4144 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 14, NO. 8, AUGUST 2015
A distributed multi-service resource allocation algorithm for
multi-homing terminals is proposed in [8]. To improve the low
system efficiency due to users’ selfish behavior, Haddad, et al.
in [9] propose a concise network load broadcasting scheme
to coordinate and assist users’ network selections. Practical
learning algorithms for network selection in dynamic and un-
certain environments are discussed in [10]. Authors in [11]
propose a probability model to analyse users’ network selection
behaviors. Game theory based network selection is discussed
in [12].
In centralized schemes, a centralized controller is responsi-
ble for inter-network resource allocation, network selection of
users and bandwidth allocation among users, etc. To exploit
the network diversity gain, the system sum-rate of orthogonal
frequency division multiple access (OFDMA) based heteroge-
neous networks under the proportional user rate constraint is
studied in [13]. On the network side, Gomes, et al. in [14]
propose an architecture and optimization algorithms to improve
network capacity and minimize the number of used base sta-
tions by splitting cells in congested areas and merging cells
in low load areas. Aiming at harvesting the integration gain of
WiFi/WiMAX networks, effective user network association al-
gorithms are proposed in [15] to achieve the max-min through-
put fairness and the proportional fairness. A hierarchical RRM
game is studied in [16] considering the admission control,
capacity reservation and bandwidth allocation of networks.
Our work differs from the above work in that the user
demand-centric perspective in RRM is proposed, where users
seek to maximize QoE in terms of classical mean opinion score
(MOS). QoE based network selection in a single user case was
first studied in [17], while our work focus on the QoE game
in a multiple user case. Although satisfaction equilibriums in
[18]–[20] have similar flavor in bounded demand, our work
is inspired by the subjective QoE levels, resulting in different
equilibrium definitions and properties and learning algorithms.
We mainly focus on heterogeneous demand scenarios and
characterize the resulting user demand diversity gain. The
simulation results in Section VI also show the superiority of
QoE equilibrium over the satisfaction equilibrium.
III. S
YSTEM MODEL
We consider a heterogeneous wireless network with N
networks coexisting in a given area. For simplicity, we use
“network” to represent a cell in cellular networks or an access
point (AP) in WLAN. The involved networks can be generally
classified as macrocell or small cell, where macrocells refer to
common 3G, 4G and 5G cellular network cells and small cells
could be picocells and femtocells in cellular networks, APs in
WLANs. The network set is denoted by N = {1,...,N}.A
set of users M = {1,...,M} locate in the networks. Each
user has a set of available networks A
m
⊆N. In particular,
users located in overlapping areas of networks can access any
one of the networks, but access only one network at any given
time.
Specifically, a user’s throughput is determined by the phys-
ical layer data rate, the load on the associated network and
the network side resource allocation policy. For network side
resource allocation policy, we assume that the proportional-
fairness and soft-QoS based service differentiation are adopted
in networks. These schemes are widely used in cellular net-
works including LTE-A. In this context, the average throughput
θ
m
of user m ∈Mgiven the accessed network n is derived by
θ
m
=
w
m
R
m,n
W
n
. (1)
where R
m,n
is the physical layer data rate between user m
and network n, w
m
is user m’s weight, W
n
=
i∈M
n
w
i
is the total user weight of network n indicating the load of
the network, M
n
is the set of users associated with network
n. The above throughput model incorporates several practical
considerations. First, the data rate R
m,n
reflects the physical
layer characteristics such as radio channel condition, modu-
lation and coding scheme. Second, the discount factor
w
m
W
n
on R
m,n
shows the nature of multiple user resource sharing.
Third, the user weight here differentiates users in the same
network with diverse traffic or applications, which can be seen
as an indication of application layer information. The model is
similar to the one in [3] and much more general than [2], [5],
since we generalize the user weight from 1 to w
m
.
IV. QOEGAME IN HETEROGENEOUS WIRELESS
NETWORK RESOURCE MANAGEMENT
To exploit the user demand diversity in the RRM of heteroge-
neous wireless networks, we convert conventional throughput-
centric optimization to user demand-centric optimization. In
this section, we first present the idea of user demand-centric
optimization. Then, we propose a new game formulation, QoE
game, to model users’ behavior in the system, with an emphasis
on features different from the throughput-centric optimization.
Finally, we discuss the properties of the QoE game and present
the definition of user demand diversity gain.
A. User Demand-Centric Optimization
Most commonly, the throughput-centric optimization is used
in distributed RRM of heterogeneous wireless network, or net-
work selection. Specifically, each user attempts to maximize the
achievable throughput θ [5] or a strict increasing utility function
f(θ) of θ (e.g., a logarithmic function in [3]). The underlying
assumption is that a larger throughput is always better.In
response to the weakness of throughput-centric optimization
in exploiting user demand diversity, we propose user demand-
centric optimization, where users directly seek for maximizing
QoE. Our intuition is that from user demand perspective, users
can tolerate throughput variation to some extent. Inspired by
the widely used QoE metric, mean opinion score (MOS), we
use MOS to represent users’ goal. In MOS, users’ QoE is
classified into five levels, “Excellent”, “Good”, “Fair”, “Poor”
and “Bad”, as shown in Table I. Denote the selected network of
user m by a
m
∈A
m
, the network selection strategy profile of
all users by a =(a
1
,...,a
M
) with the joint strategy profile set
A = ×
m∈M
A
m
. We define a QoE function q(·) to represent the