A PRICING MODEL OF GPRS NETWORKS WITH WI-FI
INTEGRATION FOR “HEAVY” DATA USERS
Saravut Yaipairoj, Fotios Harmantzis, Vinoth Gunasekaran
Stevens Institute of Technology
Hoboken, NJ USA
Keywords:
Wireless Pricing, Incentive Compatible, Network Integration, 3G-like services, Self-differentiation, GPRS,
Wi-Fi.
Abstract:
As wireless services have become increasingly integrated and their demand is mounting, Wi-Fi provides an
appealing opportunity for the GSM/GPRS operators to enhance their data capability. By integrating both
networks, operators are able to provide 3G-like services. However, both networks have different data rates
and capacity, which makes pricing a challenging issue. In this paper we propose a pricing model for GPRS
networks integrated with Wi-Fi, which applies to data users with high service demand (“heavy”). Through op-
timization technique, our proposed model identifies how the integration can play a significant role in increasing
operators’ overall revenue and potentially improving the performance of GPRS networks.
1 INTRODUCTION
As wireless technologies have been emerging and im-
proving, the boundary of their applications becomes
blur. The wireless technologies, which once posi-
tioned for their own specific applications, now can
provide comparable services. For certain wireless ser-
vices, technologies being used for different applica-
tions can now be seen as alternative solutions. The ob-
vious examples are the improvement in mobility and
coverage of Wi-Fi and the increasing capacity of data
services in cellular networks. Wi-Fi has been both a
competing and a complementary technology to cellu-
lar networks (Salkintzis, 2002; Ahmavaara, 2003). It
offers fast connectivity and relatively much cheaper
services compared to 2.5G cellular networks, such as
General Packet Radio Service (GPRS). However, cov-
erage of cellular networks is much larger than that
of Wi-Fi networks. Several GPRS operators con-
sider providing Wi-Fi services along with their net-
works in order to improve their networks’ capacity
and alleviate congestion in GPRS networks. As a re-
sult, the main challenge that they would encounter is
the pricing issues of services in both networks. Tra-
ditionally, GPRS networks offer simple usage-based
pricing (Courcoubetis, 2000) for each megabyte that
users transmit over the network. On the other hand,
Wi-Fi service providers find it more difficult to come
up with a pricing plan for their service. There are
several payment options, such as a subscription fee
on monthly basis, a one-time charge per connection,
or usage-based pricing. The pricing schemes vary
among different service providers. However, most
Wi-Fi charges are based on flat pricing (Anania, 1997;
boingo) such as a connection fee, which the network
charges a user per connection in one location. To alle-
viate this pricing confusion in both networks, cellular
operators have an option to integrate their networks
with the hotspots and provide a common bill to their
customers. In addition, data access over Wi-Fi is cost
effective compared to cellular networks. A cellular
base station costs over 30 times more than a Wi-Fi
hotspot (Salkintzis, 2002). Network operators would
enjoy significant cost saving while offering broad-
band wireless services that are comparable to 3G,
namely, 3G-like services (Ahmavaara, 2003; Doufexi,
2003). With the integration of both networks, network
users, especially the ones with high service demand
(or heavy users), will be able to choose to transmit
data over either GPRS networks, (which offer wide
coverage but costly and limited transmission rate), or
Wi-Fi networks (which offer cost-effective services
and high transmission rate but limited coverage).
Network users are inherently price sensitive (Ma-
son, 1995). Using prices, the network can signal to
users, providing incentives, which influence their be-
79
Yaipairoj S., Harmantzis F. and Gunasekaran V. (2005).
A PRICING MODEL OF GPRS NETWORKS WITH WI-FI INTEGRATION FOR “HEAVY” DATA USERS.
In Proceedings of the Second International Conference on e-Business and Telecommunication Networks, pages 80-85
DOI: 10.5220/0001414800800085
Copyright
c
SciTePress
havior to choose the networks that meet their pricing
criteria (Falkner, 2000). The fact that users choose to
access networks based on prices is similar to the con-
cept of Paris Metro Pricing (PMP) (Odlyzko, 1999).
That is, the GPRS operators could promote self-
differentiation by charging different prices on those
two networks. Pricing incentive would likely to move
the network users from the congested high-priced
GPRS networks to the less congested inexpensive Wi-
Fi networks. However, PMP networks are identi-
cal networks with different prices charged to users.
GPRS and Wi-Fi networks are different in terms of
capacity and coverage. Clearly, integration between
the two networks will make the pricing problem chal-
lenging.
In this paper, we propose a simple but effective
demand-based pricing model for the integration be-
tween GPRS and Wi-Fi networks. In Section 2,
we describe the architectural overview of Wi-Fi in-
tegrated with GPRS. In the third section we propose
our optimized pricing model, followed by Section 4
where we present the results of our numerical analy-
sis. We draw our conclusions in Section 5.
2 ARCHITECTURAL OVERVIEW
OF INTEGRATION: Wi-Fi WITH
GPRS NETWORKS
Integrating GPRS and Wi-Fi gives both ubiquitous
coverage and support high data rate in strategic lo-
cations (schools, office, airports, hotels, coffee shops
etc.). If both Wi-Fi and GPRS networks are integrated
then cellular operators are able to meet some require-
ments for 3G services. This would allow them to pro-
vide high quality data services which can be perceived
as 3G-like services. The following are two types of
integration, tight coupling architecture and loose cou-
pling architecture (Salkintzis, 2002; Oliver, 2002).
2.1 Tight Coupling architecture
In this type of architecture the Wi-Fi is connected
to the GPRS network as an alternative Radio Ac-
cess Network (Salkintzis, 2002). It is connected to
the operator’s core network. The hotspot can reuse
the GPRS infrastructure like core network resources,
subscriber databases and billing systems. The mobile
users can select their network preferences or choose
to get connected at the best available network speed.
This is all done in software and will automatically
connect them to the network of their choice. Fig. 1
illustrates the tight coupling architecture for the inte-
grated network.
MS
GPRS
RAN
GPRS Core
External Packet Data
Network
WLAN
SGSN
GGSN
HLR
SGSN
Figure 1: Tight coupling architecture for GPRS integrated
with Wi-Fi networks.
2.2 Loose Coupling Architecture
The hotspots are coupled with the GPRS network in
the operator’s IP network. So the Wi-Fi data traf-
fic goes directly to the operator’s IP network, instead
of going via the GPRS core network (Oliver, 2002).
Though the Wi-Fi and cellular networks remain sep-
arate, there is a common platform for authentication,
accounting and authorization. The hot spot may be
owned by any third party carriers with roaming en-
abled via a dedicated connection between the cellular
operators and Wi-Fi providers or over an existing In-
ternet. Fig. 2 illustrates the loose coupling architec-
ture for the integrated network.
MS
GPRS
RAN
GPRS Core
External Packet Data
Network
WLAN
SGSN
GGSN
HLR
SGSN
Figure 2: Loose coupling architecture for GPRS integrated
with Wi-Fi networks.
3 PROPOSED PRICING MODEL
In our proposed model, we assume that a user is ini-
tially in the GPRS coverage and he is ready to per-
form a large file transfer. Users subscribes to both
GPRS and Wi-Fi services. There will be one com-
mon Accounting, Authentication, and Authorization
(AAA) server and billing system maintained by the
cellular operators for all integrated hotspots. Now the
user has two options: he can either perform file trans-
fer right away over GPRS network paying a higher
price, or he can search for Wi-Fi hot spots, assuming
he regularly crosses Wi-Fi networks. Once users are
in hotspot coverage, different types of hot spots would
determine if users need to pay a roaming fee (third
party hotspot case) or not (operator-owned hotspot
case). We disregard the roaming fee at this point since
ICETE 2005 - WIRELESS COMMUNICATION SYSTEMS AND NETWORKS
80
that fee is not significant enough to contribute to the
Wi-Fi charges when compared to charges from GPRS
services. Fig. 3 illustrates a blocking diagram for the
scenario we just described.
Figure 3: Pricing Block for GPRS networks with Wi-Fi in-
tegration.
As mentioned earlier, the cost of transmitting data
over a GPRS network is quite high when compared to
Wi-Fi network. This significant price difference be-
tween the two networks can influence the way users
use these networks. Some users may be willing to
search for a Wi-Fi network, if they need to perform
a large file transfer. Hence, price incentive can influ-
ence users to use either GPRS services with higher
price tag (more convenience since the network has
larger coverage) or Wi-Fi services with lower price.
We argue that the percentage of mobile users D who
accept to be charged by GPRS networks, depends
heavily on the price ratio between the two networks
(Hou, 2001). D can be mostly influenced by the de-
mand function which is a function that characterizes
the reaction of users to changes in price. In this paper
we use the demand function that appears in (Oldyzko,
2000) since it is used for different classes of users,
that fit our model. The demand function is as follows:
D = e
(
p
g
p
w
1)
2
, 0 D 1, p
h
p
o
(1)
where p
g
is the GPRS charge and p
w
is the Wi-
Fi charge for each user (p
w
could be either operator
owned or third party owned hot spot charge). We are
interested in the case when price incentive can influ-
ence decision of users. Therefore, the session volume
charged by GPRS networks must be large enough to
allow p
g
to be greater than p
w
. As we know GPRS
pricing is usage-based charges, which do not depend
on holding time but the session volume, therefore, p
g
is a linear function of the number of megabytes trans-
mitted over the network. For Wi-fi charge, it is based
on flat pricing, which is basically a connection fee.
Therefore, p
g
and p
w
can be described as follows:
P
g
= r
g
· v
P
w
= r
w
(2)
where r
g
is the charging rate per megabyte for the
GPRS network, r
w
is the connection fee of the Wi-Fi
network, and v is the session volume of data that users
transmit over the GPRS network.
Lower curve in Fig. 4 illustrates the demand func-
tion in (1). The horizontal axis represents the price ra-
tio between GPRS and Wi-Fi charges (
p
g
p
w
1). This
function works quite well in our model because, first,
the demand function begins high for small price ratio
representing the situation when users have small vol-
ume of data to transmit. The price charged by GPRS
networks would not be much different from the Wi-
Fi charge. The users have little incentive to seek for
Wi-Fi hotspots resulting in the high user demand for
GPRS usage. Then, the demand decreases rapidly as
the curve gets into a mid-range and has very narrow
tail. This part of the curve represents the increase in
GPRS charges due to the increasing session volume
from users. There is enough incentive for some users
to start migrating to Wi-Fi resulting in the reduction of
GPRS usage. For example, when the price difference
at the horizontal axis equals to one, the GPRS charge
is double the Wi-Fi charge, resulting in the GPRS de-
mand dropping to 36.79 percents.
The revenue due to integration can be determined
by the weighted sum of the revenue created by the
GPRS networks and Wi-Fi networks based on their
corresponding demand. Therefore, from equation (2),
the average revenue of the integrated network can be
determined as follows:
R
int
= D · (r
g
· v) + (1 D) · r
w
(3)
Regarding the revenue gained from GPRS network
without Wi-Fi integration, the GPRS users do not
have an alternative to migrate their traffic. Therefore,
the demand of users using non-integrated GPRS net-
works would be higher than equation (1). Since the
distribution of session volume in GPRS networks is
not available to us, we have to come up with a mean-
ingful demand function. This function needs to be
well above the demand function in equation (1), to
represent the higher demand of GPRS networks in the
absence of Wi-Fi. The demand function can be shown
as follows (Oldyzko, 2000):
D
w.o.int
=
1
1 + (
P
g
K
1)
4
(4)
where K is a constant. In our case, we set K equal
to p
w
for the purpose of fitting our demand curve ac-
cording to our assumptions. That, does not mean that
D
w.o.int
depends on the Wi-Fi charge. By compar-
ing the revenue generated in both cases, we can gain
A PRICING MODEL OF GPRS NETWORKS WITH WI-FI INTEGRATION FOR “HEAVY” DATA USERS
81
some ideas about the effect of integration on the rev-
enue stream. Fig. 4 illustrates both demand functions.
0 0.5 1 1.5 2 2.5 3
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
User demand of GPRS networks (D)
Price ratio between GPRS and Wi−Fi ((P
g
/P
w
)−1)
GPRS with Wi−Fi integration
GPRS without Wi−Fi integration
Figure 4: Demand functions.
Based on the user demand for GPRS network with-
out integration, the revenue gained from GPRS net-
work without integration is as follows:
R
w.o.int
= D
w.o.int
· (r
g
· v) (5)
In terms of performance improvement of GPRS
networks with Wi-Fi integration, we focus on the por-
tion of users’ demand that we can offload to the Wi-fi
network. Each GPRS user generates a certain amount
of session volume based on their perference. We
would need to find prices for both GPRS and Wi-fi
networks that attracts users and reduces the their de-
mand down to some target demand D. To be specific,
we will set up an optimization model to find the opti-
mal r
g
and r
w
based on target demand D
In our optimization model, we first set up our ob-
jective function. The most suitable objective function
would be equation (3) due to the fact that the opti-
mal r
g
and r
w
at any target demand should be able
to yield the maximum revenue for the integrated net-
works. The objective function is subjected to cer-
tain constriants which are r
g
, r
w
and D. r
g
and r
w
must be constrainted based on the competitive market
prices which the network operators should be able to
provide based on their cost analysis of their networks.
For the target demand D, it specifies the portion of
data users who choose GPRS networks for their data
transmission, which represent the network operation
point of GPRS networks. Therefore,we can use D
as the constraint for traffic offload to Wi-fi networks.
Hence, we can set up our objective function and its
constraints as follows:
Maximize R
int
(6)
subject to the following constraints
a r
g
b
c r
w
d
D = e
(
p
g
p
w
1)
2
= D
t
where [a, b] and [c, d] are the constraints for r
g
and
r
w
respectively, D
t
is the target demand of GPRS
users. Regarding average session volume (v), the dis-
tribution of v in GPRS networks with Wi-Fi integra-
tion is required for optimal charges in both networks.
We do not have such distribution at this point. How-
ever, in (Kilpi, 2003), Kilpi illustrates cumulative ses-
sion volume of a large number of GPRS sessions, giv-
ing an overview of typical GPRS sessions. The result
shows that the session volume for very “big” sessions
of GPRS services is hardly more than 5 MB due to
slow user speeds and structural delay of GPRS net-
works. Therefore, we would be interested in some
typical larger sessions (not more than 5 MB) that we
could use pricing mechanism to offload them to Wi-Fi
networks. By offloading the traffic to Wi-Fi, we ex-
pect that the performance of GPRS networks will be
improved significantly (it is beyond the scope of the
paper to prove that in a rigorous manner).
4 NUMERICAL ANALYSIS
In this section, we present our preliminary results
based on the numerical analysis. We illustrate the
revenue gained from network integration and the ef-
fect of Wi-Fi connection fee on the average revenue
of the integrated networks. Furthermore, we present
the results from our optimization model which allows
us to setup the optimal prices which yield maximum
revenue at a certain target user demand. The price set-
ting attract GPRS users to migrate and reduce traffic
load in GPRS networks.
4.1 Assumptions and parameters
We consider the case where users want to transmit
relatively big data session, e.g., 1 MB or more. The
large amount of users’ traffic creates pricing incentive
to seek and transmit their traffic onto less expensive
Wi-Fi networks. Smaller session volume (< 1 MB)
will not create enough incentive for users to look for
hot spots. We assume that pricing in GPRS networks
is usage-based at a rate of 6 dollars per megabyte.
Charging at Wi-Fi hot spots is flat, where users are
charged per connection; users can transmit or receive
as much traffic as they want during a connection. In
addition, we assume that users have access to Wi-Fi
hot spots, when they seek for them. The only incen-
tive that drives them to hotspots is pricing. We do not
ICETE 2005 - WIRELESS COMMUNICATION SYSTEMS AND NETWORKS
82
include the coverage or location of hot spots into our
pricing model.
4.2 Numerical Results
Fig. 5 shows the revenue gained from the integration
of networks determined by equation (3), versus the
average session volume. The Wi-Fi connection fee is
7 dollars per connection, regardless of the amount of
traffic transmission. We can see that when data vol-
ume per connection increases, users would be influ-
enced by price incentive to transmit their traffic over
Wi-Fi hot spots, resulting in additional revenue. How-
ever, the revenue starts to drop at the average usage of
2 MB, since large amount of users would migrate to
inexpensive Wi-Fi hotspots causing reduction in rev-
enue.
1 1.5 2 2.5 3 3.5 4 4.5 5
0
2
4
6
8
10
12
Average Revenue per connection (R)
Session Volume in MB/connection (v)
GPRS with Wi−Fi Integration
GPRS without Wi−Fi Integration
r
w
= $7 per connection
Figure 5: Revenue from GPRS networks with Wi-Fi inte-
gration with respect to average session volume.
1 2 3 4 5 6 7 8 9 10
0
2
4
6
8
10
12
Average Revenue per Connection (R)
Wi−Fi charging rate(r
w
)
GPRS with Wi−Fi Integration
GPRS without Wi−Fi Integration
Average session volume is 2
MB
Figure 6: Revenue gained from GPRS and Wi-Fi integration
with respect to the Wi-Fi connection fee.
Fig. 6 shows the average revenue gained from
GPRS integrated with and without Wi-Fi versus r
w
.
We assume that each user transmits an average of
1 MB per connection. The result shows that when
r
w
increases, the revenue for GPRS with integra-
tion is no longer higher than non-integrated GPRS;
users would continue using the GPRS network due
to high r
w
; there is no significant price incentive for
them to switch to Wi-Fi. We could think of r
w
that
yields the largest difference between those two rev-
enue curves, which represents the best tradeoff be-
tween revenue and traffic migration. Fig. 7 illus-
trates the revenue difference between equation (3) and
(5) (R
int
R
w.o.int
) versus r
w
and v in a three-
dimensional plane. The contour of the plane illus-
trates the line (dash line), where every point on that
line yields the largest difference in revenue and their
corresponding r
w
and v. For example, at v equals to
2.2 MB, r
w
equals to 5 dollars representing the largest
difference in the revenue curve.
Figure 7: Difference in Revenue between GPRS integrated
with Wi-Fi and non-integrated GPRS networks.
To offload the traffic from GPRS networks to Wi-
Fi, r
g
and r
w
must be set appropriately so that the
system yields maximum revenue and attracts GPRS
users to migrate to Wi-Fi networks. Based on our as-
sumption of the demand function and the proposed
optimization model, Fig.8 illustrates charging rate of
GPRS and Wi-Fi networks as well as the revenue gen-
erated from those charges. r
g
and r
w
are subject to
constraints [1,4] and [3,10] according to the pricing
information from commercial GPRS operators and
Wi-Fi aggregators. We can see that, when average
session volume equals 2 MB, the optimal r
g
is at 4
dollars per MB for any target user demand D. The
maximum revenue and user demand of the integrated
network are, however, driven by r
w
as they increase
along with r
w
. For the larger session volume,i.e.,
5 MB, at D equals 0.5, r
w
would reach the maxi-
mum market price (10 dollars per connection). The
optimization model suggests that the GPRS operator
should reduce the GPRS charge r
g
in order to meet
certain user demand and maximum revenue. Hence,
based on our assumption and the optimization model,
A PRICING MODEL OF GPRS NETWORKS WITH WI-FI INTEGRATION FOR “HEAVY” DATA USERS
83
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
User Demand (D)
Price and Revenue ($)
GPRS charging rate (r
g
)
Wi−fi Connection fee (r
w
)
Revenue (R
int
)
Session Volume = 2MB
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
2
4
6
8
10
12
14
16
User Demand (D)
Price and Revenue ($)
GPRS charging rate (r
g
)
Wi−Fi Connection fee (r
w
)
Revenue (R
int
)
Session Volume=5MB
Figure 8: Price sets generated from optimization model and
their corresponding revenue.
we can create price sets for both GPRS and Wi-Fi
networks which allow us to migrate traffic demand
between these two networks and yield maximum rev-
enue.
5 CONCLUSION
In this paper we propose a simple but effective pricing
model of GPRS networks integrated with Wi-Fi. We
propose the use of demand functions to describe the
response of users based on the prices charged in each
networks. By integrating two technologies together,
operators can attract new customers with value added
services provided by Wi-Fi networks, thereby, reduc-
ing the churn. Furthermore, the GSM/GPRS cellular
operators can delay their 3G deployments as the inte-
gration could offer 3G-like services. The integration
is not only beneficial to the cellular operator but also
to third party hotspots, because it increases revenue
by increasing traffic load at their hotspot networks.
Users who are not willing to pay high GPRS prices,
will eventually start utilizing the Wi-Fi network, tak-
ing advantage of the price difference. Thus, integra-
tion provides profitable business strategy for both the
cellular operators and the new Wi-Fi startup compa-
nies.
To extend our study, we are investigating the distri-
bution of GPRS session volume and the estimation of
traffic load migrated from GPRS to Wi-Fi.
REFERENCES
A. K. Salkintzis, C. Fors, and R. Pazhyannur (2002).
WLAN-GPRS integration for next-generation mobile
data networks. In IEEE Wireless Communications.
vol. 9, Issue. 5, October 2002, pp.112-124.
K. Ahmavaara, H. Haverinen, and R. Pichna (2003). Inter-
working architecture between 3GPP and WLAN sys-
tems. In IEEE Communications Magazine. vol.41, Is-
sue.11, November 2003, pp.74-81.
L. Anania and R. J. Solomon (1997). Flat - the mininalist
price. In L.W. McKnight and J.P. Bailey, editors, In-
ternet Economics. Cambridge, Massachusettes, 1997,
MIT Press.,pp. 91-118
J. K. MacKie-Mason and H.R. Varian (1995). Congestible
Network Resources. In IEEE Journal on Selected Ar-
eas in Communications. vol.13, issue. 7, Sep 1995,
pp.1141-1149.
M. Falkner (2000). A user’s perspective on Connection Ad-
mission Control: Integrating Traffic Shaping, Effec-
tive Bandwidths and Pricing. Doctoral thesis at Car-
leton University, Ottawa, Ontario, May 12,2000.
A.M. Odlyzko (1999). Paris Metro Pricing: The minimalist
differentiatedservices solution. In Proc. Seventh IEEE
International Workshop on Quality of Service. 1999,
pp.159-161.
C. Courcoubetis, F. P. Kelly, V. A. Siris and R. Weber
(2000). A study of simple usage-based charging
schemes for broadband networks. In Telecommuni-
cations Systems. 2000, pp.323-343.
A. Doufexi, E. Tameh, A. Nix, S. Armour, A. Molina
(2003). Hotspot wireless LANs to enhance the per-
formance of 3G and beyond cellular networks. In
IEEE Communications Magazine. vol.41, Issue 7,
July 2003, pp. 58-65.
S. Oliver, and P. Poiraud (2002). Public WLAN for mobile
operators. White paper, Atcatel, 2002.
J. Hou, J. Yang, and S. Papavassiliou (2001). Integration
of Pricing with Call Admission Control for Wireless
Networks. In Proc. Vehicular Technology Conference.
vol. 3, 2001, pp.1344 -1348.
P. C. Fishburn and A. M. Oldyzko (2000). Dynamic behav-
ior of differential pricing and quality of service op-
tions for the internet. In Decision Support Systems. 28
(2000), pp. 123-136.
J. Kilpi (2003). A portrait of a GPRS/GSM session. In 18th
International Teletraffic Congress. Germany, Septem-
ber 2003.
Boingo, http://www.boingo.com
ICETE 2005 - WIRELESS COMMUNICATION SYSTEMS AND NETWORKS
84