Multi-period design of survivable wireless access networks under capacity constraints

www.elsevier.com/locate/dsw

Decision Support Systems 38 (2005) 529–538

Multi-period design of survivable wireless access networks

under capacity constraints

Indranil Bosea,*, Enes Eryarsoyb, Ling Heb

aDepartment of Information Systems, School of Business, University of Hong Kong, Room 730, Meng Wah Complex,

Pokfulam Road, Hong Kong, ChinabDepartment of Decision and Information Sciences, Warrington College of Business Administration, University of Florida,

Gainesville, FL 32608, USA

Received 21 April 2003; received in revised form 26 September 2003; accepted 27 September 2003

Available online 19 November 2003

Abstract

Design of survivable wireless access networks plays a key role in the overall design of a wireless network. In this research,

the multi-period design of a wireless access network under capacity and survivability constraints is considered. Given the

location of the cells and hubs, the cost of interconnection, and the demands generated by the cells, the goal of the designer is to

find the best interconnection between cells and hubs so that the overall connection cost is minimized and the capacity and the

survivability constraints are met. Integer programming formulations for this problem are proposed and the problems are solved

using heuristic methods. Using different combination of network sizes, demand patterns and various time periods, a number of

numerical experiments are conducted and all of them are found to yield high quality solutions.

D 2003 Elsevier B.V. All rights reserved.

Keywords: Access networks; Integer programming; Network design; Survivability; Wireless networks

1. Introduction Association estimates that U.S wireless will penetrate

Recent developments in the area of wireless tele-

communications have resulted in an explosive growth

in its demand and a rapid reduction in the price of

wireless services. According to recent statistics

obtained from the U.S. Department of Commerce,

the U.S. cellular subscription has increased from less

than 2 million in 1988 to more than 60 million in 2000

[1]. The Cellular Telecommunication and Internet

0167-9236/$ - see front matter D 2003 Elsevier B.V. All rights reserved.

doi:10.1016/j.dss.2003.09.004

* Corresponding author. Tel.: +1-852-2241-5845; fax: +1-852-

2858-5614.

E-mail addresses: [email protected] (I. Bose),

[email protected] (E. Eryarsoy), [email protected] (L. He).

39% of the U.S population. On the other hand, the

Global wireless subscription has reached over 1027

million subscribers in 2002 (Fig. 1). There has been a

tremendous increase in the revenue earned from the

wireless telecommunication services. The local serv-

ices revenue is predicted to increase at the rate of 6%

per year. However, it is believed that the highly

competitive wireless network provider market may

soon approach saturation, and hence, only companies

that can provide high-quality wireless services will

survive in the long run. The service provider will have

to meet customers’ demand, develop advanced tech-

nologies, and provide survivability of the network in

the case of network outages so that networks are able

http://www.gsmworld.com/news/statistics/index.shtml

Fig. 1. Growth in global wireless subscription from 1992 to 2002 (Source: http://www.gsmworld.com/news/statistics/index.shtml).

Fig. 2. The partial survivable wireless network.

I. Bose et al. / Decision Support Systems 38 (2005) 529–538530

to withstand and recover from failures. The issue of

partial survivability of wireless networks is addressed

in this paper.

In the topology of a wireless network, the network,

which connects the wired public switched telephone

network (PSTN) with the wireless system, is called

the access network. The efficiency of the integration

of these two separated systems plays a critical role for

the success of the entire wireless service. Network

designers are often faced with the problem of how to

construct an access network at the least cost that

satisfies customers’ demands as well as provides a

level of survivability for the networks in the case of

network outages. Survivability in wireless networks is

different from that of terrestrial networks because

mobile users continuously enter and leave the system

and this resulting mobility often affects the reliability

of the network. At the same time, the broadcast nature

of the wireless networks make them more susceptible

to hacker attacks. In order to safeguard the network, if

the designers are unable to provide full survivability

for the network, they attempt to provide at least partial

survivability for the network. In order to understand

this design goal, we have to understand the basic

topological structure of the wireless interconnection

system.

Essentially, a wireless interconnection–access sys-

tem consists of three basic components: mobile units,

cell sites and a mobile switching center (MSC), which

switches the phones between PSTN and wireless

networks, and coordinates the traffic on the wireless

networks. Each cell of the network is connected to

MSC through hubs, or directly to MSC. Often the

underlying logical connection in such a situation is a

star topology (Fig. 2). The type of connection depends

on several factors such as homing cost, capacity of the

hubs and demand at the cells. Another important

consideration is the physical diversity of the paths.

To prevent loss of calls due to outages in the network,

the designer usually allows the cell to distribute the

traffic over several, alternate paths that are connected

to different hubs. This is done so that if one of the

http://www.gsmworld.com/news/statistics/index.shtml

I. Bose et al. / Decision Support Systems 38 (2005) 529–538 531

links connecting the cell to a hub goes down, only a

fraction of traffic from the cell to the hub is lost

instead of all the traffic originating from the cell. This

provides for better reliability of service. Though an

efficient design of the access network is a key part in

the overall design of a wireless network, not much

attention has been devoted to the design of the

wireless access networks. In the following section,

we discuss some recent efforts in this direction.

2. Literature review

Though there is a significant amount of literature

addressing the design and survivability of network

problems, to the best of our knowledge, not many

papers have been published that address the question

of survivability for the design of wireless access

networks. Refs. [7 and 14] give an overview of

techniques used for providing survivability of net-

works. The issue of survivability in case of wireless

backhaul networks has been addressed in [2]. Using a

tabu search meta-heuristic, the authors developed an

algorithm for designing least-cost wireless networks

that satisfied survivability, capacity and technological

constraints by appropriately choosing the location of

hubs, assigning traffic between nodes and hubs and

choosing types of links for interconnection of nodes

and hubs. In Ref. [8], the authors described two types

of heuristic algorithms for improving the reliability of

a wireless local access network, with a tree topology.

The goal of that research was to develop a scheme

such that the traffic loss in case of network failures

was minimized. A simulation-based approach was

used in Refs. [9] and [10] to show that the wireless

access network performance significantly worsened

when mobile users moved between cells after failures

had taken place. To address this problem, the authors

took into consideration the spatial and temporal

nature of the problem and suggested a multilayer

survivability strategy and restoration techniques.

Neural networks were used in Ref. [6] for designing

the wireless access network under quality of service

constraints. The problem addressed assumed a given

network topology and traffic load conditions and

obtained an optimal allocation of base transceiver

stations to cell site switches at minimum cost. Neural

networks proved to be a useful tool for solving this

constrained optimization problem and, when com-

pared to genetic algorithms and simulated annealing

for solving the same problem, was found to yield

solutions in a shorter period of time. A different

approach was adopted in Ref. [11] to address the

problem of efficient allocation of the radio spectrum

in the access network segment used for interconnec-

tion of the fixed network with the mobile unit. The

issues related to provision of end-to-end survivability

in wireless networks was discussed in Ref. [12] and

it was stated that the reliability of certain components

(e.g., access links) has to be improved in order to

provide better end-to-end survivability. On a similar

vein, simulation experiments were used in Ref. [13]

to show that failure frequencies of certain compo-

nents in the wireless system affected the survivability

of the network more than others. The problem of

survivable wireless access network design under

different operating conditions and constraints has

been studied in a series of papers by Kubat et al.

Dutta and Kubat [3] described how SONET ring

topology could be used to design survivable wireless

networks under capacity and diversity constraints.

Kubat and MacGregor Smith [4] considered the

design of a wireless access network under capacity

constraints over a multiple time period. Kubat et al.

[5] also focused on the design of a partially surviv-

able wireless access network. The goal of that

research was to find the optimal least cost intercon-

nection between demand generating cells and hubs or

MSCs when the underlying network topology was a

star connection. Three different models were pro-

posed in this paper and were solved using heuristic

techniques. In the first model, the capacity of the

interconnecting links was fixed and the assignment

was obtained for a single time period. In model 2, the

links were assumed to have variable capacity and in

model 3, the links were of variable capacity and the

solution was to be obtained over multiple time

periods. The paper detailed heuristic solutions for

the first two models and provided the integer

programming formulation for the third model but

did not solve the problem. In the next section, we

introduce a modified formulation of the same multi-

period problem studied in Ref. [5]. Numerical experi-

ments with this model are reported in Section 4. The

concluding remarks and directions for future research

appear in Section 5.


3. Problem formulation

In a typical wireless local access network, the

demand generating cells are usually connected to the

root node or MSC in a star topology. However, if all

the cells are connected to the MSC, then this topology

has the potential of resulting in large loss of traffic in

case of link failures. Hence, cell-hub architecture is

more commonly used in case of wireless local access

networks. In this architecture, the demand generating

cells are connected to hubs and/or to the MSC in a star

type connection. This has the advantage of providing

higher survivability of the network. For example, if a

cell is connected to a hub and to the MSC, that means

the diversity of the connection is 2 and only 50% of

the traffic generated by the cell will be carried on each

of the links. Hence, if any of the links fail, only 50%

of the traffic will be lost. However, it is to be noted

that by allowing a physical diversity of paths, we are

not able to provide full survivability but only partial

survivability of service in case of link outages. The

main goal of our research problem is to find out the

optimal interconnection between cells, hubs and MSC

such that the cost of connection is minimized over

multiple time periods. The demand generated by the

cell, the diversity requirement and the cost of inter-

connection vary over the multiple time periods. The

homing arrangement is such that, for cells with

diversity more than one, the cells must home to two

distinct nodes on two distinct trees. We propose two

different models in this section. In model 1, the

optimization is conducted over multiple time periods

using fixed capacity of the interconnecting links. In

model 2, the optimization is conducted over multiple

time periods using variable capacity for interconnec-

tion links. Special cases of the models 1 and 2 for a

single time period are presented and solved in Ref.

[5]. The following assumptions hold for our model.

Assumptions:

� The topology used is the tree topology, the tree root

is MSC, and the location of the cells and hubs are

known.� Cells are connected either to hubs or to MSC

directly.� To guarantee partial survivability, cells are allowed

to diversify their generated traffic over two or three

completely disjoint paths equally.

� Hubs only transmit the demand from cell to MSC

and do not generate demand.

Notations

V {v1, v2,. . .,vN}: cell nodes of cardinality N

H {h1, h2,. . .,hM}: hub nodes of cardinality M

(not including the root node)

N VvH

Q trees: {T1,T2,. . .,TQ}; for any two trees,

Ti\Tj = 0, trees are rooted at node #0 in

MSC

R H + 0; all hub nodes plus the root node

L set of all links used in the interconnection

network

Z annual cost of interconnect network ($)

t index for time period; t= 1, 2, 3. . .ci,j,t cost of connecting cell i to hub j in time

period t ($/year)

Bl,t cost of interconnection link in time period

t ($/year)

Di,t demand in DS0 circuits for each cell i to

be delivered to root node #0 in time period

t

si,t diversity requirement for cell i in time period

t; si,t = 1, 2, 3

Kl capacity (in DS0 circuits) for link l

yl,t the number of DS0 units to be leased for link

l in time period t

ul,t dummy variable used to replace yl,taj,l,t predefined data coefficients; aj,l,t = 1 if link l

is on the path from the root to hub j in time

period t, aj,l,t = 0 otherwise

Decision variables

xi,j,t xi,j,t = 1 if there exists a connection between

cell i and hub j in time period t, xi,j,t = 0

otherwise

3.1. Model 1: multi-period demand, fixed link

capacity

In this model, the capacity of each link from hub to

MSC is fixed and is denoted by Kl. The objective

function minimizes the total cost of interconnection.

The formulation is stated below.

Minimize Z1 ¼X

iaV

X

jaR

X

t

xi;j;tci;j;t ð1Þ


Subject to:

X

jaR

xi;j;t ¼ si;t for all iaV ; t ð2Þ

X

iaV

X

jaR

ðDi;t=si;tÞaj;l;txi;j;tKl for all laH ; t ð3Þ

X

jaTq

xi;j;tV1 for all iaV ; qaQ and t ð4Þ

xi;j;taf0; 1g for all iaV ; jaR and t ð5Þ

Constraint (2) guarantees the diversity requirement of

each cell in every time period, constraint (3) ensures

that link capacity is always greater than or equal to the

assigned demand, constraint (4) ensures that the tree

diversity constraints hold (i.e., only one branch in one

tree is homed, in case the link of the tree to the MSC

failed), constraint (5) is the binary integer constraint.

3.2. Model 2: multi-period demand, variable link

capacity

The difference between model 1 and model 2 is

that in model 2, the capacity of the link is allowed to

vary. Hence, while in constraint (3) in model 1, the

LHS is Kl, in constraint (8) in model 2, the LHS is

Kyl,t, where K is a constant and can take any nonneg-

ative value. The other notable difference is in the

objective function which includes an additional term

representing the cost of the interconnecting link. The

ceiling function of yl,t is considered since the DS0

units can be procured only in integral quantities. It is

to be noted that in our formulation, we allow yl,t to

take any non-negative real value. The objective func-

tion for this model is given below:

Minimize Z2 ¼X

iaV

X

jaR

X

t

xi;j;tci;j;t þX

lah

X

tap

Bl;t qyl;t a

ð6ÞSubject to:

X

jaR


X

iaV

X

jaR

ðDi;t=si;tÞaj;l;txi;j;tKyl;t for all laH ; t ð8Þ

X

jaTq



yl;tz0 for all laH ; t ð11Þ

In model 2, note that yl,t denotes the actual capacity

used in the network and the ceiling function of yl,tdenotes the actual capacity that has to be procured for

the network, though it may not be used in its entirety.

However, the presence of the ceiling function in the

objective function makes the objective function for

model 2 nonlinear and hence difficult to solve. In order

to make model 2 more easily solvable, we propose the

following modified formulation for model 2 and call it

model 2A. This involves introduction of a new variable

ul,t in the modified formulation. It is to be noted that to

obtain the optimal design, we want yl,t values to be

close to an integer value or 0. However, in order to save

in procurement cost, we would like yl,t values to

approach integer borders from below. The dummy

variables ul,t represent these integer borders. Accord-

ing to the formulation of model 2A, the objective

function will try to push down ul,t in order to minimize

cost but at the same time constraint (15) will try to push

yl,t up in order to satisfy the demand. So in this way, the

dummy variable ul,t that takes on integer values will

serve the same purpose as the ceiling function.

Model 2A:

Minimise Z2A¼X

iaV

X

jaR

X

tap

xi;j;tci;j;tþX

lah

X

tap

Bl;tul;t

ð12ÞSubject to:

yl;tzul;t for all laH ; t ð13Þ

X

jaR


X

iaV

X

jaR

ðDi;t=si;tÞaj;l;txi;j;tVKyl;t for all laH ; t

ð15ÞX

jaTq




yl;tz0 for all laH ; t ð18Þ

ul;taf0; 1; 2 . . . ng for all laH ; t ð19Þ

Using a dummy variable ul,t, solutions to model

2A can be obtained easily since it transforms the

nonlinear objective function (Eq. (6)) to a linear

objective function (Eq. (12)).

4. Numerical results

In order to numerically experiment with the pro-

posed models, we randomly created three categories

of datasets: small, medium and large (Tables 1 and 2),

based on the number of hubs and cells. For small

dataset, the number of cells varies from 5 to 14 and

the number of hubs varies from 2 to 4. For medium

dataset, the number of cells varies from 15 to 25 and

the number of hubs from 5 to 7. For large dataset, the

number of cells varies from 26 to 32 and the number

of hubs varies from 6 to 8. We use similar problem

parameters as used in Ref. [5]. The cost of intercon-

nection is assumed to follow a uniform distribution

with the cost of connection to the MSC being modeled

by U(1800,3200) $/link/year and the cost of connec-

Table 1

Solutions obtained using LP relaxation and the heuristic for model 1

Size Cases Cells Hubs periods Demand

Small size 1 5 2 3 INC and D

2 8 3 2 INCR

3 12 4 3 DECR

4 14 4 2 DECR

5 14 4 2 INCR

Medium size 1 15 5 3 INC and D

2 20 5 2 INCR

3 20 7 2 DECR

4 22 7 2 INCR

5 25 7 2 DECR

Large size 1 27 8 2 INCR

2 30 6 2 DECR

3 32 6 2 INCR

4 32 6 2 DECR

5 32 7 2 DECR

tion to the other hubs being modeled by U(1800,2500)

$/link/year. The base line demand generated by each

cell is assumed to be U(300,700) DS0 circuits/unit

time. In the multi-period case, we assumed that the

demand can undergo three changes—increase, de-

crease or increase-and-decrease. If the demand is in

the ‘increase’ phase, then the rate of increase follows

U(0,1). If it is in the ‘decrease’ phase, then the rate of

decrease follows U(0,0.5). If it is in the ‘increase-and-

decrease’ phase, then increase and decrease cases are

combined, i.e., a 0–100% increase in demand is

followed by a 0–50% decrease in demand. The

number of time periods is either 2 or 3. The diversity

of each cell takes a value 1, 2, or 3. For each of the

models 1 and 2A, 15 different datasets were run for

different network sizes. The solution is obtained by

LP-relaxation and subsequent application of a heuris-

tic procedure. The main purpose of the heuristic is to

rearrange the solution obtained from the LP-relaxation

of the problem with minimum change in the total

interconnection cost, such that no fractional xi,j,tvalues remain in the solution. The algorithmic steps

of the heuristic are shown in Fig. 3. In Fig. 3, a direct

link represents a connection between the cell and the

MSC and an indirect link stands for a connection

between the cell and a hub. The heuristic used for

solving this problem is similar to that used in Kubat et

al. [5]. There are two main differences—our heuristic

is able to solve the problem over multiple time

periods. Secondly, unlike [5], if necessary, we allow

Trees LP_OPT ($) HEUR ($) % Diff. HEUR

vs. LP_OPT

EC 1 37840.27 38590 0.02

1 52300.6 54247 0.04

2 103022.1 104111 0.01

1 86220 89354 0.04

2 67646.1 69016 0.02

EC 1 113261 115406 0.02

1 111229 114301 0.03

2 111615 116590 0.04

1 126540 130201 0.03

2 126737 130109 0.03

2 148310 155411 0.05

2 162959.9 168977 0.04

1 187174.9 191815 0.02

2 179706.4 183523 0.02

2 182722.3 185928 0.02

Fig. 3. Flowchart showing the algorithmic steps of the heuristic.



the capacity of the hub with minimum capacity cost to

be increased by 1 unit to meet demand. The total cost

of interconnection is increased by an amount equal to

the capacity cost of one additional hub unit as a result

of this process. By doing this, we allow more con-

nections from any cell to the hub with the lowest

capacity cost. The heuristic in Ref. [5] does not

provide this flexibility and is forced to make a

connection from a cell to a more ‘costly’ hub. The

overall effect of increasing the capacity of the hub in

our heuristic is that it results in a lower total inter-

connection cost.

The solution to model 1 appears in Table 1. The

column ‘LP_OPT’ indicates the optimal value

obtained using LINGO, by relaxing the integrality

constraints of model 1. The column ‘HEUR’ denotes

the results obtained using our heuristic. Since the

percentage difference listed is quite low for all of

the test cases we can say that our heuristic solution for

model 1 is very close to the optimum.

In Table 2, we list the solutions obtained for model

2A for different network sizes and demand scenarios

using the heuristic method. We compare the solutions

with that obtained using LP-relaxation with LINGO

(i.e., LP_OPT) and with the solution obtained using

the heuristic developed by Kubat et al. [5] (i.e.,

K_OPT). We observe that as in Table 1, our solution

is very close to the solution obtained using LINGO

with LP-relaxation. Additionally, we observe that we

are able to obtain significant improvement in the

Table 2

Solutions obtained using LP relaxation and the heuristic for model 2A

Size Cases Cells Hubs Periods Demand Trees LP

Small size 1 5 2 3 INC and DEC 1 5

2 8 3 2 INCR 1 6

3 12 4 3 DECR 2 11

4 14 4 2 DECR 1 10

5 14 4 2 INCR 2 8

Medium size 1 15 5 3 INC and DEC 1 14

2 20 5 2 INCR 1 13

3 20 7 2 DECR 2 13

4 22 7 2 INCR 1 13

5 25 7 2 DECR 2 17

Large size 1 27 8 2 INCR 2 17

2 30 6 2 DECR 2 21

3 32 6 2 INCR 1 21

4 32 6 2 DECR 2 22

5 32 7 2 DECR 2 23

quality of the solution than that obtained by Kubat

et al. [5]. The improvement comes from the fact that

we consider qyl,ta instead of yl,t in the objective functionand we also consider the possibility of increasing the

capacity of the hub if needed. This leads to significant

cost savings in the overall optimization problem. We

can conclude from this table that no matter what the

network size, number of time period or the nature of

demand, with the help of our modified formulation

and our modified heuristic, we are able to obtain

better quality solutions than Kubat et al. [5] in a

reasonable amount of time.

5. Conclusion and future work

In this paper, we formulate the problem of design

of wireless access network under capacity and surviv-

ability constraints over multiple time-periods. We

solve two varieties of this problem, namely, the fixed

link capacity and the variable link capacity. The

problem is solved using heuristic techniques. Through

numerical experiments conducted using different

combinations of network sizes, nature of demand

and variable time periods, we are able to establish

that our solution process is able to solve the multi-

period network design problem and yields solutions

that are very close to the optimal solution for both the

fixed and the variable capacity cases. We are also able

to establish that our modified formulation yields better

_OPT HEUR % Diff. HEUR

vs. LP_OPT

K_OPT % Diff. K_OPT

vs. HEUR

5127.49 56534 0.03 58965 0.04

8883 70177 0.02 73664.35 0.05

8456.8 119599 0.01 126153.2 0.05

6217.4 107300 0.01 114552.1 0.06

9608.98 90618 0.01 96242.99 0.06

4570.5 147338 0.02 163351.41 0.10

3905.6 141575 0.06 143733.65 0.02

3438.3 136007 0.02 150259.39 0.09

7613.1 145786 0.06 156558.24 0.07

1619.6 175320 0.02 177710.00 0.01

1619.6 175320 0.02 179209.38 0.02

2505.1 223774 0.05 228152.26 0.02

2117.8 219636 0.04 235981.81 0.07

0789.8 227010 0.03 235211.82 0.03

7279.8 241248 0.02 253839.39 0.05


solutions than that presented in Kubat et al. [5] for the

variable link capacity case.

In the future, extensions to this research can include

wireless access network design for ring networks.

Synchronous Optical Network (SONET) is a popular

choice for ring networks. These rings are often called

self-healing rings since they can provide immediate

restoration of services in case of a link outage. In case

of ring networks, the hubs are all connected in a ring

topology and the MSC also belongs to the ring. Hence,

the design for survivability is somewhat different from

our study due to this difference in topology. Another

area of extension can be to address the issue of wireless

network design where the requirements of the wireless

as well as the wired networks are considered in unison.

A third area of extension will be to work on capacity

expansion problems for wireless access networks over

multiple time periods with varying demand. This could

involve decisions about locations of hubs, intercon-

nection of links as well as routing decisions for the

wireless network. In this research, the calls are as-

sumed to have a uniform quality of service. However,

in reality, the delay requirements for different types of

traffic may be different. An important extension of this

research in future will be to include quality of service

constraints in the model to account for the delay

requirements for the different types of traffic to be

routed over the wireless network.

Acknowledgements

The authors would like to thank the two anony-

mous reviewers for their many excellent comments

which have improved the quality and the readability

of the paper.

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ity and survivability of infrastructure-oriented wireless net-

works, Proceedings of the 26th Annual IEEE Conference on

Local Computer Networks, 2000, pp. 611–618.

[14] D. Zhou, S. Subramaniam, Survivability in optical networks,

IEEE Network (2000) 16–23.

Indranil Bose is an Assistant Professor of

Information Systems at the School of Busi-

ness, University of Hong Kong. His degrees

include B. Tech. (Electrical Engineering)

from Indian Institute of Technology, M.S.

(Electrical and Computer Engineering) from

University of Iowa, M.S. (Industrial Engi-

neering) and Ph.D. (Management Informa-

tion Systems) from Purdue University. He

has research interests in telecommunica-

tions—design and policy issues, data mining

and artificial intelligence, electronic commerce, applied operations

research and supply chain management. His teaching interests are in

telecommunications, database management, systems analysis and

design, and data mining. His publications have appeared in Com-

puters and Operations Research, Decision Support Systems and

Electronic Commerce, Ergonomics, European Journal of Operational

Research, Information and Management and in the proceedings of

numerous international and national conferences.


Enes Eryarsoy is a PhD student at the Department of Decision and

Information Sciences at the University of Florida.

Ling He is a PhD student at the Department

of Decision and Information Sciences at the

University of Florida. She graduated from

the University of International Business and

Economics in Beijing, China with a BA

degree in Economics, and received her

MS in DIS at the University of Florida.

Her research interests include machine

learning theory and applications, statistical

learning theory, data mining, database, ge-

netic algorithm and e-commerce.

Documents

Multi-period design of survivable wireless access networks under capacity constraints