
networks is due to the time-varying channel
conditions. Approaches to these problems may
include off-line optimal solutions with the
assumption of entire traffic and channel information,
on-line model-based solutions, and heuristic/greedy
algorithms. Heuristic algorithms play an important
role in real-time scheduling problems because
(typically) the optimal scheduling problem is NPcomplete and simplicity is a desirable feature. In the
wireline world, it is sometimes the case that
complicated scheduling schemes do not have
significant performance gains over simple schemes,
such as static priority or earliest-deadline-first. A
similar situation may be expected to hold for wireless
networks.
Another challenging problem is to minimize the
average packet delay. Although many schemes can
stabilize the queues, to control the average delay
performance is much more challenging.
Multi-carrier System Opportunistic scheduling is
based on the premise that the wireless channel is
time-varying, and we can schedule users to transmit
at those times that are opportunistically “relatively
good.” This idea can be extended to the frequency
domain: we opportunistically schedule users to
frequencies (and time) that are relatively good [19].
An example of such systems is an OFDM system. A
concern of opportunistic scheduling in such systems
is the signaling cost. Because each sub-carrier is very
narrow in OFDM systems, signaling should be
carefully designed to ensure good channel estimation
of users on different sub-carriers while avoiding
significant signaling overhead.
Physical Layer The performance of opportunistic
scheduling schemes is closely related to physicallayer designs. As explained earlier, estimation errors
occur in all opportunistic scheduling schemes. On
one hand, we need a better understanding of the
effect of channel estimation errors on scheduling
schemes. On the other hand, it calls for better channel
estimation techniques and smart coding schemes
(e.g., incremental redundancy transmission schemes
with turbo codes). Further, it is also important to
study the performance of opportunistic scheduling in
multiple antenna systems. In summary, a better
understanding of physical-layer technologies or even
layer-breaking designs can be potentially beneficial.
Admission Control The opportunistic scheduling
problems studied here have the net effect of increasing the overall effective capacity of the wireless
network. This means that the network can now
accommodate more users or higher-data-rate users.
Thus, we know that keeping all else fixed, the
admissible region of the wireless network will
increase by using opportunistic scheduling schemes.
A challenging problem that still remains is how to
make intelligent admission control decisions on
whether or not to allow a new user into a cell.
Although admission control is a difficult problem in
wireless systems whether or not opportunistic
scheduling is used, it is more challenging in the
context of opportunistic scheduling because
opportunistic scheduling increases the system
dynamics.
Multi-hop Networks Most of the current research on
opportunistic scheduling focuses on the downlink of
a cellular system. In such a system, there exists a
natural central controller, the base station. An
interesting question is whether and how to exploit the
time-domain diversity in a distributed multi-hop
environment, such as an ad-hoc network
[15,20,24,28].
5. Conclusion
To meet the increasing demand for wireless services,
especially affordable wireless data services, wireless
spectrum efficiency is becoming increasingly important. In wireless networks, users experience
unreliable, location-dependent, and time-varying
channel conditions. Traditionally, the channel
variation is considered as a negative factor for
reliable communication, and should be mitigated by
methods such as time interleaving, power control,
and multiple antennas. On the other hand,
opportunistic scheduling is designed to exploit the
variation of channel conditions to improve spectrum
efficiency. It adds an additional degree of freedom to
the system: time-domain diversity or also called
multi-user diversity. It improves spectrum efficiency,
especially for delay-tolerant data transmissions.
Various opportunistic scheduling schemes have been
studied. A common objective is to improve/maximize
system performance (e.g., throughput) under various
fairness and QoS constraints. In many cases, the
optimal policies are given in a simple parametric
form, hence lending themselves to easy
implementations. The advantages of opportunistic
scheduling also include the ability to work with other
resource management mechanisms. A good example
of this is the joint scheduling and power-allocation
scheme [23]. In summary, opportunistic scheduling,
with its own advantages and limitations, is an
excellent illustration of cross-layer design.
6. Acknowledgement
This research is supported in part by NSF awards
ANI-0207728, ANI-0099137, EIA-0130599, ECS0098089 and ANI-0207892, and the Indiana 21st
century center for wireless communications and
networking.
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