Capacity Allocation and Pricing Strategies for Wireless Femtocell Services Lingjie Duan Department of Information Engineering, The Chinese University of Hong Kong {[email protected]} Biying Shou Department of Management Sciences, City University of Hong Kong, Hong Kong, [email protected]Jianwei Huang Department of Information Engineering, The Chinese University of Hong Kong, [email protected]Indoor cell phone users often suffer from poor connectivity. One promising solution, fem- tocell technology, has been rapidly developed and deployed over the past few years. One of the biggest challenges for femtocell deployment is lack of a clear business model. This paper investigates the economic incentive for the cellular operator (also called macrocell op- erator) to enable femtocell service by leasing spectrum resource to an independent femtocell operator. On the one hand, femtocell services can increase communication service quality and thus increase the efficiency of the spectrum resource. On the other hand, femtocell services may introduce more competition to the market. We model the interactions between a macrocell operator, a femtocell operator, and users as a three-stage dynamic game, and derive the equilibrium pricing and capacity allocation decisions. We show that when spec- trum resources are very limited, the macrocell operator has incentive to lease spectrum to femtocell operators, as femtocell service can provide access to more users and efficiently in- crease the coverage. However, when the total spectrum resource is large, femtocell service offers significant competition to macrocell service. Macrocell operator thus has less incentive to enable femtocell service. We also investigate the issue of additional operational cost and limited coverage of femtocell service on equilibrium decisions, consumer surplus and social welfare. Key words: game theory; simulation: analysis; telecommunications 1. Introduction Today there are over 5 billion cell phone users in the world (Global mobile statistics 2011), and many of them experience poor indoor reception at home or office. This is because in the current cellular network (also called macrocell network), a base station covers an area 1
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Capacity Allocation and Pricing Strategies for WirelessFemtocell Services
Lingjie DuanDepartment of Information Engineering, The Chinese University of Hong Kong {[email protected]}
Biying ShouDepartment of Management Sciences, City University of Hong Kong, Hong Kong, [email protected]
Jianwei HuangDepartment of Information Engineering, The Chinese University of Hong Kong, [email protected]
Indoor cell phone users often suffer from poor connectivity. One promising solution, fem-
tocell technology, has been rapidly developed and deployed over the past few years. One
of the biggest challenges for femtocell deployment is lack of a clear business model. This
paper investigates the economic incentive for the cellular operator (also called macrocell op-
erator) to enable femtocell service by leasing spectrum resource to an independent femtocell
operator. On the one hand, femtocell services can increase communication service quality
and thus increase the efficiency of the spectrum resource. On the other hand, femtocell
services may introduce more competition to the market. We model the interactions between
a macrocell operator, a femtocell operator, and users as a three-stage dynamic game, and
derive the equilibrium pricing and capacity allocation decisions. We show that when spec-
trum resources are very limited, the macrocell operator has incentive to lease spectrum to
femtocell operators, as femtocell service can provide access to more users and efficiently in-
crease the coverage. However, when the total spectrum resource is large, femtocell service
offers significant competition to macrocell service. Macrocell operator thus has less incentive
to enable femtocell service. We also investigate the issue of additional operational cost and
limited coverage of femtocell service on equilibrium decisions, consumer surplus and social
welfare.
Key words: game theory; simulation: analysis; telecommunications
1. Introduction
Today there are over 5 billion cell phone users in the world (Global mobile statistics 2011),
and many of them experience poor indoor reception at home or office. This is because in
the current cellular network (also called macrocell network), a base station covers an area
1
Macrocell coverage
Wireline central office to
address cellular traffics
Wireline Home Internet connections
Macrocell users
Femtocell users
DSL router
Macrocell base
station
Femtocell base station
Figure 1: Coexistence of femtocell service and macrocell service, where a macrocell and threefemtocells are deployed
of a radius from several hundred to several kilometers. The high-frequency and low-power
wireless signals often have difficulty in effectively traveling from an outdoor macrocell base
station to indoor cell phones through (several layers of) walls. As a result, indoor cell phone
users often experience dropped calls and reduced wireless data rates (Sandler 2009).
As one promising solution to the indoor reception problem, femtocell technology has been
rapidly developed and deployed over the past few years. Figure 1 provides an illustration of
four homes covered by one macrocell base station, and three of them have installed femtocell
base stations. Femtocell is a small base station with a size similar to a wireless router. An
indoor femtocell base station is much closer to users’ indoor cell phones. It can pick up
the cell phones’ signals much more effectively, and deliver the voice and data signals to the
cellular network through users’ home wireline Internet connection. Femtocell technology can
significantly increase the quality of voice calls and improve the speed of data communications
(Shetty et al. 2009).
Major operators worldwide are enthusiastic about the femtocell technology due to its
capability of improving customers’ experiences. In the United States, AT&T, Sprint Nextel,
and Verizon Wireless are already offering femtocell services to their customers. T-Mobile
and Vodafone in Europe, NTT DoCoMo and Softbank in Japan, and Unicom in China have
been testing the technology and planning to roll out nationwide femtocell services. In June
2010, UK research firm Informa Telecoms & Media reported that femtocell deployments had
more than doubled in the past 12 months, with more and more tier-one operators jumping
2
on the bandwagon (Informa Telecoms & Media 2011). Shipments of femtocell base stations
are estimated to grow from 0.2 million units in 2009 to 12 million units worldwide in 2014
(Berg Insight 2009).
One of the biggest challenges to an operator’s large scale femtocell deployment, however,
is the lack of a clear business model. As Emin Gurdenli, Chief Technology Officer of Deutsche
Telekom AG’s T-Mobile U.K., put it (The Wall Street Journal, Feb. 2009):
“The rationale for femtocells is well-established, but a quantitative business case with a
clear business model in terms of how we go to market is not there yet.”
The purpose of this paper is to develop a quantitative model to examine the business
trade-off of femtocell deployments. In particular, we look at the following research questions:
• Should a macrocell operator deploy femtocell services? How would the operator allocate
bandwidth (capacity) resources and make pricing decisions? There are two common
approaches to the deployment of femtocell service. In an integrated system, a macro-
cell operator directly provides femtocell service to users and fully controls bandwidth
resource allocation and femtocell service price. We have a comparison paper focusing
on the economic operation of such an integrated system (Duan et al. 2011a). In a
distributed system, a macrocell operator leases its spectrum resources to a femtocell
operator. The femtocell operator determines the service provision and pricing indepen-
dently. Examples of distributed systems are abundant in the industry: Sprint leases
licensed spectrum to Virgin Mobile USA to provide femtocell service (Fitchard 2009),
and BT Mobile is using Vodafone’s resource to provide femtocell service (Atkinson
2011). Research results on the distributed system started to energy recently (e.g.,
Hong and Tsai 2010 and Chen et al. 2011), and this paper focuses on the distributed
system. In such a system, a macrocell operator may increase its revenue by leasing re-
sources to the femtocell operator, meanwhile will have less resources for its own services
and face an increased market competition from the femtocell operator.
• How would users choose between femtocell and macrocell services? By using the in-
door femtocell base station, users can avoid the poor reception problem and achieve the
maximum quality of service (QoS). In contrast, when users choose to use the outdoor
macrocell base stations, the QoS highly depends on the user locations and the commu-
nication environments (which is summarized by a user-dependent spectrum efficiency
parameter). Apparently such QoS differentiation justifies different prices of the two
3
services. A user needs to balance the QoS with the payment when choosing between
macrocell and femtocell services.
Our main results are summarized as follows:
• Characterization of equilibrium decisions: We derive a threshold structure in terms
of the spectrum efficiency parameter, which separates users who prefer femtocell to
macrocell services. We further characterize the femtocell operator’s femtocell price and
the macrocell operator’s capacity allocation and pricing decisions at the equilibrium.
• Sensitivity analysis of macrocell’s total capacity: Wireless spectrum is a very scarce
resource, so macrocell operators often face capacity constraints. In the U.S. 700MHZ
spectrum auction in March 2008, the total bid price is nearly $20 Billion (WNN Wi-Fi
Net News 2008). The key (counter-intuitive) conclusion is that macrocell operator has
more incentive to lease spectrum to the femtocell operator when its capacity is small,
but chooses to offer only macrocell service when its capacity is large.
• Calculation of consumer surplus and social welfare: With no additional operational
cost and full coverage, femtocell service can increase both the total consumer surplus
and social welfare. However, we show that some users might experience a smaller payoff
from the adoption of the femtocell service if, for example, they do not experience much
service quality improvement with the femtocell service but need to pay a higher price.
In addition, we have examined two extensions of the basic model. The first is with
additional femtocell operational cost. Although femtocells are low in deployment costs, the
femtocell service may incur additional operational cost compared to macrocell service. For
instance, femtocell operators may be charged by internet service providers for routing traffic
through wireline broadband internet to reach the cellular network (McKnight et al. 1997).
The impact of the additional operator cost on the femtocell operator is obviously negative;
its impact on the macrocell operators, however, is unclear and deserves detailed exploration.
The second is the impact of limited femtocell coverage. A femtocell base station typically
has a smaller spatial coverage. For instance, a femtocell base station may only cover a
region with a radius of tens of meters, whereas a macrocell base station covers a larger range
with a radius from hundreds of meters to several kilometers. The femtocell service may
have limited coverage (comparing with the macrocell) when the number of femtocell base
4
stations is small. We examine the impact of such limited coverage on macrocell and femtocell
operators’ profits.
The rest of the paper is organized as follows. We introduce the network model of macro-
cell service in Section 3, which serves as a benchmark for later analysis. In Section 4, we
introduce the network model of femtocell service and analyze how the macrocell operator
and femtocell operator make capacity and pricing decisions to maximize their own profits.
Then, in Sections 5 and 6, we extend the results in Section 4 by examining the various
effects of femtocell operational cost and limited femtocell coverage. In Section 7 we present
the conclusion to our study and discuss future work.
2. Literature Review
Our work is closely related to two main streams of literature: i) studies of femtocell deploy-
ment in the telecommunication literature, and ii) studies of dual channel competition in the
management science and operations research literature.
Most existing work on femtocell deployment in the telecommunication literature (e.g.,
Chandrasekhar and Andrews 2009) focus on various technical issues in service provision such
as access control, resource management, and interference mangement. Only a few papers
discuss the economic issues of femtocells (e.g., Claussen et al. 2007, Yun et al. 2011, Shetty
et al. 2009, Chen et al. 2011), examining the impact of network deployment costs and
femtocells’ openness to macrocell users. The key difference between our paper and such
existing literature is that we study the provision of dual services in terms of both spectrum
allocations and pricing decisions. We also characterize the impact of the femtocell operational
cost and limited femtocell coverage on the service provision.
Our work is also closely related to the literature on dual channel competition in the area
of management science and operations research. In this body of literature, there are usually
two types of decision makers: a manufacturer and a retailer. The manufacturer can sell the
products through a direct channel, a retailer channel, or both. Chiang et al. study whether
and how a manufacturer should operate a new direct channel when it already has a retailer
partner. They show that direct marketing can indirectly increase the flow of profits through a
retail channel by reducing the degree of double marginalization. Also, the direct channel may
not be a threat to the retailer since the wholesale price is driven down. Tsay and Agrawal
2004 further exploit several means whereby the manufacturer can mitigate channel conflict
5
between the direct channel and the retailer channel, including adjustments of wholesale price,
paying a commission to a retailer, and entirely conceding demand fulfillment on the part of
the retailer. More general results are obtained motivated by the models in Chiang et al. 2003
and Tsay and Agrawal 2004. For example, Huang and Swaminathan 2009 posit a stylized
deterministic demand model where each channel relies on prices, degree of substitution across
channels, and the overall market potential. Dumrongsiri et al. 2008 investigate the influence
of demand variability on prices and manufacturer’s incentive to open direct channel.
In our context of femtocell deployment, we can view the macrocell operator as the man-
ufacturer, the femtocell operator as the retailer, and the macrocell service as the direct
channel. Our paper has four key differences from prior literature.
First, we consider a different order of introducing the new channel. Instead of introducing
the direct channel after the retailer channel, as is the case in Chiang et al. 2003, Tsay and
Agrawal 2004a, Huang and Swaminathan 2009, Dumrongsiri et al. 2008, we consider the
case in which the manufacturer owns the direct channel first and decides on the best way to
open the retailer channel.
Second, the limited capacity model considerably complicates the analysis of our model.
The dual channel literature generally assumes unlimited potential supply, i.e., that the man-
ufacturer can produce as many products as possible (with a production cost) to maximize
its profit.However, a macrocell operator often has only a limited total capacity in the deci-
sion time scale considered here. This is because the spectrum allocation to cellular service
providers are often regulated by government authorities (e.g., FCC in USA and Ofcom in
UK). The macrocell operator often obtains spectrum licenses that last for years or decades.
The long license period ensures enough motivation for the macrocell providers to invest in
the necessary network infrastructure, which is often very expensive.
Third, the heterogeneity of users in our model is motivated by the unique characteristics
of wireless communications, and is thus different from that considered by prior literature.
In particular, users have different channel conditions (and thus different evaluations of the
same resource allocation) under the macrocell service (direct channel), but have the same
maximum channel condition under the femtocell service (retailer channel). In contrast,
prior literature either assumes that users are homogenous or are different in willingness
to pay. Moreover, the users’ utility functions here are also motivated by today’s wireless
communication technologies, which renders some of the prior generic analysis inapplicable.
Finally, we characterize the impact of limited femtocell coverage on the new service
6
provision. Very few prior studies have considered a similar constraint. Rubin 1978 considers
a related constraint where the monitoring costs of company-owned outlets rise with physical
distance from headquarters, and thus direct channel becomes non-profitable in suburban
areas. What we considered is the limitation of coverage of the retailer channel, and the
model thus is different.
3. Benchmark Scenario: Macrocell Service Only
Throughout this paper, we focus on the monopoly case in a two-tier market with a single
macrocell operator and a single femtocell operator. This is motivated by some monopoly
examples in macrocell services worldwide (e.g., America Movil (the world’s fourth largest
mobile network operator) in Mexico and many places in Latin America, and MTS in some
central Asian countries). Also, since femtocell service just emerged from last decade, many
fetmocell operators are still local monopolists (e.g., Virgin Mobile USA in US and BT Mobile
in UK). We believe that a thorough understanding of the monopoly case is critical before
studying the more general oligopoly market in the future.
As a benchmark case, we first look at how the macrocell operator prices the macrocell
service to maximize its profit without introducing the femtocell service. When we consider
the introduction of femtocell service in Sections 4 and 5, the macrocell operator needs to
achieve a profit no worse than this benchmark case.
For the sake of discussion, we will focus on the operation of a single macrocell. In general,
a macrocell operator owns multiple macrocells. Non-adjacent macrocells can share the same
frequency (called frequency reuse). The analysis of this paper can be extended to the more
general case without changing the main managerial insights.
The macrocell operator owns wireless spectrum (also called bandwidth) with a limited
capacity; a user needs to access the bandwidth in order to complete its wireless communi-
cations (e.g., voice calls, video streaming, data transfer). A larger bandwidth means more
resources to the user and thus better communication QoS, but also leads to a greater expense.
As shown in Fig. 2, we model the interactions between the macrocell operator and end
users as a two-stage Stackerberg game. In Stage I, the macrocell operator determines the
macrocell price pM per unit bandwidth. In Stage II, each user decides how much bandwidth
to purchase. The operator wants to maximizes its profit, while the users want to maximize
their payoff. Such usage-based pricing scheme is widely used in today’s cellular macrocell
7
networks, especially in Europe and Asia (Courcoubetis and Weber 2003, Altmann and Chu
2001). In US, AT&T (since a year ago) and Verizon (since July 2011) have adopted the
usage-based pricing for wireless data services. Usage-based pricing for femtocells has just
started. For example, AT&T’s femtocell service counts the femtocell data usage as part
of the regular cellular usage (together with the macrocell data usage), which is subject to
usage-based pricing (AT&T 2011). Due to the exponential growth of wireless data traffic
and the scarce spectrum resource, we envision that usage-based pricing for both macrocell
and femtocell services will become more and more common in the near future.
Next, we solve this two-stage Stackelberg game by backward induction (Myerson 1997).
The proof of Lemma 6 is given in our online technical report (Dual et al. 2011b).
5.2. Stage I: Macrocell Operator’s Spectrum Allocations and Pric-ing Decisions
Now let us study Stage I, where the macrocell operator determines pM , BF , and BM to
maximize its profit. Let us denote its equilibrium decisions as p∗M , B∗F , and B∗M .
Notice that Lemma 5 shows that it is optimal for the macrocell operator to serve all users
with θ ∈[
pM
p∗F (pM ,BF ), 1]
by the macrocell service. By using the fact that BM = B − BF , we
can eliminate variable BM . The macrocell operator’s profit is
πMacro(pM , BF ) = pMB∗R(BF , pM) + pM
∫ 1
pMp∗F
(BF ,pM )
(1
pM− 1
θ
)dθ. (20)
21
The macrocell operator’s profit-maximization problem is
maxBF ,pM
πMacro(pM , BF ),
subject to 0 ≤ BF +
∫ 1
pMp∗F
(BF ,pM )
(1
pM− 1
θ
)dθ ≤ B,
0 < pM ≤ 1− C, (21)
where B∗R(BF , pM) and p∗F (BF , pM) are given in (18) and (19), respectively. The second
constraint shows that the total cost C + pM to femtocell operator should be less than 1.
Otherwise, the femtocell price pF needs to be larger than C + pM and thus larger than 1,
and no user will subscribe to the femtocell service.
5.3. Numerical Results
Problem (21) is not convex and is difficult to solve in closed-form, but can be solved easily
using numerical methods. Similar to Section 4, we can see that dual services degenerate to
the macrocell service only benchmark when capacity is large. Here we will focus on how
cost C will affect the division of two capacity regimes and the performance when capacity is
small.
5.3.1. Impact of C on Capacity Regime Boundary
Figure 11 illustrates how cost C affects the boundary between the low capacity and high
capacity regimes. Recall that the boundary is 4.77 when C = 0 (i.e., Figures 5, 6, and
7). When C increases, the femtocell price p∗F increases and demand for femtocell service
decreases. This makes it less attractive to provide femtocell service. On the other hand,
the increase of price p∗F also reduces the market competition, which makes the macrocell
operator more willing to lease spectrum to the femtocell operator. The interactions of these
two factors determine the boundary of the two capacity regimes. More specifically, with
a small cost C ≤ 0.12, the decrease of femtocell demands dominates and the boundary
decreases. With a large cost C > 0.12, the decrease of competition dominates and the
boundary increases. We will discuss these two factors in more details at a later point.
Figure 12 explicitly illustrates that a larger C decreases the gap between users’ finalized
partition threshold θth =p∗Mp∗F
and the threshold θ̃th = 11
p∗M− 1
p∗F
+1that the macrocell operator
prefers, and thus makes the service competition less fierce. This gives more incentive to the
macrocell operator to lease spectrum to the femtocell operator.
22
0 0.1 0.2 0.3 0.43.5
4
4.5
5
5.5
Cost C
Bou
ndar
y be
twee
n tw
o ca
paci
ty r
egim
es
Figure 11: The boundary between low andhigh capacity regimes change with femtocelloperational cost C.
0 0.1 0.2 0.3 0.40
0.05
0.1
0.15
0.2
0.25
Cost C
Diff
bet
wee
n p M*
/ p F*
and
1/ (
1/ p
M* −
1/ p
F*+
1)
B=1.1B=2.1
Figure 12: The difference between users’partition threshold θth =
p∗Mp∗F
and macro-
cell operator’s preferred threshold θ̃th =1
1p∗M− 1
p∗F
+1as a function of C and B
Observation 3. As cost C increases in femtocells, the femtocell operator has less incentive
to provide femtocell service. However, the macrocell operator may benefit from the increase
of C in terms of its profit since the service competition from femtocell operator become less
intense.
When cost C increases but is still small, we can show that femtocell price increases to
compensate cost, and the macrocell operator will face the decrease of femtocell demands.
In this case, less femtocell band is needed and the macrocell operator’s profit decreases in
C (see Fig. 13). However, when cost C is large, competition between dual services reduces
and the macrocell operator can tolerate the existence of femtocell service even for a large B.
For example, Fig. 11 shows that under C = 0.4 the macrocell operator still wants to lease
bandwidth to femtocell operator even with B = 5.2, which is not the case when C = 0.
5.3.2. Impact of C on Consumer Surplus and Social Welfare
In Figures 14 and 15, we investigate how the cost C affects total consumer surplus and social
welfare. We focus on the low capacity regime only.
Figure 14 shows that the total consumer surplus is larger with dual services when C < 0.3,
but is smaller with dual services when C > 0.3. In the latter case, femtocell users experience
only small QoS improvements due to the high cost p∗F , and macrocell users experience a p∗M
23
0 0.1 0.2 0.3 0.40.34
0.36
0.38
0.4
0.42
0.44
0.46
0.48
0.5
Cost C
Mac
roce
ll op
erat
or’s
equ
ilibr
ium
pro
fit
B=1.1B=2.1
Figure 13: Macrocell operator’s equilibriumprofit as a function of cost C and capacity B
0 0.1 0.2 0.3 0.4 0.5 0.6
0.16
0.165
0.17
0.175
0.18
0.185
0.19
0.195
0.2
Cost C
Tot
al c
onsu
mer
sur
plus
Macrocell service onlyDual services
Figure 14: Comparison of total consumer sur-plus between dual services and macrocell ser-vice only benchmark as functions of C. Herewe fix B = 1.1.
larger than pbenchM . Note that macrocell price increases since all users can be served. As a
result, the total consumer surplus decreases with dual services.
Figure 15 shows that social welfare is always larger with dual services for all possible
values of C. Together with Figure 14, this shows that the macrocell operator obtains a
larger profit by sacrificing the consumer surplus when C > 0.3.
Observation 4. After introducing femtocell service, total consumer surplus increases only
when the cost C is small. The social surplus always increases.
6. Extension II: Limited Femtocell Coverage
In Section 4, we assume that femtocell service has the same ubiquitous coverage as the
macrocell service. In this section, we look at the general case where the femtocell service
only covers η ∈ (0, 1) portion of the user population, as illustrated in Figure 1. Then 1− ηportion of users can only access the macrocell service. Figure 16 illustrates the users’ possible
service partitions over space and macrocell spectrum efficiency θ. We call the η fraction users
overlapped users, and the rest 1−η non-overlapped users. We are interested in understanding
how the limited coverage affects the provision of femtocell service.
The three-stage decision process is similar to that depicted in Figure 4. The analysis of
Stage III is the same as Section 4.3. Next we focus on Stage II.
24
0 0.1 0.2 0.3 0.4 0.5 0.6 0.70.45
0.5
0.55
0.6
0.65
0.7
Cost C
Soc
ial w
elfa
reMacrocell service onlyDual services
Figure 15: Comparison of social welfare be-tween dual services and macrocell service onlyas functions of cost C. Here the total capacityis fixed at B = 1.1
Users’ normalized population
1
0 *
Mp 1Macrocell spectrum efficiency θ
*
th
Macrocell service
Femtocell
service
Macrocell
service
No service
Figure 16: Users’ possible service partitionsover space and macrocell spectrum efficiencyθ
Following a similar analysis as in Lemma 2, we can also conclude that overlapped users
with θ ∈ [θprth , 1] will be served by macrocell service, and the other overlapped users will be
served by femtocell service. That is, θth = θprth . Then we can similarly derive the following
result.
Lemma 7. In Stage II, the femtocell operator’s equilibrium femtocell price is
p∗F (pM , BF ) = max
(2
1pM
+ 1,−pMη +
√(pMη)2 + 4pMBFη
2BF
), (22)
and its leased bandwidth from macrocell operator is
B∗R(pM , BF ) = min
(ηpM
(1
(pM )2− 1
4
), BF
), (23)
which equals overlapped users’ total preferred demand in femtocell service.
6.1. Macrocell Operator’s Spectrum Allocations and Pricing inStage I
Now we are ready to study Stage I, where the macrocell operator’s profit-maximization
problem is
maxpM ,BF
πMacro(pM , BF ) = pMB∗R(pM , BF ) + pM
∫pM
p∗F
(pM ,BF )
(1
pM− 1
θ
)dθ,
subject to, 0 < BF +
∫pM
p∗F
(pM ,BF )
(1
pM− 1
θ
)dθ ≤ B, (24)
where p∗F (pM , BF ) and B∗R(pM , BF ) are respectively given in (22) and (23).
25
0.2 0.4 0.6 0.8 10.35
0.4
0.45
0.5
0.55
Femtocell coverage η
p F∗ B=1.1B=2.1
0.2 0.4 0.6 0.8 10.2
0.25
0.3
0.35
Femtocell coverage η
p M*
B=1.1B=2.1
Figure 17: Equilibrium prices p∗F and p∗M asfunctions of η and B
0.2 0.4 0.6 0.80.16
0.165
0.17
0.175
0.18
0.185
0.19
0.195
0.2
Femtocell coverage η
Tot
al c
onsu
mer
sur
plus
Macrocell service onlyDual services
Figure 18: Comparison of total consumersurplus between dual services and macrocellbenchmark under B = 1.1.
6.2. Numerical Results
Problem (24) is not convex and is difficult to solve in closed-form, but can be solved easily
using numerical methods. As in Sections 4.4 and 5.3, we can again clearly observe different
behaviors in two capacity regimes: dual services degenerate to the macrocell service only
benchmark in the high capacity regime. Unlike Section 5.3, the femtocell coverage η does
not affect the boundary of the two capacity regions (i.e., always at B = 4.77). The two effects
(QoS improvement and competition brought by femtocell service) coexist in the overlapping
coverage area.
We can show that as η increases, it is more attractive to provide femtocell service and
the equilibrium femtocell (macrocell) band B∗F (B∗M) increases (decreases). Yet both prices
p∗F and p∗M increase in η (see Fig. 17). Intuitively, as η increases, more users are served
and the total femtocell demand increases, which leads to a larger p∗F . The overall wireless
service (macrocell plus femtocell) becomes more efficient and the total user demand (of both
services) increases. Thus we can observe a larger p∗M . Since the macrocell operator can sell
its total capacity with a higher price, its profit increases in η.
Figure 18 further shows that the total consumer surplus is larger with dual services than
macrocell service only benchmark. This result is similar to Fig. 9 in Section 4.4.
Observation 5. As femtocell coverage expands, the overall wireless service (macrocell plus
femtocell) becomes more efficient. The macrocell operator’s profit, total consumer surplus,
and social welfare increase in η.
26
7. Conclusion
This paper studies the economic incentives for a macrocell operator to deploy new femtocell
service in addition to its existing macrocell service. The femtocell service is provided by an-
other party, the femtocell operator, who needs to lease the macrocell operator’s capacity. We
model the interactions among macrocell operator, femtocell operator, and users as a three-
stage dynamic game, and derive the equilibrium capacity allocation and pricing decisions.
Our analysis shows that the macrocell operator has an incentive to enable both macrocell
and femtocell services when its total bandwidth is small, as femtocell service enhances user
coverage and improves profits for both macrocell and femtocell operators. Notice that not
all users will experience a payoff increase by the introduction of femtocell service in this case.
However, when the total bandwidth is large, femtocell service becomes a severe competitor
to macrocell service, and the macrocell operator thus has less incentive to lease its bandwidth
to the femtocell operator. In this case, only macrocell service is provided to users.
Also, we further study the impact of operational cost of femtocell service. On one hand,
we show that the increase of operational cost of femtocell service makes both operators’
profits decrease. On the other hand, we show that the operational cost can mitigate femtocell
operator’s competition with macrocell operator. Finally, we investigate the impact of limited
femtocell coverage where only some users have access to femtocell service.
There are several directions to extend the results in this paper.
• We can further consider the “shared carriers” scheme besides “separate carriers”, where
femtocell service and macrocell service share part of or the whole spectrum. We need
to optimize the pricing and spectrum allocation decisions by trading off the increased
spectrum efficiency and mutual interferences between macrocell and femtocell services.
• We can also consider the frequency spectrum reuse, where multiple femtocells can reuse
the same spectrum if they do not overlap with each other in terms of coverage. In this
case, femtocell service will become more attractive to the femtocell operator, as a single
frequency band may support more users. However, frequency reuse might make the
interference management complicated in areas where femtocells are densely deployed.
• We can consider a more practical model for users’ utility functions, by incorporating
their heterogeneous willingness to pay and sensitivities to achieved data rates.
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• Finally, we will extend the monopoly case to oligopoly case, where multiple macrocell
(femtocell) operators compete with each other. Intuitively, we can envision no provision
of femtocell service only when all macrocell operators have adequate bandwidth. But
the macrocell and femtocell prices will go down due to the new horizontal competitions.
References
Altmann, J., K. Chu. 2001. How to charge for network services-flat-rate or usage-based?
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Atkinson, J. 2011. Vodafone and BT mobile mvno renew contract for five years. http://www.
mobiletoday.co.uk/News/11089/Vodafone and BT Mobile MVNO renew contract for