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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 57, NO. 4, JULY 2008 2509
Call Admission Control Optimizationin WiMAX Networks
Bo Rong, Member, IEEE , Yi Qian, Senior Member, IEEE , Kejie Lu, Senior Member, IEEE ,Hsiao-Hwa Chen, Senior Member, IEEE , and Mohsen Guizani, Senior Member, IEEE
Abstract—Worldwide interoperability for microwave access(WiMAX) is a promising technology for last-mile Internet access,particularly in the areas where wired infrastructures are notavailable. In a WiMAX network, call admission control (CAC) isdeployed to effectively control different traffic loads and preventthe network from being overloaded. In this paper, we proposea framework of a 2-D CAC to accommodate various features of WiMAX networks. Specifically, we decompose the 2-D uplink anddownlink WiMAX CAC problem into two independent 1-D CACproblems and formulate the 1-D CAC optimization, in which thedemands of service providers and subscribers are jointly taken
into account. To solve the optimization problem, we develop autility- and fairness-constrained optimal revenue policy, as wellas its corresponding approximation algorithm. Simulation resultsare presented to demonstrate the effectiveness of the proposedWiMAX CAC approach.
Index Terms—Call admission control (CAC), optimization,orthogonal frequency-division multiple access (OFDMA), time-division duplex (TDD), worldwide interoperability for microwaveaccess (WiMAX).
I. INTRODUCTION
THERE exist many regions in the world where wired
infrastructures (i.e., T1, DSL, cables, etc.) are difficultto deploy for geographical or economic reasons. To pro-
vide broadband wireless access to these regions, many re-
searchers advocate worldwide interoperability for microwave
access (WiMAX) [1], which is an IEEE 802.16 standardized
wireless technology based on an orthogonal frequency-division
multiplexing (OFDM) physical-layer architecture.
Manuscript received April 17, 2007; revised August 12, 2007 andSeptember 24, 2007. This work was supported in part by the National Science
Foundation (NSF) under Award 0424546 and an NSF Experimental Programto Stimulate Competitive Research start-up grant in Puerto Rico and in part bythe National Science Council of Taiwan under Grant NSC96-2221-E-110-035and Grant NSC96-2221-E-110-050. The review of this paper was coordinatedby Dr. E. Hossain.
B. Rong and K. Lu are with the Department of Electrical and ComputerEngineering, University of Puerto Rico at Mayagüez, Mayagüez, PR 00681USA (e-mail: [email protected]; [email protected]).
Y. Qian is with the National Institute of Standards and Technology,Gaithersburg, MD 20899 USA (e-mail: [email protected]).
H.-H. Chen is with the Department of Engineering Science, National ChengKung University, Tainan 701, Taiwan, R.O.C. (e-mail: [email protected]).
M. Guizani is with the Department of Computer Science, Western MichiganUniversity, Kalamazoo, MI 49008-5201 USA (e-mail: [email protected]).
Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TVT.2007.912595
To support a variety of applications, IEEE 802.16 has defined
four types of service [2]: 1) unsolicited grant service (UGS);
2) real-time polling service (rtPS); 3) non-real-time polling
service (nrtPS); and 4) best effort (BE) service. In a WiMAX
network with heterogeneous traffic loads, it is essential to find
a call admission control (CAC) solution that can effectively
allocate bandwidth resources to different applications. Moti-
vated by this, in this paper, we propose a WiMAX CAC frame-
work, which effectively meets all operational requirements of
WiMAX networks. In this CAC framework, we decomposethe 2-D uplink (UL) and downlink (DL) WiMAX CAC prob-
lem into two independent 1-D CAC problems. We further
formulate the 1-D CAC as an optimization problem under a
certain objective function, which should be chosen to maximize
either the revenue of service providers or the satisfaction of
subscribers.
With respect to 1-D CAC optimization problems, most pre-
vious studies were focused only on two approaches: 1) the
optimal revenue strategy (also known as the stochastic knap-
sack problem) [3]–[9] and 2) the minimum weighted sum
of blocking strategy [10]. In this paper, we will show that
these two strategies are, in fact, equivalent. Therefore, we
can mainly concentrate on the investigation of the optimalrevenue strategy and view the minimum weighted sum of
blocking strategy as the basis for fast calculation algorithms.
Clearly, the optimal revenue policy only considers the profit
of service providers. As an effort to conduct a multiobjec-
tive study, in this paper, we will also take into account the
requirements from WiMAX subscribers and develop a policy
with a satisfactory tradeoff between service providers and
subscribers.
The major contributions of this paper include the following:
1) the development of a framework of CAC for WiMAX
networks; 2) the investigation on various CAC optimization
strategies; and 3) the proposal of a series of constrained greedyrevenue algorithms for fast calculation. Through detailed per-
formance evaluation, the study carried out in this paper will
show that the proposed CAC solution can meet the expectations
of both service providers and subscribers.
The rest of the paper is outlined as follows: We first introduce
the CAC model for WiMAX networks in Section II. We will
then calculate the UL and DL capacity in Section III. In
Sections IV and V, we will introduce different 1-D CAC
optimization strategies and develop their corresponding ap-
proximation algorithms. In Section VI, the performance of
the proposed CAC optimization approach is demonstrated by
simulation results. Finally, Section VII concludes this paper.
0018-9545/$25.00 © 2008 IEEE
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2510 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 57, NO. 4, JULY 2008
Fig. 1. CAC deployment in a WiMAX PMP network.
II. CAC DEPLOYMENT IN WIMAX NETWORKS
A. WiMAX Networks
WiMAX technology promises to support both mesh and
point-to-multipoint (PMP) networks. A WiMAX mesh network
usually suits for constructing wide-area wireless backhaul net-
works such as citywide wireless coverage. On the other hand,
a WiMAX PMP network is used for providing the last-mile
access to broadband ISPs. In this paper, we will only discuss
the issues related to the WiMAX PMP network, which consists
of one base station and N subscribers.
As specified in the IEEE 802.16 standards [11], [12],
WiMAX employs OFDM in its physical-layer architecture.
In particular, IEEE 802.16 standards have defined a special
flavor of the OFDM system, namely, orthogonal frequency-
division multiple access (OFDMA), which employs a largerfast-Fourier-transform space (2048 and 4096 subcarriers) that
can be further divided into subchannels. The subchannels
are introduced to separate the data into logical streams on
DL transmission. Those logical streams may employ different
modulation/coding schemes and amplitude levels to address
subscribers with different channel characteristics. The subchan-
nels are also used for multiple-access purposes on UL. In prac-
tice, subscribers are assigned with subchannels through media
access control messages sent in the downstreams. Without the
loss of generality and for discussion brevity, in this paper,
we mainly concern ourselves with the scenario where each
WiMAX subscriber occupies exactly one subchannel.
To satisfy different operational environments, WiMAX
OFDMA supports five types of subcarrier allocation schemes to
formulate subchannels: 1) partial usage of subchannels (PUSC)
on UL and DL; 2) optional PUSC on UL; 3) full usage of
subchannels (FUSC) on DL; 4) optional FUSC on DL; and
5) adaptive modulation and coding (AMC) on UL and DL.
The first four subcarrier allocation schemes employ distributed
subcarrier permutation, whereas AMC employs adjacent sub-
carrier permutation. Since distributed subcarrier permutation
performs well in both fixed and mobile environments, it
becomes the dominant subcarrier permutation strategy for
WiMAX applications.
Once the subcarrier allocation is determined, the powerassigned to each subcarrier becomes another important issue
Fig. 2. Decomposition of UL CAC and DL CAC.
that affects the data transmission rate of a certain subscriber. For
UL, the transmission power of each subscriber depends on its
own transmitter. For DL, all subscribers share the total power onthe base station. To simplify the implementation, most WiMAX
base stations employ an equal power assignment scheme, which
grants every subcarrier the same DL power.
Frequency-division duplex (FDD) and time-division duplex
(TDD) are two of the most prevalent duplexing schemes used
in wireless systems. WiMAX can employ either of them to
separate UL and DL communication signals. FDD is usually
deployed in symmetric communication scenarios, where the
applications require equal bandwidth on UL and DL. On the
contrary, TDD is usually deployed in asymmetric communica-
tion scenarios.
In this paper, we assume that WiMAX is to provide the“last-mile” Internet access, which is a typical asymmetric
communication scenario. Accordingly, we will study WiMAX
OFDMA with TDD duplexing. For the kth WiMAX subscriber,
we assume that its UL and DL data transmission rates are trU kand trDk , respectively. If α% time slots on the subchannel are
allocated to DL traffic, then the DL bandwidth capacity is given
by BDk = α%trDk (thus, α% becomes the TDD DL bandwidth
proportional factor). Similarly, the UL bandwidth capacity can
be calculated by BU k = (1 − α%)trU k .
B. CAC Deployment
To handle a multiservice WiMAX network, it is very impor-tant to implement the CAC mechanism [13], [14]. First, CAC
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RONG et al.: CALL ADMISSION CONTROL OPTIMIZATION IN WiMAX NETWORKS 2511
TABLE IPARAMETER DECOMPOSING MODEL (reravg
i= (rerU
ibU i+ rerD
ibDi)/(bU
i+ bD
i))
is a critical step for the provision of quality-of-service (QoS)-
guaranteed services, because it can prevent the system from
being overloaded. Second, CAC can help a WiMAX network
provide different classes of traffic loads with different priorities
by manipulating their blocking probabilities.
As illustrated in Fig. 1, we propose to add a CAC manager
to the WiMAX base station. This CAC manager provides CAC
functions to all N subscribers under the base station. Moreover,
the access bandwidth capacity and the traffic load profile of
different subscribers are distinct and independent. Accordingly,
the CAC manager is composed of N CAC modules, in which
the kth CAC module only takes care of the kth subscriber’s
local network. In the rest of this paper, our study will be
concentrated on the design of an individual CAC module.When an application in the kth subscriber’s local network
initiates a connection to access the Internet, it sends a connec-
tion request to the kth CAC module with upstream bandwidth
requirement bU and downstream bandwidth requirement bD.
Then, the CAC manager simultaneously performs an admission
control check on the kth subscriber’s UL and DL. In this re-
spect, the CAC in a WiMAX network can naturally be modeled
by a 2-D CAC problem.
C. Decomposition of WiMAX CAC
A 2-D model for the WiMAX CAC can be formulated as fol-lows. For the local network of a given WiMAX subscriber, sup-
pose that M classes of bidirectional traffic loads share BU units
of UL bandwidth resource and BD units of DL bandwidth
resource, respectively. With regard to class i traffic, we assume
the following: 1) The requests arrive from a random process
with an average rate λi; 2) the average connection holding
time is 1/µi s; 3) the UL and DL bandwidth requirements
of a connection are fixed to bU i and bDi , respectively; and
4) the UL and DL revenue rates of a connection are rerU iand rerDi , respectively. Then, the WiMAX CAC is responsible
for accepting or rejecting a connection request according to a
certain policy.For investigation simplicity, we decouple the 2-D WiMAX
CAC problem into two independent 1-D CAC problems in this
paper. As shown in Fig. 2, the CAC module employs a UL CAC
policy and a DL CAC policy to separately make an admission
test on UL and DL, and only the connection requests that passes
both admission tests can be eventually accepted.
Either UL CAC or DL CAC can be modeled as a 1-D
CAC problem as follows. For the local network of a given
WiMAX subscriber, suppose that M classes of traffic loads
share B units of access bandwidth resource. With respect
to class i traffic, we assume the following: 1) The requests
arrive from a random process with an average rate λi; 2) the
average connection holding time is 1/µi s; 3) the bandwidthrequirement of a connection is fixed to bi; and 4) the revenue
Fig. 3. Framework for UL CAC or DL CAC.
rate of a connection is reri. We can then define the bandwidthrequirement vector as b = (b1, b2, . . . , bM ) and the system state
vector as n = (n1, n2, . . . , nM ), where ni is the number of
class-i connections in the system. Based on these parameters,
we can further define ΩCS as the set of all possible system
states, which can be expressed as ΩCS = n|n · b ≤ B. Under
this definition, the subscript CS stands for “complete sharing,”
which means that an incoming connection will be accepted if
sufficient bandwidth resources are available in the system. We
can now define a CAC policy, which is denoted by Ω, as an
arbitrary subset of ΩCS. Given Ω, a connection request will be
accepted if and only if the system state vector remains in Ω after
the connection is accepted.In this paper, we decompose the WiMAX CAC into UL
CAC and DL CAC with the parameter setup, as shown in
Table I. Although UL CAC and DL CAC are running as two
independent 1-D processes, their parameters are still related.
On one hand, UL CAC and DL CAC have their own special
characteristics such as distinct bandwidth capacity and band-
width requirements. On the other hand, they do share some
common features such as the number of traffic classes M ,arrival rate λi, service time 1/µi, and revenue rate ravgi . It is
noted that in Table I, we confer the same revenue rate ravgi to
UL CAC and DL CAC, despite the fact that originally, the UL
revenue rate is rU i
and the DL revenue rate is rDi
. The reason
is that the revenue could be achieved from a connection if and
only if it can pass both UL and DL CAC tests. Therefore, from
the perspective of 2-D WiMAX CAC, UL CAC and DL CAC
should have the same revenue rate. In this paper, we name this
mechanism as UL/DL revenue rate binding.
D. Framework for WiMAX CAC
The aforementioned CAC manager is composed of N CAC
modules, in which the kth CAC module contains two inde-
pendent parts, i.e., UL CAC and DL CAC. To fit the special
features of a WiMAX environment, we present a WiMAX CAC
framework in Fig. 3, which can be applied to either UL CAC orDL CAC.
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2512 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 57, NO. 4, JULY 2008
As illustrated in Fig. 3, the proposed framework consists of
three major modules: 1) CAC policy; 2) traffic load estimation;
and 3) bandwidth capacity estimation. Clearly, the CAC policy
is the most important module of all. To construct a successful
WiMAX network, the CAC policy has to consider the expec-
tations of both service providers and subscribers. Here, we
suppose that the UL and DL CAC policies independently work with their parameter setups, as shown in Table I, and utilize the
same optimization strategy.
In a WiMAX network, the traffic load and the subcarrier
channel condition are changing from time to time. Conse-
quently, UL and DL CAC policies have to be adaptive to these
dynamics. The traffic load estimation module should record
every connection request, regardless of whether it is eventually
accepted or not. Then, the UL and DL traffic load profiles
are periodically captured based on this record and sent to the
CAC policy module. As for the dynamic of channel condition,
the bandwidth estimation module retrieves the channel state
information (CSI) from the physical layer at regular intervals
of time. Then, the UL and DL bandwidth capacities of a given
subscriber are calculated from the CSI and sent to the CAC
policy module. To operate adaptively, the CAC policy module
should adjust its parameters based on the updated information
from the other two modules.
To mitigate the channel errors in the physical layer, it is ap-
propriate to apply link-layer fragmentation and retransmission
to WiMAX [15]. In this respect, the CAC policy module also
needs to interact with the WiMAX link layer. In particular, after
a connection request is accepted, the CAC policy module has to
transfer the bit error rate (BER) requirement of this connection
to the fragmentation and retransmission module in the link
layer.For the proposed framework in Fig. 3, we need to consider
two major issues: 1) how to calculate UL and DL bandwidth ca-
pacity and 2) what the design of a 1-D CAC policy is. Although
it is also important to capture the traffic load profile, we do not
particularly discuss this issue here as it has been extensively ad-
dressed in many previous works on wired networks [16], [17].
In Section III, we will investigate the UL and DL bandwidth ca-
pacity of a given subscriber. In Sections IV and V, we will study
the design of a 1-D CAC policy as an optimization problem.
III. BANDWIDTH CAPACITY
In this section, we calculate the UL and DL bandwidthcapacity of the kth subscriber based on CSI. We begin with the
approach for DL capacity, and then, this approach will be easily
extended to UL.
Fig. 4 illustrates the N -subscriber WiMAX DL channel
model, in which H k(f ) and N k(f ) denote the channel fre-
quency response function and noise power density function of
the kth subscriber, respectively. The quality of each subscriber’s
subchannel is indicated by the signal-to-noise ratio (SNR)
function SNRk(f ), which is defined as
SNRk(f ) = |H k(f )|2 /N k(f ) (1)
where SNRk(f )(1 ≤ k ≤ N ) is the CSI that the CAC man-ager needs. Since the CAC manager is placed in the base
Fig. 4. WiMAX DL channel model.
station, it can collect SNRk(f ) easily from the physical
layer.
For analytical simplicity, in this paper, we are only interestedin the investigation of the most common scenario, where each
WiMAX subscriber occupies exactly one subchannel. Once the
subcarrier allocation and power assignment of the subchannels
are known, the DL bandwidth capacity of the kth WiMAX
subscriber can be calculated with the following notations:
N number of subscribers;
J number of subcarriers;
S J set of all subcarriers, defined as 1, 2, . . . , j , . . . , J ;
∆f physical bandwidth of each subcarrier;
Dk subcarrier set assigned to subscriber k;
SNRk[ j] the SNR function of subscriber k on the frequencyof subcarrier j;
p[ j] transmit power on subcarrier j;
ck[ j] achievable transmission efficiency (data rate per
hertz) of subscriber k on the frequency of
subcarrier j, assuming that subcarrier j is allo-
cated to subscriber k( j ∈ Dk).
To assign subcarrier set Dk to subscriber k, we assume that
a nonoverlapped partition is used such thatDk
Dl = φ, k = lN
k=1 Dk ⊆ S J (2)
where φ is a null set.
According to [18]–[20], ck[ j] can be expressed as
ck[ j] = f [log2 (1 + βp[ j]SNRk[ j])] (3)
where β = 1.5/ − ln(5BER) is a constant, and f (.) depends
on the adaptation scheme. For example, if the continuous-rate
adaptation is concerned, we have f (x) = x; if a variable M -ary
quadrature amplitude modulation (M -QAM) with modulation
levels 0, 2, 4, 6,. . . is employed, we have f (x) = 2(1/2)xinstead.
Then, the DL data transmission rate of subscriber k is
given by
trDk =j∈Dk
ck[ j]∆f. (4)
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RONG et al.: CALL ADMISSION CONTROL OPTIMIZATION IN WiMAX NETWORKS 2513
Consequently, the DL bandwidth capacity of the kth subscriber
can be calculated by BDk = α% trDk . Equations (1)–(4) can
also be used to compute the UL data transmission rate of
subscriber k, denoted as trU k , if the variables in these equa-
tions are replaced by UL parameters. Then, the UL bandwidth
capacity of the kth subscriber can be obtained by BU k = (1 −
α%) trU k .
IV. ONE -D IMENSIONAL CAC OPTIMIZATION
In this section, we first review the existing CAC optimization
strategies in the literature. We then propose a utility- and
fairness-constrained optimal revenue strategy as an effort to
benefit both service providers and subscribers.
A. Existing 1-D CAC Optimization Strategies
The previous study on 1-D CAC optimization was mainly
focused on two approaches, i.e., the optimal revenue strategy
and the minimum weighted sum of blocking strategy.
1) Optimal Revenue Strategy: In general, service providers
expect a CAC policy that can produce high revenues. To achieve
this goal, [3]–[9] studied the CAC optimization problems with
the optimal revenue strategy, which is also known as the sto-
chastic knapsack problem. The optimal revenue strategy can be
introduced in the context of WiMAX as follows.
Let rerUGS, rerrtPS, rernrtPS, and rerBE be the revenue
rates of UGS, rtPS, nrtPS, and BE service, respectively. Then,
we use reri to denote the revenue rate of a class-i connection,
which can be one of rerUGS, rerrtPS, rernrtPS, and rerBE, de-
pending on which type of service is required. Correspondingly,
we can calculate the “long-term average revenue” of a CACpolicy by
R(Ω) =n∈Ω
(n · r)P Ω(n) (5)
where P Ω(n) is the steady-state probability that the system is
in state n, r = (r1, r2, . . . , rM ) is the reward vector, and ri =reribi is the average revenue generated by accepting a class-iconnection. For a given WiMAX system, (5) can be separately
applied to UL and DL. In the most common case, UL and
DL have different parameter setups but have the same revenue
rate reri.In this paper, we use Ω∗ to denote the optimal revenue policy.
Intuitively, Ω∗ prefers the traffic load with a high-revenue
output.
2) Minimum Weighted Sum of Blocking Strategy: A CAC
optimization strategy was proposed in [10] to minimize the
“weighted sum of blocking,” which is defined as
W B = weighted sum of blocking =
M i=1
wiP bi (6)
where P bi stands for the blocking probability of class-i traffic,
and wi stands for the weight of class-i traffic. By adjusting the
value of wi, the minimum weighted sum of blocking strategycan give different traffic classes different priorities.
B. Equivalence of Two CAC Optimization Strategies
It is noted that if a policy Ω satisfies the coordinate convex
condition and the arrival and service processes are both memo-
ryless, then P Ω(n) can be calculated by (as shown in [21])
P Ω(n) =1
G(Ω)
M i=1
ρniini! , n ∈ Ω (7)
where G(Ω) =
n∈Ω
M i=1 ρnii /ni!, and ρi = λi/µi.
Moreover, the blocking probability of class-i traffic is
P bi(Ω) =G
Ωbi
G(Ω)
(8)
where Ωbi = n|n ∈ Ω & n + ei /∈ Ω, and ei is an
M -dimension vector of all zeros, except for its ith element.
Based on the above equations, we can have the following
lemma.
1) Lemma 1: For any CAC policy that satisfies the coordi-nate convex condition, the long-term average revenue defined
in (5) can always be calculated by
R(Ω) = A − W B (9)
where A =M
i=1 riρi is a constant, W B =M
i=1 wiP bi, and
wi = riρi.In (9), R(Ω) is the revenue that policy Ω can achieve or
the revenue of accepted traffic, A =M
i=1 riρi is the revenue
of arriving traffic, and W B =M
i=1 wiP bi =M
i=1 riρiP biis the revenue of rejected traffic. Obviously, the revenue of
accepted traffic can be calculated by subtracting the revenue of rejected traffic from the revenue of arriving traffic. Therefore,
Lemma 1 holds for any policy that satisfies the coordinate
convex condition.
Lemma 1 also implies that the revenue can be maximized
when the weighted sum of blocking is minimized. Therefore,
the minimum weighted sum of blocking strategy is equivalent
to the optimal revenue strategy if the condition wi = riρiholds. In this paper, we mainly consider the optimal revenue
strategy, since it has more explicit meaning in practice. As for
the minimum weighted sum of blocking strategy, we consider
it only as an alternative way to express the optimal revenue
strategy, which will be employed to develop fast calculation
algorithms in Section V.
C. Utility- and Fairness-Constrained Optimal
Revenue Strategy
The optimal revenue strategy highlights only the demand of
service providers. Nevertheless, in a practical WiMAX system,
we also need to consider the requirements of subscribers.
1) Utility Requirement: Generally speaking, subscribers
prefer a CAC policy that can achieve maximal utility or, equiva-
lently, the maximum access bandwidth [22], [23]. Let B denote
the physical access bandwidth and SB denote the statistical
bandwidth that the subscriber can achieve after the CAC policytakes effect. Then, the utility function is defined as SB/B.
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2514 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 57, NO. 4, JULY 2008
Since B is a constant, the maximization of the utility function
leads to the maximization of the statistical bandwidth SB . In
this paper, we use Ω+ to denote the optimal utility CAC policy.
Different from Ω∗, which denotes the optimal revenue policy,
Ω+ allocates more bandwidth resources to the traffic load that
can yield high utility.
Following (5), we derive the “statistical bandwidth” thatpolicy Ω can achieve as
SB(Ω) =n∈Ω
(n · b)P Ω(n) (10)
where we have replaced the reward vector r given in (5) with
the bandwidth requirement vector b.
Based on (10), the “utility” of policy Ω is given by
U (Ω) =1
BSB(Ω) =
1
Bn∈Ω
(n · b)P Ω(n). (11)
It is noted that if all traffic classes have the same revenue rate,
i.e., rer1 = rer2 = · · · = rerM , Ω∗ turns into Ω+.
2) Fairness Requirement: When the optimal revenue or op-
timal utility strategy is employed, there may exist a great bias
among the blocking probabilities of different traffic classes.
This bias can result in unfairness such that some traffic classes
is severely blocked, whereas others can easily access the net-
work. Therefore, in addition to the utility requirement, the
fairness among different traffic classes becomes another major
issue that subscribers might be concerned about [24], [25].
Fairness requirement guarantees that the blocking probabilities
of all traffic classes will be kept relatively uniform such that no
particular traffic class will be unfairly treated.
In this paper, we mainly address the fairness at the CAC
level, which means that the applications of every service class
have a chance to achieve access bandwidth. Therefore, different
fairness policies can be applied in the underlying service model,
such as a service policy of packet scheduling. For instance,
in the packet scheduling level, unfairness may be necessary to
guarantee the QoS provisioning.
To achieve absolute fairness (AF), each traffic class is given
the same blocking probability, whereas the utility of the CAC
policy is maximized. This paper mainly considers the scenarioof a stressful network where the arriving traffic load is higher
than the bandwidth capacity. Then, the blocking probability of
each traffic class is given by
P bAF = 1 −U (ΩAF)BM i=1
biλiµi
≥ P bAFlb (12)
where P bAFlb = 1 − (B/M
i=1 biλi/µi) is the lower bound of
P bAF. As defined, the AF policy has the highest utility among
all policies that can offer equal blocking probabilities. There-fore, in practice, P bAF can have a value very close to P bAFlb .
3) Constrained Optimal Revenue Strategy: The objective
of CAC optimization can be chosen to satisfy either service
providers or subscribers. Usually, a contradiction exists be-
tween the expectations of service providers and subscribers.
Therefore, we have to develop a constrained CAC optimization
strategy that can give a good tradeoff. In other words, we need
a CAC policy that can balance the optimal revenue requirementfrom the service providers and the optimal utility and fairness
requirements from the subscribers. This leads to a concept of a
utility- and fairness-constrained optimal revenue policy, which
is proposed in this paper.
The fairness constraint requires that the highest blocking
probability among all traffic classes (or, in short, the highest
blocking probability) is lower than the threshold P Bth. In this
paper, we use ΩF ∗ to represent the fairness-constrained opti-
mal revenue policy. Clearly, the blocking probability threshold
P Bth must be higher than P bAFlb ; otherwise, no CAC policy
can be found to meet the fairness constraint. Therefore, P Bth
is subject to the relationship P bAFlb < P Bth < 1. Correspond-
ingly, we define the normalized blocking probability thresh-
old as pbth, which ranges from zero to one (0 < pbth < 1).
The relationship between pbth and P Bth can be formulated
by pbth = (P Bth − P bAFlb )/(1 − P bAFlb ) or P Bth = (1 −P bAFlb ) pbth + P bAFlb .
The utility constraint requires that the utility of a CAC policy
must be higher than the threshold U th. In this paper, we use
ΩUF ∗ to represent the utility and fairness constrained optimal
revenue policy. If the fairness constraint is already known, it
is clear that the utility threshold U th must satisfy 0 < U th <U (ΩF +), where U (ΩF +) denotes the utility of the fairness-
constrained optimal utility strategy. Otherwise, no ΩUF ∗ can
be found to satisfy both utility and fairness constraints. Corre-spondingly, we define the normalized utility threshold as uth,
which satisfies U th = uththU (ΩF +) (0 < uth < 1). It is also
noted that when P Bth = 1 or pbth = 1, ΩUF ∗ degenerates into
the utility-constrained optimal revenue policy ΩU ∗.
Practically, it is convenient to use uth and pbth, instead of
U th and P Bth, to describe the utility and fairness constraints,
since the valid ranges of U th and P Bth depend on the band-
width capacity and traffic load, whereas the valid ranges of uth
and pbth are always from zero to one.
V. ONE -D IMENSIONAL CAC OPTIMIZATION ALGORITHMS
In this paper, we mainly study the optimal revenue policy Ω∗
and constrained optimal revenue policies ΩU ∗, ΩF ∗, and ΩUF ∗,
which are likely to be used by service providers to construct a
commercial WiMAX network. In addition, we are interested in
Ω+ as well, since it can serve as a benchmark for utility perfor-
mance. To specify the above policies, brute-force searching is a
straightforward method. For example, to achieve Ω∗, one needs
to calculate the long-term average revenue of each possible pol-
icy using (5). To achieve ΩUF ∗, one needs to calculate the long-
term average revenue, the blocking probabilities, and the utility
of each possible policy using (5), (8), and (11). Nevertheless,
the previous studies pointed out that the brute-force searching
has an unbearable complexity [3], [5]. Even if the optimalsolution could be found, it is usually very complicated and,
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RONG et al.: CALL ADMISSION CONTROL OPTIMIZATION IN WiMAX NETWORKS 2515
therefore, extremely difficult to implement due to excessively
high storage and table lookup time requirements. As a result,
many researchers endeavored to develop some simply struc-
tured approximate solutions. For example, to find the optimal
revenue policy of a “complete partition” (CP) structure, Ross
and Tsang [3] proposed a finite-stage dynamic programming
algorithm, which has a complexity of O(B2
M ). Here, thealgorithm complexity is measured by the size of the searching
space that a CAC optimization algorithm has to explore [3]. In
the rest of this section, we will develop a series of CP-structured
heuristic algorithms, which have a complexity of O(BM ).
A. CP-Structured Admission Control Policy
A CP policy allocates each traffic class a certain amount of
nonoverlapped bandwidth resource. In this manner, the block-
ing rate of one traffic class will not influence that of others.
Because of this partitioning characteristics, a CP policy can
be decomposed into M independent subpolicies, and the ith
subpolicy takes care of class-i traffic. In other words, a CPpolicy separates the overall bandwidth resource B into M nonoverlapped parts, denoted by B1
CP, B2CP, . . . , BM
CP, where
BiCP belongs to class-i traffic.
For a given CP policy, the ith subpolicy can be modeled by an
M/M/N/N queuing system, in which the number of servers is
si = BiCP/bi. Therefore, according to (5) and (7), the long-term
average revenue obtained from class-i traffic is given by
Ri(CP) =
sij=0
ri j
ρj
i
j!sik=0
ρki
k!
(13)
where the overall long-term average revenue of the CP policy
is defined as R(CP) =M
i=1 Ri(CP). Moreover, the statistical
bandwidth of class-i traffic is given by
SBi(CP) =
sij=0
bi j
ρj
i
j!sik=0
ρki
k!
. (14)
Correspondingly, the overall statistical bandwidth and
the utility of the CP policy can be calculated by
SB(CP)=M
i=1SBi(CP) and U (CP)=(1/B)M
i=1SBi(CP),
respectively.
According to the Erlang B formula, the blocking probabilityof class-i traffic is [26]
P bi(CP) = B(si, ρi) =
ρsii
si!sik=0
ρki
k!
. (15)
It is noted that the Erlang B formula can be calculated by the
following recursion [26]:
B(si + 1, ρi) =ρiB(si, ρi)
si + 1 + ρiB(si, ρi)(16)
where we have B(0, ρi) = 1.
The above discussions have shown that the optimal CPproblem is to find the best bandwidth partitioning scheme.
In this paper, we define the CP policy of “optimal revenue,”
“optimal utility,” “utility-constrained optimal revenue,”
“fairness-constrained optimal revenue,” and “utility- and
fairness-constrained optimal revenue” as CP∗, CP+,
CPU ∗, CPF ∗, and CPUF ∗, respectively, which can be viewed
as the approximate solution for Ω∗, Ω+, ΩU ∗, ΩF ∗, and
ΩUF ∗
. In the following sections, we will address the issues ondeveloping heuristic algorithms for CPF ∗ and CPUF ∗. With
some appropriate adjustment, these heuristic algorithms can be
used to approximate CP∗, CP+, and CPU ∗.
B. Fairness-Constrained Greedy Revenue Algorithm to
Approximate CPF ∗
To achieve a heuristic algorithm for CPF ∗, we have to deal
with the issues on the optimal revenue strategy and the fairness
constraint. In the following text, we first develop a greedy
revenue approximation method for the optimal revenue strategy,
and then, we will add the fairness constraint to it.
Supposing that class-i traffic is assigned j ( j = BiCP/bi)
servers, from Lemma 1, we can derive the corresponding rev-
enue as
Ri(CP)|BiCP
=jbi = riρi − riρiB( j,ρi). (17)
If one server is withdrawn or the server number is reduced to
( j − 1), the following equation holds:
Ri(CP)|BiCP
=(j−1)bi = riρi − riρiB( j − 1, ρi). (18)
Accordingly, we define the revenue brought by the jth server as
RiS( j,ρi) = Ri(CP)
BiCP
=jbi − Ri(CP)BiCP
=(j−1)bi
= riρi [B( j − 1, ρi) − B( j,ρi)]
= riF iS( j,ρi) (19)
where F iS( j,ρi) = ρi[B( j − 1, ρi) − B( j,ρi)] is the load car-
ried by the jth server in the M/M/N/N queuing system,
andsi
j=1 RiS( j,ρi) = Ri(CP). Then, the revenue rate of the
jth server is
r
i
S( j,ρi) =
RiS( j,ρi)
bi =
riρi [B( j − 1, ρi) − B( j,ρi)]
bi .(20)
Initially, (19) was introduced in the theory of marginal eco-
nomic analysis [27] by intuition. In this paper, we use Lemma 1
to give it a detailed explanation. Since F iS( j,ρi) is decreas-
ing with j [28], RiS( j,ρi) and riS( j,ρi) are decreasing with
j as well.
Based on the above analysis, we propose a greedy revenue
approximation method to obtain the optimal revenue. The
greedy revenue approximation method always allocates the
bandwidth resource to the traffic class of the highest revenue
rate in each iteration. Taking into account the fairness constraint
as well, a fairness-constrained greedy revenue algorithm toapproximate CPF ∗ is presented in Algorithm 1.
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2516 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 57, NO. 4, JULY 2008
Algorithm 1: Fairness-Constrained Greedy Revenue Algo-
rithm for CPF ∗
1) Input pbth;
2) Capture the traffic load profile in the kth subscriber’s
local network;
3) Collect the CSI from the physical layer, calculate BU k
for UL CAC or BDk for DL CAC, and let B = B
U k or
B = BDk ;
4) /∗ PHASE 1: Allocate bandwidth resources to satisfy
the fairness constraint ∗/
5) Bfree= B; P bAFlb = 1−(B/M
i=1 biλi/µi); P Bth= pbthP bAFlb ;
6) for i = 1 to M do
7) BiCP = 0; si = 0; B(si, ρi) = 1; P bi = B(si, ρi);
8) end for
9) for i = 1 to M do
10) while P bi > P Bth do
11) Bfree= Bfree−bi; BiCP = Bi
CP + bi; B(si + 1,ρi) = (ρiB(si, ρi)/si + 1 + ρiB(si, ρi));
12) P bi = B(si + 1, ρi); SBi = SBi + biρi[B(si,ρi) − B(si + 1, ρi)]; si = si + 1;
13) end while
14) BiCP(F ) = Bi
CP;
15) end for
16) /∗ PHASE 2: Allocate the remaining free bandwidth
resources according to optimal revenue strategy ∗/17) I = M + 1;
18) for all i(0 ≤ i ≤ M ): B(si + 1, ρi) = (ρiB(si, ρi)/si+1 +ρiB(si, ρi)); riS = (riρi[B(si, ρi)−B(si+1,ρi)]/bi);
19) while I > 0 do
20) I = arg max1≤i≤M riS;21) if bI ≤ Bfree then
22) /∗ allocate bI bandwidth resource to class I
traffic ∗/23) Bfree= Bfree−bI ; BI
CP= BI CP+bI ; sI = sI +1;
24) B(sI +1, ρI )=(ρI B(sI , ρI )/sI +1+ρI B(sI , ρI ));
rI S = (rI ρI [B(sI , ρI )−B(sI +1, ρI )]/bI );
25) else
26) rI S = 0;
27) if M
i=1 riS = 0 then
28) I = −1; // bandwidth allocation is finished.
29) end if
30) end if 31) end while
32) return BiCP(F ), 1 ≤ i ≤ M as the bandwidth allo-
cation to satisfy fairness constraint;
33) return BiCP, 1 ≤ i ≤ M as the final bandwidth al-
location decision for CPF ∗;
As for the dynamic of traffic load, the DL traffic load
estimation module records every connection request in its
database, regardless of whether it is accepted or not. Then,
the traffic load profile is periodically captured based on this
record and sent to the CAC policy module. As for the dynamic
of channel condition, the DL bandwidth estimation module
retrieves the CSI from the physical layer at regular intervalsof time. Then, the DL bandwidth capacity of a given sub-
scriber is calculated from the CSI and sent to the CAC policy
module.
Algorithm 1 proceeds in two phases. In the first phase, it
allocates class-i traffic BiCP(F ) bandwidth resource so that the
fairness constraint can be guaranteed. In the second phase, it
iteratively employs the greedy method to implement the optimal
revenue strategy. For instance, steps 18 and 24 of the algorithminitialize and update the revenue rates of different traffic classes,
respectively, and then, step 20 picks up one of the maximum
revenue rates.
Algorithm 1 can exactly locate CPF ∗ before step 26 is
reached. The iterations may incur approximation errors if and
only if the bandwidth capacity boundary condition Bfree <max1≤i≤M bi becomes true. If so, the greedy method cannot
be thoroughly implemented because the capacity limit can
interfere with the process of locating the traffic class of the
maximal revenue rate. If compared to CPF ∗, the revenue error
generated by Algorithm 1 can be strictly bounded by the
following inequality:
Rerr < R(CPF ∗, B) − R
CPF ∗, B − max
1≤i≤M bi
(21)
where Rerr stands for the revenue approximation error, and
R(Ω, C ) stands for the revenue obtained from policy Ω with
bandwidth capacity C .Next, we investigate the complexity of the fairness-
constrained greedy revenue algorithm. Clearly, the first phase of
this algorithm has a complexity of O(B). Moreover, there are
O(B) iterations in the second phase of this algorithm. During
each iteration, this algorithm searches through M possible
system states to locate the traffic class that yields the maximalrevenue rate. Therefore, the size of the whole searching space
or the complexity of the second phase is O(BM ). Combining
phases 1 and 2, we can conclude that this algorithm has a
complexity of O(BM ).
It is noted that if we let pbth = 1, Algorithm 1 degenerates
into the pure greedy revenue algorithm for CP∗.Ifwelet rer1 =rer2 = · · · = rerM = 1, Algorithm 1 degenerates into the
fairness-constrained greedy utility algorithm for CPF +. If we
let pbth = 1 and rer1 = rer2 = · · · = rerM = 1, Algorithm 1
degenerates into the pure greedy utility algorithm for CP+.
C. Utility- and Fairness-Constrained Greedy
Revenue Algorithm
To develop a CP-structured heuristic algorithm for ΩUF ∗, we
have to address three issues: 1) optimal revenue; 2) fairness
constraint; and 3) utility constraint. Since the optimal revenue
and the utility constraint have been discussed in the previous
sections, we focus only on the utility constraint in this section.
Similar to the revenue, for class-i traffic, we define the
statistical bandwidth brought by the jth server as
SB iS( j,ρi) = biF iS( j,ρi) = biρi [B( j − 1, ρi) − B( j,ρi)]
(22)where the relation SBi(CP) =
sij=1 SB i
S( j,ρi) holds.
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RONG et al.: CALL ADMISSION CONTROL OPTIMIZATION IN WiMAX NETWORKS 2517
Then, the utility of the jth server is given by
U iS( j,ρi) =SB i
S( j,ρi)
bi
= F iS( j,ρi)
= ρi [B( j − 1, ρi) − B( j,ρi)] . (23)
To deal with the utility constraint, we can use (23) to cal-
culate the utility in each iteration step. Combining the utility
constraint with the CP-structured heuristic algorithm for ΩF ∗,
we obtain a utility- and fairness-constrained greedy revenue
algorithm to approximate CPUF ∗, as presented in Algorithm 2.
Algorithm 2: Utility- and Fairness-Constrained Greedy Rev-
enue Algorithm for CPUF ∗
1) Input uth, pbth;
2) Capture the traffic load profile in the kth subscriber’s
local network;
3) Collect the CSI from the physical layer, calculate BU k
for UL CAC or BDk for DL CAC, and let B = BU
k or
B = BDk ;
4) /∗ PHASE 1: Allocate bandwidth resource for fairness
constraint and calculate U th ∗ /5) Achieve Bi
CP(F ), 1 ≤ i ≤ M and locate CPF + by
running Algorithm 1 with parameter setup rer1 =rer2 = · · · = rerM = 1;
6) Bfree = B −M
i=1 BiCP(F ); U th = uthU (CPF +);
7) for i = 1 to M do
8) BiCP = Bi
CP(F ); si = BiCP(F )/bi; B(si, ρi) =
(ρsii /si!/sik=0 ρki /k!); B(si + 1, ρi) = (ρiB(si,
ρi)/si + 1 + ρiB(si, ρi)); riS = (riρi[B(si, ρi) −
B(si + 1, ρi)]/bi); U iS = ρi[B(si, ρi) − B(si +
1, ρi)]; SBi =si
j=0 bi j(ρji/j!/si
k=0 ρki /k!);
9) end for
10) /∗ PHASE 2: Allocate the remaining free bandwidth
resources according to utility constrained optimal rev-
enue strategy. ∗/11) T = M + 1;
12) while T > 0 do
13) SetU = i|i satisfies (U iSbi +M
i=1 SBi/(B −Bfree + bi)) > U th; /∗ the set of traffic classes
qualified for utility constraint. ∗/
14) T = arg maxi∈SetUr
i
S;15) if bi|i=T ≤ Bfree then
16) Bfree = Bfree − bi|i=T ; BiCP|i=T = Bi
CP|i=T +bi|i=T ;
17) SBi|i=T = SBi|i=T + U iSbi|i=T ; si|i=T =si|i=T + 1;
18) B(si+ 1, ρi)|i=T = (ρiB(si, ρi)/si+1 +ρiB(si,ρi))|i=T ;
19) riS |i=T = (riρi[B(si, ρi)−B(si+1, ρi)]/bi)|i=T ;20) U iS |i=T = ρi[B(si, ρi) − B(si + 1, ρi)]|i=T ;21) else
22) /∗ Capacity limit begins to take effect. ∗/23) riS |i=T = 0; U iS |i=T = 0;
24) U th = 0; /∗ change to use the pure greedy rev-enue algorithm. ∗/
25) if M
i=1 riS = 0 then
26) T = −1; /∗ the algorithm is completed. ∗/27) end if
28) end if
29) end while
30) Return BiCP, 1 ≤ i ≤ M as the final bandwidth al-
location decision;
There are two phases in Algorithm 2. In the first phase,
we employ Algorithm 1 to allocate each traffic class a certain
amount of bandwidth resource such that the fairness constraint
can be guaranteed. In the meantime, Algorithm 1 can also locate
CPF +, from which U th is calculated.
Then, in the second phase, we employ the utility-constrained
optimal revenue strategy to allocate the remaining bandwidth.
To meet the utility constraint, in each iteration of phase 2, only
the traffic classes that can make the utility higher than U th
are chosen as qualified candidates for bandwidth allocation (as
shown in step 13). Moreover, this algorithm can achieve high
revenues as well, since it always selects the candidate with the
highest revenue rate to assign bandwidth resource (as shown in
step 14). It is noted that if we let pbth = 1, Algorithm 2 de-
generates into the utility-constrained greedy revenue algorithm
for CPU ∗.
Next, we will address the issues on complexity of the utility-
and fairness-constrained greedy revenue algorithm. Clearly, in
the first phase, Algorithm 1 is employed, and its complexity is
O(BM ). In the second phase, there are O(B) iterations. During
each iteration, this algorithm searches through O(M ) possible
system states in SetU to locate the traffic class of maximal
revenue rate. Therefore, the size of the whole searching space
or the complexity of the second phase is O(BM ). Combiningphases 1 and 2, we can conclude that this algorithm has a
complexity of O(BM ).
VI. SIMULATION RESULTS
In this section, we conduct a simulation study to evaluate
the performance of our proposed WiMAX CAC optimization
scheme. The simulations are programmed on the Matlab plat-
form, using the analytical results developed in the previous
sections. In particular, we first compare the capability of dif-
ferent 1-D CAC policies, then study the 2-D WiMAX CAC in
a subscriber’s local network, and finally, we show the overallbenefit of our proposed WiMAX CAC scheme in a WiMAX
PMP network.
For the 1-D CAC optimization, we present the numerical
results as shown in Figs. 5–7 to demonstrate the performance
of different CAC policies with three metrics (revenue, utility,
and fairness) while varying the arrival rate of class-3 traffic.
Here, Ω∗, Ω+, ΩU ∗, ΩF ∗, and ΩUF ∗ are obtained by brute-
force searching. In this simulation scenario, the total bandwidth
capacity B is set to be 75 Mb/s, the revenue rate is priced
as rerUGS = 5, rerrtPS = 2, rernrtPS = 1, and rerBE = 0.5,
and the traffic load is configured as those shown in Table II.
Moreover, for the utility constraint, we set uth = 90%, and for
the fairness constraint, we set pbth = 65%. In Figs. 5 and 6,the revenue and utility are normalized by R(Ω∗) and U (Ω+),
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2518 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 57, NO. 4, JULY 2008
Fig. 5. Revenue of different CAC optimization policies while varying thearrival rate of class-3 traffic.
Fig. 6. Utility of different CAC optimization policies while varying the arrivalrate of class-3 traffic.
respectively. In Fig. 7, the highest blocking probability remains
unchanged.
As shown in Figs. 5–7, Ω∗/Ω+ gives a good performance
only in terms of revenue/utility. On the other hand, ΩU ∗/ΩF ∗
performs well in terms of both revenue and utility/fairness.
Finally, Ω
UF ∗
satisfactorily performs in terms of all threemetrics, including revenue, utility, and fairness.
To reduce the algorithm complexity, we have developed
a utility- and fairness-constrained greedy revenue algorithm
for ΩUF ∗. This approximation algorithm can also be utilized
to approximate Ω∗, Ω+, ΩU ∗, and ΩF ∗ if we appropriately
degenerate the utility or fairness constraint. Numerical results
are shown in Table III to illustrate the average error of the
approximation algorithm, whereas the traffic load is configured
the same as that listed in Table II. For convenience, the revenue
and utility approximation errors are normalized by R(Ω∗) and
U (Ω+), respectively. We can conclude from Table III that our
approximation algorithm can provide an adequate approxima-
tion to the exact solution. Here, the CP → Ω error means the er-ror generated from the CP-structured solution if compared with
Fig. 7. Highest blocking probability of different CAC optimization policieswhile varying the arrival rate of class-3 traffic.
the exact solution, the CP approximation error means the error
generated from the approximation algorithm if compared with
the CP-structured solution, and the total approximation error
means the sum of the CP → Ω error and the CP approximation
error.
Next, we evaluate the performance of 2-D WiMAX CAC in
a subscriber’s local network using the decomposing approach
proposed in Section II. In the simulation scenario, we em-
phasize the utility- and fairness-constrained optimal revenue
policy ΩUF ∗ and its approximation algorithm, because they
take into account all the requirements of service providers and
subscribers. Considering the parameter decomposing model
given in Table I, we suppose that UL CAC and DL CAC employthe same policy, i.e., ΩUF ∗ or its approximation algorithm, with
normalized utility threshold uth and normalized blocking prob-
ability threshold pbth identically configured for UL and DL.
Numerical results are shown in Figs. 8 and 9 to demonstrate the
performance of ΩUF ∗ and its approximation algorithm based
2-D WiMAX CAC while varying uth and keeping pbth con-
stant at 65%. In the simulation, we set the UL/DL bandwidth
capacity in a subscriber’s local network to be 60/75 Mb/s.
Moreover, the UL traffic load is configured the same as that
given in Table IV, whereas the DL traffic load is configured in
Table II, except that the arrival rate of class-3 traffic is fixed
to be 64 calls/h. The revenue rates of both UL CAC and DLCAC are priced as rerUGS = 5, rerrtPS = 2, rernrtPS = 1,
and rerBE = 0.5.
Fig. 8 illustrates the revenue and utility of 2-D WiMAX
CAC, which can be derived from the UL/DL revenue and utility
as follows: 1) The revenue of 2-D CAC is defined as the sum
of the UL revenue and the DL revenue, and 2) the utility of
2-D CAC is defined as the average of the UL utility and the
DL utility. For analytical simplicity, in Fig. 8, the revenue is
normalized by that of the ΩF ∗ based 2-D CAC, and the utility
is normalized by that of the ΩF + based 2-D CAC.
As illustrated in Fig. 8, when uth = 0, ΩUF ∗ turns to be ΩF ∗,
yielding a solution of high revenue but low utility. Similarly,
when uth = 1, ΩUF ∗ turns to be ΩF +, yielding a solutionwith high utility but low revenue. Thus, we should choose an
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RONG et al.: CALL ADMISSION CONTROL OPTIMIZATION IN WiMAX NETWORKS 2519
TABLE IITRAFFIC LOAD CONFIGURATION
TABLE IIIAVERAGE ERROR OF THE APPROXIMATION ALGORITHM (REVENUE /UTILITY /HIGHEST BLOCKING PROBABILITY)
Fig. 8. Revenue and utility of ΩUF ∗ and its approximation algorithm in2-D CAC.
Fig. 9. Highest blocking probability of ΩUF ∗ and its approximation algo-rithm in 2-D CAC.
appropriate value for uth (i.e., 90% in this case) to give ΩUF ∗
balanced revenue and utility. In addition, Fig. 8 also shows that
the approximation algorithm has similar performance as ΩUF ∗.
The fairness feature of 2-D WiMAX CAC is illustrated inFig. 9, which indicates that the highest blocking probability
of ΩUF ∗ and its approximation-algorithm-based 2-D CAC is
strictly bounded by the blocking probability threshold derived
from pbth.
Finally, we investigate the performance of ΩUF ∗ and its
approximation-algorithm-based 2-D CAC in a WiMAX PMP
network, which employs a OFDMA–TDD mode of 32 sub-
scribers with PUSC on the UL and FUSC on the DL. In our
simulations, the UL and DL channels are assumed to have
a bad-urban delay profile [29] and suffer from shadowing
with 8-dB standard deviation. Let the amount of available
subcarriers be 1024 and each subcarrier occupy 10 kHz of
physical bandwidth. The distances between the subscribers and
the base station are randomly chosen from 2 to 10 km, and the
acceptable BER is set to be 10−6. We assign each subcarrier the
same UL and DL power resource and configure the TDD DL
proportion factor α% as 60%.As for the traffic pattern, 32 subscribers are programmed to
have different UL and DL traffic loads, which are uniformly
distributed in [40 Mb/s, 100 Mb/s] and [60 Mb/s, 140 Mb/s],
respectively. To emulate an environment of broadband wireless
access, we suppose that the WiMAX network is dominated
by multimedia applications. Correspondingly, among the UL
and DL traffic loads of a certain subscriber, the proportions of
UGS, rtPS, nrtPS, and BE traffic, which are denoted by P P UGS,
P P rtPS, P P nrtPS, and P P BE, are set to be random variables,
which are defined as follows:
P P BE uniformly distributed in [10%, 30%];
P P UGSuniformly distributed in
[10%(1 − P P BE),
30%(1 − P P BE)];P P rtPS uniformly distributed in [20%(1 − P P BE),
60%(1 − P P BE)];P P nrtPS defined as (1 − P P BE − P P UGS − P P rtPS).
As for the revenue rate, we assume that rerUGS = 5,
rerrtPS = 2, rernrtPS = 1, and rerBE = 0.5. As for the utility
constraint and the fairness constraint, we set uth = 90% and
pbth = 65% for both UL CAC and DL CAC.
Simulation results are presented in Figs. 10 and 11 to demon-
strate the average performance of the 2-D CAC using ΩUF ∗
or its approximation algorithm among 32 subscribers. As men-
tioned earlier, Ω∗ and Ω+ have the best performance in terms
of revenue and utility, respectively. To facilitate the analysis,in Fig. 10, we use the average revenue/utility of Ω∗/Ω+ to
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2520 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 57, NO. 4, JULY 2008
TABLE IVUPLINK TRAFFIC LOAD CONFIGURATION
Fig. 10. Average revenue and utility of ΩUF ∗ and its approximation algo-rithm in 2-D WiMAX CAC of 32 subscribers.
Fig. 11. Average highest blocking probability of ΩUF ∗ and its approximation
algorithm in 2-D WiMAX CAC of 32 subscribers.
normalize the average revenue/utility. Figs. 10 and 11 show that
the 2-D CAC with ΩUF ∗, or its approximation algorithm, can
achieve high revenue and utility while still meeting the fairness
constraint.
VII. CONCLUSION
In this paper, we have proposed a framework for WiMAX
CAC, in which the 2-D CAC problem is decomposed into
two independent 1-D CAC problems. Then, we make the
1-D CAC an optimization problem and evaluate its differentstrategies. From the perspective of service providers, optimal
revenue is the major concern. However, from the perspective of
subscribers, optimal utility and fairness are the requirements.
To successfully deploy a WiMAX system, we have to take
into account the expectations of both service providers and
subscribers. Accordingly, we develop a utility- and fairness-
constrained optimal revenue policy, as well as its approximation
algorithm. Simulation results verify that our proposed WiMAX
CAC approach can meet the requirements of both service
providers and subscribers.
REFERENCES
[1] S. J. Vaughan-Nichols, “Achieving wireless broadband with WiMAX,”Computer , vol. 37, no. 6, pp. 10–13, Jun. 2004.
[2] R. Marks, C. Eklund, K. Stanwood, and S. Wang, The 802.16 Wireless- MAN MAC: It’s Done, but What Is It?, Nov. 2001. Tutorial on the IEEE802.16-01/58r1.
[3] K. W. Ross and D. H. K. Tsang, “The stochastic knapsack problem,” IEEE Trans. Commun., vol. 37, no. 7, pp. 884–895, Jul. 1989.
[4] K. W. Ross and D. D. Yao, “Monotonicity properties for the stochas-tic knapsack,” IEEE Trans. Inf. Theory, vol. 36, no. 5, pp. 1173–1179,Sep. 1990.
[5] A. Gavious and Z. Rosberg, “A restricted complete sharing policy for astochastic knapsack problem in B-ISDN,” IEEE Trans. Commun., vol. 42,
no. 7, pp. 2375–2379, Jul. 1994.[6] E. Altman, T. Jimenez, and G. Koole, “On optimal call admission con-trol in resource-sharing system,” IEEE Trans. Commun., vol. 49, no. 9,pp. 1659–1668, Sep. 2001.
[7] E. L. Ormeci, “Dynamic admission control in a call center with one sharedand two dedicated service facilities,” IEEE Trans. Autom. Control, vol. 49,no. 7, pp. 1157–1161, Jul. 2004.
[8] B. C. Dean, M. X. Goemans, and J. Vondrdk, “Approximating the sto-chastic knapsack problem: The benefit of adaptivity,” in Proc. 45th Annu.
IEEE Symp. Found. Comput. Sci., Oct. 2004, pp. 208–217.[9] V. Sarangan, D. Ghosh, N. Gautam, and R. Acharya, “Steady state distri-
bution for stochastic knapsack with bursty arrivals,” IEEE Commun. Lett.,vol. 9, no. 2, pp. 187–189, Feb. 2005.
[10] C. C. Beard and V. S. Frost, “Prioritized resource allocation for stressednetworks,” IEEE/ACM Trans. Netw., vol. 6, no. 5, pp. 618–633, Oct. 2001.
[11] IEEE Standard for Local and Metropolitan Area Networks—Part 16: Air Interface for Fixed Broadband Wireless Access Systems, IEEE 802.
16-2004, Oct. 2004.[12] I. Koffman and V. Roman, “Broadband wireless access solutions based
on OFDM access in IEEE 802.16,” IEEE Commun. Mag., vol. 40, no. 4,pp. 96–103, Apr. 2002.
[13] B. Rong, Y. Qian, and K. Lu, “Integrated downlink resource managementfor multiservice WiMAX networks,” IEEE Trans. Mobile Comput., vol. 6,no. 6, pp. 621–632, Jun. 2007.
[14] B. Rong, Y. Qian, and K. Lu, “Downlink call admission control inmultiservice WiMAX networks,” in Proc. IEEE ICC , Jun. 2007,pp. 5082–5087.
[15] S. Sengupta, M. Chatterjee, S. Ganguly, and R. Izmailov, “ImprovingR-score of VoIP streams over WiMax,” in Proc. IEEE ICC , Jun. 2006,vol. 2, pp. 866–871.
[16] A. Sang and S. Li, “A predictability analysis of network traffic,” in Proc. IEEE Infocom, Mar. 26–30, 2000, pp. 342–351.
[17] B. Rong, B. Tremblay, M. Bennani, and M. Kadoch, “Integrating traffic
aggregation mechanism into SIP based IP telephony over MPLS net-work,” in Proc. IEEE Globecom. St. Louis, MO, Nov. 28–Dec. 2, 2005,pp. 797–801.
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RONG et al.: CALL ADMISSION CONTROL OPTIMIZATION IN WiMAX NETWORKS 2521
[18] X. Qiu and K. Chawla, “On the performance of adaptive modulation incellular systems,” IEEE Trans. Commun., vol. 47, no. 6, pp. 884–895,Jun. 1999.
[19] G. Song and Y. G. Li, “Cross-layer optimization for OFDM wire-less networks—Part I: Theoretical framework,” IEEE Trans. WirelessCommun., vol. 4, no. 2, pp. 614–624, Mar. 2005.
[20] G. Song and Y. G. Li, “Cross-layer optimization for OFDM wire-less networks—Part II: Algorithm development,” IEEE Trans. Wireless
Commun., vol. 4, no. 2, pp. 625–634, Mar. 2005.[21] J. S. Kaufman, “Blocking in a shared resource environment,” IEEE Trans.Commun., vol. COM-29, no. 10, pp. 1474–1481, Oct. 1981.
[22] S. Shenker, “Fundamental design issues for the future Internet,” IEEE J.Sel. Areas Commun., vol. 13, no. 7, pp. 1176–1188, Sep. 1995.
[23] Z. Jiang, Y. Ge, and Y. Li, “Max-utility wireless resource management forbest-effort traffic,” IEEE Trans. Wireless Commun., vol. 4, no. 1, pp. 100–111, Jan. 2005.
[24] Y.-C. Lai and Y.-D. Lin, “A novel admission control for fairly admittingwideband and narrowband calls,” IEEE Commun. Lett., vol. 7, no. 4,pp. 186–188, Apr. 2003.
[25] R.-H. Hwang and C.-F. Chi, “Fairness in QoS guaranteed networks com-munications,” in Proc. IEEE ICC , May 2003, vol. 1, pp. 218–222.
[26] D. Jagerman, “Some properties of the Erlang loss function,” Bell Syst.Tech. J., vol. 53, no. 3, pp. 525–551, Mar. 1974.
[27] A. Jensen, Moe’s Principle. Copenhagen, Denmark: Copenhagen Tele-phone Co. (K.T.A.S.), 1950.
[28] R. W. Wolff and C.-L. Wang, “On the convexity of loss probabilities,” J. Appl. Probab., vol. 39, no. 2, pp. 402–406, Jun. 2002.
[29] G. L. Stuber, Principles of Mobile Communication, 2nd ed. Norwell,MA: Kluwer, 2000.
Bo Rong (M’07) received the B.S. degree fromShandong University, Jinan, China, in 1993, the M.S.degree from the Beijing University of Aeronauticsand Astronautics, Beijing, China, in 1997, and thePh.D. degree from the Beijing University of Postsand Telecommunications in 2001.
After receiving the Ph.D. degree, he was a Soft-ware Engineer with a startup company in Beijingfor one year. Then, he was a Postdoctoral Fellowwith the Department of Electrical Engineering, Ecolede Technologie Superieure, Universite du Quebec,
Quebec City, QC, Canada, for three years. He is currently a Postdoctoral Fellow
with the Department of Electrical and Computer Engineering, University of Puerto Rico at Mayagüez. His current research interests focus on modeling,simulation, and performance analysis for next-generation wireless networks.
Yi Qian (M’95–SM’07) received the Ph.D. degreein electrical engineering with a concentration intelecommunication networks from Clemson Univer-sity, Clemson, SC.
He is currently with the National Institute of Stan-dards and Technology, Gaithersburg, MD. He was anAssistant Professor with the Department of Electri-cal and Computer Engineering, University of Puerto
Rico at Mayagüez (UPRM), from July 2003 to July2007. At UPRM, he regularly taught courses onwireless networks, network design, network manage-
ment, and network performance analysis. Prior to joining UPRM in July 2003,he worked for several start-up companies and consulting firms in the areas of voice over IP, fiber optical switching, Internet packet video, network optimiza-tions, and network planning as a Technical Advisor and a Senior Consultant. Hewas also with the Wireless Systems Engineering Department, Nortel Networks,Richardson, TX, as a Senior Member of Scientific Staff and as a TechnicalAdvisor for several years. While with Nortel Networks, he was a Project Leaderfor various wireless and satellite network product design projects, customerconsulting projects, and advanced technology research projects. He was also incharge of wireless standard development and evaluations. He has publicationsand is a holder of patents in all these areas. He is a coauthor of the book
Information Assurance: Dependability and Security in Networked Systems
(Morgan Kaufmann, 2008). His current research interests include network secu-rity, network design, network modeling, simulations and performance analysis
for next-generation wireless networks, wireless sensor networks, broadbandsatellite networks, optical networks, high-speed networks, and the Internet.
Dr. Qian is a member of the Association for Computing Machinery.
Kejie Lu (S’01–M’04–SM’07) received the B.S.and M.S. degrees in telecommunications engineeringfrom the Beijing University of Posts and Telecom-munications, Beijing, China, in 1994 and 1997,respectively, and the Ph.D. degree in electrical en-gineering from the University of Texas at Dallas,Richardson, in 2003.
From 2004 and 2005, he was a Postdoctoral Re-search Associate with the Department of Electrical
and Computer Engineering, University of Florida,Gainesville. Since July 2005, he has been an As-
sistant Professor with the Department of Electrical and Computer Engineer-ing, University of Puerto Rico at Mayagüez. His research interests includearchitecture and protocol design for computer and communication networks,performance analysis, network security, and wireless communications.
Hsiao-HwaChen (S’89–M’91–SM’00) received theB.Sc. and M.Sc. degrees from Zhejiang University,Zhejiang, China, in 1982 and 1985, respectively, andthe Ph.D. degree from the University of Oulu, Oulu,Finland, in 1991.
He is currently a Full Professor with the Depart-
ment of Engineering Science, National Cheng KungUniversity, Tainan, Taiwan, R.O.C. He is the authoror a coauthor of more than 250 technical papers inmajor international journals and conference proceed-ings and five books and three book chapters in the
areas of communications. He served or is currently serving as an EditorialBoard Member and/or Guest Editor of the Wireless Communications and
Mobile Computing Journal and the International Journal of CommunicationSystems. He is the founding Editor-in-Chief of the Security and Communication
Networks Journal.Dr. Chen has served as the Symposium Cochair of major international
conferences, including the IEEE Vehicular Technology Conference (VTC), theIEEE International Conference on Communications (ICC), the IEEE GlobalCommunications Conference (Globecom), and the IEEE Wireless Communica-tions and Networking Conference (WCNC). He served or is currently servingas an Editorial Board Member and/or Guest Editor of IEEE Communications
Magazine, the IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, IEEE Wireless Communications Magazine, the IEEE TRANSACTIONS ON
WIRELESS COMMUNICATIONS, and IEEE Vehicular Technology Magazine.
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2522 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 57, NO. 4, JULY 2008
Mohsen Guizani (S’87–M’90–SM’98) received theB.S. (with distinction) and M.S. degrees in elec-trical engineering and the M.S. and Ph.D. degreesin computer engineering from Syracuse University,Syracuse, NY, in 1984, 1986, 1987, and 1990,respectively,
He is currently a Full Professor and Chair of theDepartment of Computer Science, Western Michigan
University, Kalamazoo. He was the Chair of the De-partment of Computer Science, University of WestFlorida, Pensacola, from 1999 to 2003. He was an
Associate Professor of electrical and computer engineering and the Director of graduate studies with the University of Missouri, Columbia, from 1997 to 1999.Prior to joining the University of Missouri, he was a Research Fellow withthe University of Colorado at Boulder. From 1989 to 1996, he held academicpositions at the Computer Engineering Department, University of Petroleumand Minerals, Dhahran, Saudi Arabia. He has more than 140 publicationsin refereed journals and conference proceedings in the areas of high-speednetworking, optical networking, and wireless networking and communications.He currently serves on the editorial boards of many national and international
journals, such as the Journal of Parallel and Distributed Systems and Networks
and the International Journal of Computer Research. He was a Guest Editor forthe Journal of Communications and Networks and several other publications.He is the Founder and Editor-in-Chief of Wireless Communications and MobileComputing.
Dr. Guizani currently serves on the editorial boards of the IEEETRANSACTIONS ON VEHICULAR TECHNOLOGY and IEEE Communications
Magazine. He has served as a Guest Editor for the IEEE Communications Mag-azine and the IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS.He served as the General Chair of the International Conference Parallel andDistributed Computing Systems (PDCS) in 2002 and 2003, the IEEE VehicularTechnology Conference (VTC) in 2003, and the International Conference onWireless Networks, Communications, and Mobile Computing (WirelessCom)in 2005. He has also served as the Program Chair for many conferences. He wasdesignated by the IEEE Computer Society as a Distinguished National Speakerthrough 2005.