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A mathematical optimization approach for cellular radio networkplanning with co-siting

Lina Al-Kanj • Zaher Dawy • George Turkiyyah

Published online: 10 February 2012

� Springer Science+Business Media, LLC 2012

Abstract Wireless network operators are continuously

enhancing their networks by deploying newly developed

wireless technologies. In order to reduce the deployment

costs, the operators try to reuse as many components of the

existing networks as possible. This includes the possibility

of reusing base station sites in order to reduce costs such as

site rental, site acquisition, and backhaul connectivity. In

this paper, we model the problem of base station co-siting

as a nested mixed integer optimization problem in order to

optimize target objectives that are a function of perfor-

mance and cost. The formulated problem takes as input an

area of interest with existing fixed sites and obtains as

output the optimal number and locations of required sites

including newly deployed and co-sited with the fixed sites.

The goal is to minimize the deployment cost of the new

network by reusing as many existing sites of the existing

network as possible while guaranteeing that the outage

probability is below a target threshold. We propose and

implement an algorithm to solve the formulated optimi-

zation problem as a function of the mobile station distri-

bution and the existing fixed site locations. A UMTS/GSM

co-siting scenario is used as a case study in order to

evaluate the performance of the proposed algorithm.

Results show that the optimal solution depends on the

mobile station distribution and the existing sites in addition

to a threshold parameter that provides a tradeoff between

the deployment cost and the outage probability.

Keywords Base station co-siting �Network dimensioning � Network optimization �UMTS/GSM co-siting � Wireless network deployment

1 Introduction

Existing wireless technologies are being enhanced and new

wireless technologies are being developed in order to cope

with the steadily increasing demands of end users in terms

of high bit rate multi-service capabilities. Therefore,

wireless operators are continuously upgrading their net-

works to be inline with the technology advances. Due to

high network deployment costs, wireless operators nor-

mally try to reuse as many components as possible from the

already existing networks. This can include sharing core

network elements, base station sites, antenna and RF

modules, backhaul connectivity, etc. This also reduces the

operational expenditure on transmission, power, site rental,

and operation and maintenance.

For example, due to the wide global existence of GSM/

GPRS networks and due to coordinated 3GPP standardi-

zation between GSM/GPRS and UMTS-WCDMA, it is

possible for a UMTS network and a GSM network to share

various components including base station sites. A com-

prehensive study of interference, coverage, and capacity

issues while reusing GSM900/1800 sites for UMTS900/

1800 is done in [1]. It has been shown in [2] that UMTS900

can be co-sited with GSM900 but with more limited cov-

erage. The cell coverage area becomes even smaller with

UMTS2100 due to signal propagation losses at higher

L. Al-Kanj (&) � Z. Dawy

Department of Electrical and Computer Engineering,

American University of Beirut, Beirut, Lebanon

e-mail: [email protected]

Z. Dawy


G. Turkiyyah

Department of Computer Science,

American University of Beirut, Beirut, Lebanon


123

Wireless Netw (2012) 18:507–521

DOI 10.1007/s11276-012-0415-6

frequencies. Therefore, simply reusing part or all of the

existing GSM sites would not be satisfactory in terms of

UMTS coverage and capacity needs and, thus, the

deployment of additional new UMTS sites would be a

necessity, for example, see [3].

Base station co-siting saves the operator major costs

such as site acquisition, establishment, rental, and main-

tenance costs. If the existing BS is enabled to support the

new cellular technology being deployed, then software

configuration is normally performed to upgrade it. If not,

then there is a need to install major additional hardware

modules. In addition, the cost of reusing a site depends on

whether the operator wants to upgrade the existing antenna

system or deploy a separate antenna system [4]. In both

cases, isolation techniques are required to avoid interfer-

ence between the two systems. In the case of separate

antenna systems, the UMTS antenna should be spaced

appropriately from the existing GSM antenna with the

requirement of more expensive feeder cables. An alterna-

tive would be to replace or upgrade the existing antennas to

multi-band antennas where the isolation is provided by the

diplexers used to de-multiplex the signals to and from the

GSM and UMTS BSs. This reduces the number of separate

physical antennas and the used space. Reusing an existing

site can be also done by several operators to decrease the

rental and operational cost provided that each one of them

has its own antenna system that are spaced appropriately

for isolation requirements. For example, to co-locate sep-

arate antenna systems for GSM and UMTS a horizontal

separation of 0.9–1 m or a vertical separation of 1.8–2.0 m

is recommended [4].

In practice, a network operator normally tries to reuse as

many sites as possible from the existing GSM networks;

these sites can in principle belong to its own network or to

another operator’s network, even though it is more com-

mon to reuse own sites. Then, they perform capacity and

coverage analysis for the resulting UMTS network, identify

weaknesses/deficiencies in their network plan, and then

deploy additional new UMTS sites to fill the gaps. This

approach is heuristic and not based on a pre-planned

optimized procedure.

There is no previous work that studies base station

(BS) co-siting for wireless cellular networks in an opti-

mized framework that takes into account both deploy-

ment cost and performance metrics. In this paper, we are

presenting a new mathematical approach of BS co-siting

to minimize the deployment cost as a function of various

system and design parameters. The proposed approach is

independent of whether the existing sites belong to the

same operator or to another operator since what it

requires are the locations of the existing sites and the cost

of reusing a site. An algorithm that involves mathemati-

cal programming and heuristics is proposed and

implemented to solve the formulated problem. The

adopted radio network planning approach minimizes the

deployment cost while meeting a target outage probabil-

ity. To compute the target outage probability, we will

consider the signal-to-interference ratio (SIR) quality

constraints for both the uplink (UL) and downlink (DL)

directions. Moreover, we will consider power control

mechanisms to guarantee that the transmission powers are

adjusted to meet the target SIRs taking the actual inter-

cell and intracell interference into account. The perfor-

mance gains and characteristics of the proposed algorithm

are evaluated using a UMTS/GSM co-siting scenario.

Depending on the scenario, we demonstrate that it is not

always optimal to reuse all existing sites. Our algorithm

provides as output the set of sites that should be reused in

addition to the locations of the new sites that should be

deployed to minimize the overall cost while meeting the

quality of service constraints.

The paper is organized as follows. Section 2 reviews

related literature on radio network planning with emphasis

on UMTS networks since results are presented for a

UMTS/GSM co-siting case study. Section 3 presents the

mathematical formulation and the solution of the co-siting

optimization problem. Results are presented in Sect. 4 for a

UMTS/GSM case study as a function of different mobile

stations (MSs) distributions, existing site locations and

target outage probability. Finally, conclusions are drawn in

Sect. 5.

2 Related literature

Radio network planning and optimization (RNPO) is an

essential step for operators seeking to design and imple-

ment a wireless network regardless of the applied tech-

nology. The aim of RNPO is to provide a cost-effective

solution for the wireless network taking into account area

coverage, user capacity, and quality of service (QoS)

requirements in addition to the possibility of future net-

work growth. The initial phase of RNPO is network

dimensioning which is also called configuration planning.

Network dimensioning is a process that includes pre-

liminary coverage analysis and capacity evaluation in

addition to estimation of the number of BS sites, for

example, see [5, 6].

In UMTS, the amount of traffic that can be served by a

BS is limited by the interference level in the service area

unlike the case of TDMA-based systems where it is

limited by a fixed channel assignment [7]. In UMTS radio

network planning, the cell range is a function of the

number of active mobile stations that the BS can support

and, thus, there is an existing tradeoff between coverage

508 Wireless Netw (2012) 18:507–521

123

and capacity (cell breathing effect). In general, coverage

and capacity can be either UL or downlink DL limited

depending on the scenario under consideration. Several

mathematical and heuristic optimization models and

algorithms have been proposed in the literature, which

consider selected network planning aspects in addition to

system-level UMTS features such as power control and

soft handover. Optimization models for BS locations and

configurations considering quality constraints, such as the

service-dependent SIR target, for the UL direction are

presented in [8–10] where it is argued that the UL is more

limited than the DL from a capacity point of view for

voice calls. Optimization models for the DL direction are

presented in [11] which is considered to be more relevant

in the presence of asymmetrical traffic. Moreover, opti-

mization models for both UL and DL directions consid-

ering also SIR constraints are presented in [12–16]. Most

of the works assume the existence of a discrete set of

possible BS locations out of which a smaller set is chosen

that satisfies a given set of constraints where each BS is

allocated a certain cost [8–15, 17–19]. Only few works

consider continuous BS locations [16, 20, 21] where the

BS locations are allowed to take any location within a

given area. All these models consider the deployment of a

given wireless network without any BS co-siting. In [22],

we have presented a preliminary work on UMTS/GSM

co-siting where we consider that UMTS radio network

planning should meet a target load capacity per cell in the

DL direction only.

In this work, we address the problem of radio network

planning with BS co-siting where we assume the existence

of discrete locations for the existing sites and continuous

locations for the new sites to be deployed. This work is not

similar to the previous works that differentiate the BSs with

a cost vector only. It is different in the sense that the fixed

locations are kept fixed throughout the problem whereas

the newly added sites are allowed to take any location

within the area to be covered which gives the optimal

minimum cost. The proposed algorithm places the newly

added sites at optimized locations that satisfy a given

outage probability and minimize the deployment cost. The

problem is formulated as an optimization problem and

solved using mathematical programming and heuristic

techniques. In this work, we consider more aspects for

UMTS radio network planning where a target outage

probability should be met in both UL and DL directions

depending on SIR constraints that are calculated using

power control mechanisms taking intercell and intracell

interference into account. Network operators can use the

obtained results in order to decide which existing fixed BS

sites to reuse and in what areas to deploy new BS sites in

order to minimize the overall deployment cost subject to a

target outage probability.

3 Mathematical formulation and solution

of the problem

In this section, we formulate and solve the BS co-siting

problem. First, the network model is described. Second, the

problem is formulated as a nested mixed integer optimi-

zation problem which is NP-hard, consequently, a heuristic

solution is proposed to solve the optimization problem.

Finally, the convergence analysis for the proposed algo-

rithm is presented. For clarity, we present the parameters

and notations of the proposed system model in Table 1.

Table 1 Main system and design parameters

Parameter Description

K Number of active MSs

q(s) MS density distribution

e Outage probability threshold

c1 Cost of reusing an existing site

c2 Cost of deploying a new site

Nb Input number of BSs

nfixed Input number of fixed existing BS

narb Input number of arbitrary BS

zj = (xj, yj) Coordinates of the BSs

zj,fixed = (xj,fixed, yj,fixed) Coordinates of the fixed locations

of the BSs

C(n1, n2) Total deployment cost

n1 Output number of fixed reused sites

n2 Output number of newly deployed sites

No Output number of BSs (newly

deployed?co-sited)

Pmaxu Maximum MS transmit power

Pmaxd Maximum BS transmit power

SIRtargetu /SIRtarget

d Target SIRs for UL/DL

Kservedu /Kserved

d Number of MSs served in UL/DL

Kserved Number of MSs served in both UL and DL

Pout Outage Probability

Pdreceived;k

DL received power at MS k

Pureceived;k UL received power at BS from MS k

Iuin;k=Id

in;kIntracell interference at MS k for UL/DL

Iuout;k=Id

out;kIntercell interference at MS k for UL/DL

Pid Total transmit power of BS i

Pku Transmit power of MS k

Pi,kd Allocated power by BS i to MS k

gi,k Pathloss between MS k and BS i

b(k) BS serving MS k

Vi/Ci Voronoi region i or cell i

r2 Noise power

SF Spreading factor

ku/kd Orthogonality factor for UL/DL

keq Constant pathloss parameter

l Pathloss exponent

Wireless Netw (2012) 18:507–521 509

123

3.1 Network model

In this work, we will assume the input data to be the

following:

1. An MS density distribution q(s) where s = (x, y)

represents the coordinates of a given point within the

area. The total number of MSs is K. Given q(s), a

discrete snapshot for the MS distribution will be also

generated. A snapshot represents a set of MSs (or test

points) using the physical channel at a given instant of

time.

2. c1 and c2 which are the cost of reusing an already

existing site and of deploying a new one, respectively,

where (c1 \ c2).

3. A set of BSs whose cardinality is Nb that contains nfixed

existing fixed sites and narb new BS sites distributed

arbitrarily. The coordinates of the fixed sites are

defined by zj;fixed ¼ ðxj;fixed; yj;fixed) where j ¼1; . . .; nfixed: The BSs are assumed to be omnidirec-

tional and at the center of the cells.

4. A target outage probability e:

The output is the set of optimal locations zi; ði ¼1; . . .;NoÞ; of BSs that achieve the objectives of the plan-

ning. The number of output locations No is is less than or

equal to Nb and contains n1 out of the nfixedfixed locations

(co-sited BSs) and n2 out of the narb arbitrary locations

(newly added BSs). Given ziði ¼ 1; . . .;NoÞ BS sites or

generating points, a Voronoi Tessellation is a subdivision

of the space into No cells, one for each site zi, with the

property that every point in a given cell is closer to its site

than to any other [23]. A centroidal Voronoi tessellation is

a Voronoi tessellation whose generating points are the

centroids (centers of mass) of the corresponding Voronoi

regions. In this work, the generating points or sites are the

BS locations, and their corresponding cells are the cent-

roidal Voronoi regions Vi. We will use Lloyd algorithm

[23] which is a known technique from the literature to

generate the centroidal Voronoi regions. We chose this

algorithm due to its high convergence rate and its func-

tionality which minimizes the following cost function:

Fðzi;ViÞ ¼XNo

i¼1

Z

s2Vi

qðsÞjs� zij2ds ð1Þ

The optimal placement of the BSs is at the centroids of a

centroidal Voronoi tessellation of the area to be covered

[23], using the population density q(s) as a density func-

tion. According to (1), the MSs will use the BSs nearest to

them. It is obvious that this algorithm minimizes the utility

of the MSs in terms of their distances from the serving BS.

It does not account for intercell interference and intracell

interference. However, we will add more constraints to the

developed optimization problem to account for these two

important metrics (see Sect. 3.2).

The metric in (1) which is usually referred to as energy

[23] has the following properties:

– In the case of a 1D space and irrespective of the MS

distribution function when the number of generators

(i.e, BSs) gets large, then the energy is equally

partitioned among the regions. In the case of uniform

MS distribution, each Voronoi region will accommo-

date the same number of MSs.

– In the case of a 2D space and with uniform MS

distribution, the energy proved to vary from a centroi-

dal Voronoi tessellation to another with a factor that is

proportional to 1/n3 [24], where n is the number of

generators or BSs. Hence, as the number n increases,

this factor decreases. For a large n, this will result in the

same number of MSs in every region or cell.

This function minimizes the utility of the MSs in terms

of their distances from the serving BS. This translates to

minimizing the variance of the number of MSs among the

Voronoi regions or tessellations for a uniform MS distri-

bution function. For non-uniform MS distribution func-

tions, such as a Gaussian distribution, more regions or BSs

will be assigned in the hotspots.

3.2 Problem formulation

The objective of the optimization problem is to minimize

the deployment cost while maintaining a target outage

probability. This results in a multi-objective optimization

problem. Conversion of the multi-objective problem into a

single-objective one is usually done by either aggregating

all objectives in a weighted function or simply transform-

ing all but one of the objectives into constraints. Trans-

forming all objectives but one into constraints can be

formulated by using nested optimization. This paper pre-

sents a mixed integer nested formulation of BS co-siting in

wireless networks.

The BS co-siting optimization problem can be formu-

lated as follows:

Minimizes:t:

Cðn1; n2Þ ¼ c1n1 þ c2n2 ð2Þ

Minimize Fðzi;ViÞ ¼XNo

i¼1

Z

s2Vi

qðsÞjs� zij2ds ð3Þ

zj ¼ zj;fixed j ¼ 1; . . .; n1 ð4Þ

Pout� e ð5Þ

The objective in (2) minimizes the total cost of deployed

sites defined by C(n1, n2), (3) represents the constraint

that minimizes the MSs’ utility as explained earlier,

510 Wireless Netw (2012) 18:507–521

123

(4) represents the constraint to have fixed BS locations that

can be reused, and (5) represents the constraint that the

outage probability Pout is below a certain target threshold e:The mathematical formulation of the problem involves

both integer and continuous optimization variables. Thus, it

is formulated as a nested optimization problem where the

inner optimization is continuous and is formed of (3)

subject to (4). Solving the unconstrained equation (3) gives

the optimal locations of the BSs with a locally minimum

utility of the MSs. Solving (3) subject to (4) minimizes the

utility of the MSs given that n1 locations are fixed and n2

can move to take the optimized locations that minimize the

utility. The obtained utility in this case is larger or equal to

the utility of the unconstrained case. Since these n2 loca-

tions can take any position within the given area, this

represents a continuous optimization problem.

The outer objective is an integer optimization problem

that finds the number of reused sites n1 and the number of

new deployed sites n2 that minimize the cost of deployment.

The cost decreases whenever an existing site is reused since

c1 is smaller than c2. Only the fixed sites that do not violate

the outage probability constraints will be reused. The for-

mulated problem can be modified to take as input a traffic

distribution instead of an MS distribution. This might be, for

example, more applicable in network scenarios with MSs

belonging to different service classes.

3.2.1 Outage probability evaluation

For a given snapshot that represents the distribution of cur-

rently active MSs or active connections, we aim to find the

number of MSs that are being served. The outage probability

is the ratio of the number of MSs that are not served, i.e, that

have not met their target SIR to the total number of MSs in the

network K. Thus, it can be formulated as follows:

Pout ¼ 1� Kserved

Kð6Þ

where Kserved is the number of served MSs. The outage

probability can be adapted to any technology. In UMTS,

MSs rely on channelization and scrambling codes in

order to suppress multipath and multiuser interference.

Quality of service (QoS) constraints require the SIR to

exceed a minimum value which depends on the service

characteristics. We will calculate the number of served

MSs for both the UL (Kservedu ) and the DL (Kserved

d )

directions. The number of served MSs is the network is

Kserved B min(Kserved, Kd

servedu ) which represents the num-

ber of MSs that are served in both UL and DL directions

successfully.

The DL and UL SIR expressions for MS k can be

expressed as follows (e.g., [7, 25]):

SIRdk ¼ SF

Pdreceived;k

r2 þ kdIdin;k þ Id

out;k

ð7Þ

SIRuk ¼ SF

Pureceived;k

r2 þ kuIuin;k þ Iu

out;k

ð8Þ

where Preceived, kd is the DL received power at MS k,

Preceived, ku is the UL received power at the BS from MS k,

Iin, kd and Iout, k

d represent DL intracell and intercell

interference affecting MS k, respectively, Iin, ku and

Iout, ku represent the UL intracell and intercell interference,

respectively, affecting MS k, SF is the spreading factor, r2

is the thermal noise power, and k is the orthogonality factor

(0.4 B kd B 0.9 in the DL and ku = 1 in the uplink [25]).

Since we need to satisfy the SIR constraint for all MSs, we

express the received power and interference components in

(7) and (8) more explicitly for MS k as follows:

Pdreceived;k ¼ gbðkÞ;kPd

bðkÞ;k Pureceived;k ¼ gbðkÞ;kPu

k ð9Þ

Idin;k ¼ gbðkÞ;k Pd

bðkÞ � PdbðkÞ;k

� �Iuin;k ¼

X

j2CbðkÞ;j6¼k

gbðkÞ;jPuj

ð10Þ

Idout;k ¼

XNo

i¼1;i 6¼bðkÞgi;kPd

i Iuout;k ¼

XNo

i¼1;i 6¼bðkÞ

X

j2Ci

gi;jPuj ð11Þ

where No is the number of BSs, Pid is the total transmit

power of BS i, Pi,kd is the power allocated by BS i to MS k

(subject to MS k being covered by BS i), gi,k is an esti-

mate of the pathloss between MS k and BS i calculated

according to Cost 231-Hata model [26], and b(k) is

defined as the BS serving MS k and calculated by con-

structing the Voronoi tessellations associated with the BS

locations.

Consequently, Pb(k),kd is the transmit power allocated to

MS k by its serving BS, Pb(k) is the total transmit power

of the BS serving MS k and gb(k),k is an estimate of the

pathloss between MS k and its serving BS. The notation

j 2 Ci means all MSs {j} covered by cell i. Conse-

quently, j 2 CbðkÞ means all MSs covered by the same BS

as k.

The pathloss coefficients gi,k can be written strictly in

terms of the BS and MS locations in addition to some con-

stants as gi;k ¼ 1keqðdi;kÞ�l; di;k ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðxi � ukÞ2 þ ðyi � vkÞ2

q

where (xi, yi) are the BS locations and (uk, vk) are the MS

locations, with keq and l chosen according to Cost-231 Hata

Model. In UMTS radio network planning, shadowing and

fading are compensated for via link budget margins [25, 26].

Based on the derivation above, (7) can be rewritten in

terms of the powers Pi,kd allocated to MSs which are the DL

state variables as follows:

Wireless Netw (2012) 18:507–521 511

123

SFþ SIRdtargetk

d

SIRdtarget

!gbðkÞ;kPd

bðkÞ;k � kdgbðkÞ;kX

j2CbðkÞ

PdbðkÞ;j

0@

1A

�XNo

i¼1;i 6¼bðkÞgi;k

X

l2Ci

Pdi;l

!¼ r2 ð12Þ

Similarly, (8) can be rewritten in terms of the MS transmit

powers Pku which are the uplink state variables as follows:

SFþ SIRutargetk

u

SIRutarget

!gbðkÞ;kPu

k � kuX

j2CbðkÞ

gbðkÞ;jPuj

0

@

1

A

�XNo

i¼1;i 6¼bðkÞ

X

l2Ci

gi;lPdl

!¼ r2 ð13Þ

where SIRdtarget and SIRu

target are the target SIRs to achieve

the required QoS for the DL and the UL, respectively.

Equations (12) and (13) can be expressed in matrix format

as follows:

Gd� �

K�K� Pd� �

K�1¼ r2� �

K�1ð14Þ

Gu½ �K�K� Pu½ �K�1¼ r2� �

K�1ð15Þ

where Gd and Gu are square matrices with size K 9 K, Pd is

a column vector with size K 9 1 corresponding to the

downlink MS powers Pid, Pu is a column vector with size

K 9 1 corresponding to the uplink MS powers Pid, r2 is the

thermal noise power column vector with size K 9 1. The kth

row of Gd and Gu corresponds to MS k with each row

representing one of the K equations, and the columns can be

separated into blocks corresponding to the BSs according to

the number of MSs in each BS. The first term of (12)

and (13) will appear in the diagonal of Gd and Gu,

respectively, the second term represents intracell

interference and appears in the block corresponding to

the BS serving MS k, the third term represents intercell

interference and will appear in the blocks corresponding

to all BSs except the serving BS. Solving the power

assignment problem with SIR-based power control

reduces to solving this set of equations which adjusts

the transmit powers given a specific propagation model so

as to meet the target SIRs [26, 27]. To calculate the

number of MSs served in the DL Kservedd , we solve the

following DL power control optimization problem:

minPd

X

k

PdbðkÞ;k ð16Þ

s.t.ð14Þ;Pd� 0;Pdi �Pd

maxi ¼ 1; . . .;No ð17Þ

The objective (16) minimizes the total DL transmit powers

subject to the constraint presented in (14), the constraint

that all powers are greater or equal to zero and the

constraint that the total BS transmit power does not exceed

a maximum threshold Pdmax. Similarly for the UL, we solve

the following UL power control optimization problem:

minPu

X

k

Puk ð18Þ

s:t:ð15Þ;Pu� 0;Puk �Pu

max ð19Þ

where Pmaxu is the maximum transmit power of the MS in

the UL. If the optimization problem is infeasible, this

means that some MSs are in outage. So, iteratively we drop

the worst MS in the network and re-solve the optimization

problem until both problems can be solved. This deter-

mines Kservedd and Kserved

u and, consequently, this determines

the number of served MSs, Kserved, in the network.

3.3 Proposed solution for the optimization problem

The co-siting problem is formulated as a multi-objective

optimization problem as described in Sect. 3.2. In multi-

objective optimization problems, there normally exists a

set of acceptable trade-off optimal solutions between the

objectives. This set is called the Pareto front which is

considered useful in the sense that it provides better

understanding of the system where all the consequences of

a decision with respect to all the objectives can be explored

[28]. In this section, we will propose an algorithm that

provides the Pareto set between the deployment cost and

the outage probability that the network planner can use to

select the preferred or most desirable solution.

First, we present in Algorithm 1 the Lloyd algorithm

described in [23] which is a main component in the pro-

posed heuristic algorithm to solve the formulated problem.

We propose Algorithm 2 to solve the formulated co-siting

optimization problem. Initially, a sufficient number of BS

locations is considered (existing fixed BS locations in

addition to arbitrarily added BS locations denoted as var-

iable BS locations). The input BS locations are much more

than the needed BSs to guarantee that the initial outage

probability is below the target threshold. Algorithm 2 will

Algorithm 1 Lloyd Algorithm

Step 1. Select an initial set of No points fzigNo

i¼1:

Step 2. Construct the Voronoi tessellation fVigNo

i¼1 associated with

the points fzigNo

i¼1:

Step 3. Compute the mass centroids of Voronoi regions fVigNo

i¼1

found in Step 2; these centroids are the new set of points and are

computed as

TðZÞ ¼R

VisqðsÞdsR

ViqðsÞds

(20)

Step 4. If this new set of points meets some convergence criterion,

terminate; otherwise, return to Step 2.

512 Wireless Netw (2012) 18:507–521

123

choose the optimal locations and drop the unnecessary ones

while meeting the target outage probability. As the algo-

rithm drops more BSs, the outage probability becomes

higher and higher until it meets the target threshold.

As long as the target outage probability is not achieved,

three steps are applied accordingly. In the first step, the

Lloyd algorithm is applied to minimize the utility of the

MSs. But in the iterations of the Lloyd algorithm, the fixed

site locations are kept in their locations which might affect

the reached utility of the MSs relative to the unconstrained

case obtained when solving (3) alone. In the unconstrained

case, Lloyd algorithm has the freedom to move the loca-

tions of all BSs and, consequently, will converge to the

minimal utility of the MSs. But when co-siting is intro-

duced, the obtained utility will be equal or higher. The

second step of the algorithm checks the reached utility

F(zi, Vi) of the first step; if Lloyd algorithm meets a utility

that is below a set threshold VT, a variable BS site is

dropped, and if it is not able to meet this threshold, a fixed

site is dropped. Selecting the threshold VT is very critical to

the outage probability. If this threshold is very high, the

system can be in outage in few iterations since some of the

cells will accommodate more MSs than what they can

serve. And if it is very low, most of the fixed sites will be

dropped. More analysis on the selection of VT will be

presented in Sect. 4.2.1. The third step computes the outage

probability of the network. First, the Voronoi regions and

the pathloss matrices for both the UL and the DL are

constructed. Then, the number of served MSs in the UL

and the DL will be calculated to determine the outage

probability as explained in Sect. 3.2.1.

The first two steps of the algorithm are generic and can

be applied to any newly deployed technology. The third

step computes the outage probability of the network and it

is composed of several sub-steps where only the third sub-

step is specific to the UMTS technology. To compute the

number of MSs served in the UL and DL directions, two

power control optimization problems are solved that meet

the target SIR of the MSs taking intercell and intracell

interference into account. For other technologies, the SIR

expressions might take a different form and power control

need not be implemented in the same way as in UMTS.

Consequently, other optimization problems might be nec-

essary to formulate and solve in order to derive the outage

probability in the network which is usually feasible to

calculate. Thus, the algorithm is generic in most of its steps

except for the outage probability calculation which should

be adapted according to the newly deployed technology.

3.4 Convergence and complexity analysis

The convergence of Lloyd algorithm for computing cent-

roidal Voronoi tessellations has been discussed in several

works [23, 29]. According to Theorem 2.11 in [29], the

Lloyd algorithm is globally convergent in one dimension

for any positive and smooth density function. Thus,

applying Lloyd algorithm to the unconstrained case of (3)

converges globally in one dimension for positive and

smooth density functions. In two dimensional regions,

under some fairly non-restrictive assumptions regarding

MS/demand distribution q(s), the objective function in (3)

is convex near a stationary point and therefore the fixed-

point iteration of the unconstrained Lloyd map converges

to a minimum in that neighborhood. The assumption on

models of MS distribution requires that q(s) be log-con-

cave, which can be obtained, for example, by linear and

Gaussian distributions and a variety of composition rules

involving them. The addition of known fixed sites as given

in (4) retains the convexity of the inner optimization

problem which is then also convergent. Algorithm 2

determines all solutions of the mutli-objective problem that

Algorithm 2 Proposed solution of the optimization problem

n1 = nfixed, n2 = narb, No = Nb.

while Pout\e {While Pout is below a target threshold e} do

Step 1. Solve (3) subject to (4).

Solve (3) by applying Lloyd’s algorithm while keeping in every

iteration the positions of the fixed BSs given by (4).

Step 2. Solve (2) subject to (3) and (4). Decision on dropping

either a fixed or a variable site.

if Lloyd algorithm met the required utility of the MSs, i.e.,

F(zi, Vi) B VT then

Merge the locations of the variable BS location that has the

smallest number of MSs with the closest variable BS location by

replacing them with their midpoint coordinates.

n2 = n2 - 1.

else

Merge the locations of the fixed BS location that has the smallest

number of MSs with the closest variable BS location by

replacing them with their midpoint coordinates.

n1 = n1 - 1.

end if

No = No - 1.

Step 3. Calculate the outage probability:

a. Construct the Voronoi tessellation corresponding to the

BS locations fzgNo

i¼1 and find the distance between each (BS ,

MS) pair.

b. Construct the pathloss matrices Gd and Gu based on the

estimated pathloss for each (BS , MS) pair in the UL and the DL.

c. Solve the optimization problem (16) subject to (17) to

calculate Kdserved and solve (18) subject to (19) to calculate

Kservedu .

d. Calculate the number of MSs that are successfully served

in both UL and DL directions Kserved B min(Kservedd , Kserved

u ).

e. Calculate the outage probability Pout ¼ 1� Kserved

K :

end while

Wireless Netw (2012) 18:507–521 513

123

are optimal in the Pareto sense as explained in Sect. 3.3.

Therefore, the convergence depends on a threshold that we

set in order to favor an objective over the other.

The complexity of the formulated optimization problem

can be computed as follows. As stated in Sect. 3.3, the

algorithm starts with Nb BSs and drops the BSs one by one

until it reaches the required No BSs. As long as the con-

straints of the optimization are not met, Lloyd algorithm

applies b iterations for a given set of fixed and variable BSs

and then based on the reached utility either a variable or a

fixed BS is dropped. The maximum number of BSs is Nb.

To compute the Voronoi tessellations, this requires oper-

ations on the order of Nblog Nb. Besides, in every iteration,

the centroid of these tessellations is computed which requires

operations on the order of Nb. Thus, the number of oper-

ations in every iteration is on the order of Nb ? Nblog Nb.

Assume that b(Nb - No) iterations are needed to converge

to the required solution, this requires operations on the

order of b(Nb - No)(Nb ? Nblog Nb). The convergence

rate of Lloyd algorithm is quiet fast in practice. An upper

bound has been derived in [29]. It is shown that for any

smooth logarithmic concave density, the Lloyd algorithm is

globally convergent with a geometric convergence rate no

larger than a factor that depends on the relative size of a

Voronoi cell in comparison with the density distribution

and some constant factor. Our algorithm runs Lloyd algo-

rithm Nb - No times, until all the constraints are satisfied.

So, the convergence depends directly on the initial input

sites which include both the fixed and the newly added

variable sites.

3.5 Impact of mobility on radio network planning

Mobility poses two main challenges for the process of

radio network planning: first, the distribution of the loca-

tions of the MSs varies as they move inside the network

and, second, the channel variations and the power control

accuracy vary depending on the speed of the MSs. The

process of radio network planning is static, that is, its

output (number and locations of BSs in the network) can-

not be adapted in a dynamic way as mobility patterns vary

or channel conditions change. However, mobility is

accounted for during the radio network planning process

via different means.

To address the first challenge, radio network planning is

usually based on static network scenarios that correspond

to the worst case conditions at peak hours where the traffic

demand is at the highest level. Our proposed approach is

generic and applies to any distribution of MSs in the net-

work. To address the second challenge, power margins are

normally added to the link budget analysis in practice to

compensate for channel variation and its impact on power

control accuracy (e.g., [4–6]). Adding a power margin

results in decreasing the maximum transmit power capa-

bility of the MSs and the BS in order to compensate for

variations in the network. This in turn leads to more con-

servative planning as it reduces the area coverage of each

BS but it is important to avoid negative implications on

quality due to the impact of user mobility. In the UMTS

standard, fast power control is used in both the UL and DL

directions to compensate for the fast Rayleigh fading var-

iation in the channel. The power control takes place at the

rate of 1500 times per second, which is faster than the rate

of Rayleigh fades for slow to moderate mobile speeds [4],

making it unnecessary to add a power margin compensa-

tion. However, for fast moving MSs, an additional power

margin of few dBs should be added. Our proposed

approach is generic and can account for power margins by

simply modifying the values of the maximum MS and BS

transmit power input parameters.

4 UMTS/GSM co-siting case study: results and analysis

This section presents a UMTS/GSM co-siting case study in

order to evaluate the proposed algorithm as a function of

various input parameters. The considered scenario assumes

that a UMTS network needs to be deployed in a

10Km 9 10Km area that is already covered by an existing

GSM network. Relating this to the problem formulation,

the existing GSM BS locations are considered as the fixed

BS locations. In this section, basic UMTS radio network

planning aspects are introduced first, then the proposed

algorithm in Sect. 3.3 is applied to obtain the required

output UMTS BS locations in the Pareto sense. The

co-siting problem is formulated in a general way that can

accept any input MS distribution and any existing fixed site

locations. In this section, two scenarios are presented with

uniform and non-uniform MS distributions. The simulation

parameters are presented in Table 2.

4.1 UMTS radio network planning without co-siting

First, we will show the results without co-siting. This is

obtained by setting nfixed ¼ 0 and VT to a high value so that

the algorithm will function properly and drop the variable

sites. Figure 1 presents the output locations of BSs for both

uniform and non-uniform MS distributions for a target

outage probability Pout = 0.

For uniform distribution of MSs, the MS density func-

tion is q(s) = 1/A where A is the area to be covered.

Starting with 150 BS sites, 25 BSs are dropped and the

obtained number of BSs is 125. It is obvious that every BS

is covering nearly the same area since the MS distribution

is uniform. The mean number of MSs per cell is 40.

Figure 1(b) presents the output locations assuming a hot

514 Wireless Netw (2012) 18:507–521

123

spot modeled by a Gaussian distribution of MSs. In a hot

spot, the MS density is higher at the area center and

decreases along the way to the area boundary. The con-

sidered Gaussian distribution is given by

qðsÞ ¼1ffiffiffiffiffiffiffi2pc2p expððx�gÞ2þðy�gÞ2Þ=2c2

RA

1ffiffiffiffiffiffiffi2pc2p expððx�gÞ2þðy�gÞ2Þ=2c2 ds

ð21Þ

where g = 5,000 and c = 1,500. In this case, the obtained

number of BSs is 132. The areas of the cells are not equal;

the cell radius varies from few hundred meters to few

kilometers. This corresponds to typical UMTS cells that

vary from few hundred meters in urban areas to several

kilometers in rural areas [1]. Therefore, the cell range

depends on the MS concentration within an area.

4.2 UMTS radio network planning with co-siting

The UMTS/GSM co-siting problem is also investigated for

uniform and non-uniform MS distributions.

4.2.1 Decision on the threshold of the utility VT

In Algorithm 2, dropping a variable or a fixed site depends

on the threshold VT as explained in Sect. 3.3. To decide on

an optimized value of VT, we will find first the minimum

utility F(zi, Vi)min that achieves Pout = 0. In this case, all

the BSs are assumed to have continuous locations. This is

obtained by setting in Algorithm 2, nfixed = 0 and VT to a

high value so that the algorithm will function properly and

consider the variable sites only. When the algorithm con-

verges, we will check the minimum reached utility

F(zi, Vi)min. In the co-siting case, the threshold of the utility

VT can be modeled as VT ¼ a � Fðzi;ViÞmin, where a C 1.

For example, Fig. 2 shows the effect of the threshold VT on

the network deployment cost for different outage proba-

bilities assuming uniform user distribution and the exis-

tence of 75 fixed BS sites. Figure 2 shows the decrease in

the deployment cost of the co-siting case compared to

the deployment cost without co-siting. Setting VT =

F(zi, Vi)min means that the utility of the MSs in the

co-siting case should match the utility of the MSs where no

co-siting is considered. The fixed sites that do not violate

F(zi, Vi)min are reused, and thus, the deployment cost is the

same for any outage probability. For Pout = 0.05, the best

value of VT is equal to 1.2F(zi,Vi)min, whereas for Poutage =

0.1, the best value of VT is equal to 1.3F(zi,Vi)min. Setting

VT to a high value results in an outage in few iterations

since some of the cells will accommodate more MSs than

what they can serve. This, consequently, increases the

deployment cost.

4.2.2 Results for uniform MS distribution

Given an area with 25 existing GSM BSs, Fig. 3 shows the

input and optimized output locations of the UMTS BSs. An

input of 150 total BS locations is considered that include

the 25 uniformly distributed GSM sites in addition to 125

Table 2 Simulation parameters

Parameter Value Description

K 5000 Number of active MSs

keq 2.75 9 1015 Pathloss parameters

l 3.52

Pumax 1 W Maximum powers

Pdmax

60 W

SF 128 Spreading factor

SIRdtarget

7 dB Target SIRs

SIRutarget 5 dB

kd 0.4 Orthogonality factors

ku 1

r2 2 9 10-14 W Noise power

0 2000 4000 6000 8000 100000

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

0 2000 4000 6000 8000 100000

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

(a) (b)

Fig. 1 Output optimal locations

of BSs (represented by

triangles) without co-siting for

Pout = 0. a A total of 125 BSs

for uniform MS distribution.

b A total of 132 BSs for

Gaussian MS distribution

Wireless Netw (2012) 18:507–521 515

123

input arbitrary sites (denoted as variable BS locations in

Sect. 3). The optimized UMTS sites co-sited with GSM are

obtained using Algorithm 2. For Pout = 0, the best utility

threshold is VT = F(zi, Vi)min, based on Fig. 2, where

F(zi, Vi)min is the minimal obtained utility for uniform MS

distribution. An overall of 125 BSs out of the 150 are

required to satisfy the constraints of the optimization

problem. The number of reused sites is 25 out of 25 which

results in 100% reuse of the existing sites with the

remaining 100 sites all newly deployed UMTS sites. The

algorithm is able to place the variable BS locations in a

way that reduces the deployment cost while achieving

Pout = 0. Consequently, the existing number of fixed sites

and their locations affect the performance of the algorithm

as will be also demonstrated below.

Given an area covered by 75 GSM BSs, Fig. 4 presents

the input and optimized output locations of the UMTS BSs.

An input of 200 BS locations is considered that includes 75

uniformly distributed GSM sites in addition to 125 input

arbitrary sites. Figure 4(b) shows the optimized output

locations for an outage probability Pout = 0. An overall of

125 BSs out of the 200 are required to satisfy the con-

straints of the optimization problem. The number of reused

GSM BSs is 24 which corresponds to 32% fixed site reuse

(the remaining 101 sites are all newly deployed UMTS

sites). Increasing the acceptable outage probability to 5%

and setting the utility threshold to VT ¼ 1:2Fðzi;ViÞmin,

based on Fig. 2, resulted in a reuse of 56 sites which cor-

responds to 74.6% fixed site reuse as shown in Fig. 4(c).

Moreover, setting the outage probability high enough to

force the algorithm to reuse all fixed sites as shown in

Fig. 4(d) resulted in an outage probability of 9.89%. The

best utility threshold is set to VT ¼ 1:3Fðzi;ViÞmin in this

case based on Fig. 2.

Figure 5 presents the obtained Pareto curves for the sce-

nario where 75 fixed GSM BSs exist and can be reused by the

network planner. They quantify the tradeoff between the costs

represented by the number of reused fixed sites and the

number of newly deployed sites and the decrease in the

deployment cost in the network versus the outage probability.

As the outage probability increases, the percentage of reusing

existing sites increases and deploying new sites decreases. For

Pout = 0, the algorithm is still able to reduce the network

deployment cost by reusing 24 existing sites. This corresponds

to decreasing the deployment cost by around 20%. For

Pout = 0.1, the deployment cost can be decreased by 60%.

1 1.5 2 2.50

10

20

30

40

50

60

70D

ecre

ase

in d

eplo

ymen

t cos

t %

α

Poutage

=0

Poutage

=0.05

Poutage

=0.1

Fig. 2 Decrease in the deployment cost of the co-siting case

compared to the deployment cost without co-siting versus a(VT ¼ a � Fðzi;ViÞmin)

0 2000 4000 6000 8000 100000

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

0 2000 4000 6000 8000 100000

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

(a) (b)

Fig. 3 Input and optimized output locations assuming 25 existing BS

sites and uniform MS distribution. a Input locations of BSs including

25 GSM fixed BS locations (marked with squares) and 125 arbitrary

BS locations (marked with triangles). b Output locations of BSs

with UMTS/GSM co-siting (total of 125 BSs with all GSM sites

reused)

516 Wireless Netw (2012) 18:507–521

123

Using Fig. 5, it is up to the network planner to take a decision

on the operational point that is most suitable.

4.2.3 Results for non-uniform MS distribution

Figure 6 presents the input and optimized output locations

of the UMTS BSs assuming a Gaussian distribution of

MSs. The input corresponds to 210 BS locations that

include 75 normally distributed GSM sites in addition to

135 input arbitrary sites. For Pout = 0.05, the best utility

threshold is VT = 1.25F(zi,Vi)min, where F(zi, Vi)min is the

minimum obtained utility for Gaussian MS distribution.

The optimized UMTS output sites are 132 including 40

co-sited with existing GSM sites and the remaining are

0 2000 4000 6000 8000 100000

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

(a)0 2000 4000 6000 8000 10000

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

(b)

0 2000 4000 6000 8000 100000

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

(c)0 2000 4000 6000 8000 10000

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

(d)

Fig. 4 Input and optimized output locations assuming 75 existing

sites and uniform MS distribution. a Input locations of BSs including


BS locations (marked with triangles). b Output locations of BSs (total

of 125 BSs with 24 GSM sites reused out of 75) for Pout = 0.

c Output locations of BSs (total of 125 BSs with 56 GSM sites reused

out of 75) for Pout = 0.05. d Output locations of BSs (total of 125

BSs with 75 GSM sites reused out of 75) for Pout = 0.0989

0 0.02 0.04 0.06 0.08 0.1 0.120

10

20

30

40

50

60

70

80

90

100

110

Num

ber

of s

ites

Outage probability (Pout

)

Reused SitesNew Sites

0 0.02 0.04 0.06 0.08 0.1 0.120

10

20

30

40

50

60

70

Dec

reas

e in

dep

loym

ent c

ost %


)

(a) (b)

Fig. 5 Pareto sets that give the

tradeoff between different cost

metrics and Pout for uniform MS

distribution. a Number of sites

versus Pout. b Decrease in

deployment cost versus Pout

Wireless Netw (2012) 18:507–521 517

123

newly added UMTS sites. The number of reused GSM

sites is 40 out of 75 which corresponds to 53% reuse. Due

to the Gaussian distribution of MSs over the considered

area, the density of the output UMTS sites (co-sited and

new) is highest at the area center and decreases along the

way to the area boundary. Figure 7 shows the Pareto

curves for the required number of sites and the decrease

in the deployment cost versus the outage probability for

the case where 75 normally distributed GSM BSs exist.

Similar to the uniform distribution case, as the outage

probability increases, the percentage of reusing existing

sites increases and deploying new sites decreases. Com-

pared to the uniform case, Fig. 7 shows that the per-

centage of reuse is lower for the same outage probability.

For Pout = 0, the number of reused sites is 20 which

decreases the deployment cost by around 15%. For

Pout = 0.1, the deployment cost can be decreased by

42%. This shows that the percentage of reuse depends on

the MS distribution and on the existing fixed sites. For

any MS distribution and existing fixed location of BSs,

the radio network planner can use Algorithm 2 to

generate the tradeoff costs as in Figs. 5 and 7 to decide

on the operational point that is most suitable. The inter-

esting observation is that even for Pout = 0, Algorithm 2

reuses existing sites and decreases, consequently, the

deployment costs.

To demonstrate the functionality of the proposed algo-

rithm for any MS distribution, we present results for

another non-uniform MS distribution modelled by the

superposition of five Gaussian functions with different

means and variances as shown in Fig. 8. We also assume

that there exist 75 fixed GSM sites distributed according to

the given MS distribution. Figure 8 presents the co-siting

results for various outage probabilities.

5 Conclusion

We have formulated a generic nested mixed integer

programming model for radio network planning with BS

co-siting. The objective is to minimize the deployment cost

of a new network while guaranteeing that the outage

0 2000 4000 6000 8000 100000

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

0 2000 4000 6000 8000 100000

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

(a) (b)


sites and Gaussian MS distribution. a Input locations of BSs including


BS locations (marked with triangles). b Output optimal locations of

BSs (total of 132 BSs with 40 reused GSM sites)

0 0.02 0.04 0.06 0.08 0.1 0.120

20

40

60

80

100

120

Num

ber

of s

ites


)

Reused SitesNew Sites

0 0.02 0.04 0.06 0.08 0.1 0.120

5

10

15

20

25

30

35

40

45

50

Dec

reas

e in

dep

loym

ent c

ost %


)

(a) (b)

Fig. 7 Pareto sets that give the

tradeoff between different cost

metrics and Pout for Gaussian

MS distribution. a Number of

sites versus Pout. b Decrease of

deployment cost versus Pout

518 Wireless Netw (2012) 18:507–521

123

probability is below a target threshold. We proposed an

algorithm that solves both the continuous part which cor-

responds to the locations of the new BSs to be deployed in

addition to the integer part concerned with locations of the

existing BSs to be reused in order to minimize the

deployment cost.

The proposed algorithm has been evaluated using a

UMTS/GSM co-siting case study for both uniform and

non-uniform MS distributions over the area of interest.

Presented results show that the percentage of reuse of fixed

sites depends on the MS distribution, on the existing sites

and on the trade-off threshold of acceptable outage

probability.

Finally, it is important to highlight that the formulated

optimization model and the proposed algorithm are generic

enough to be applied to scenarios with other wireless

technologies in addition to various input MS distributions,

existing fixed site locations, and area topologies.

Acknowledgments We would like to thank the reviewers for their

constructive feedback which helped improve the clarity and content

of the paper. This work was supported by a research grant from the

National Council for Scientific Research, Lebanon. It was also

supported by the American University of Beirut Research Board,

Dar Al-Handassah (Shair & Partners) Research Fund, and the Rath-

man (Kadifa) Fund.

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Author Biographies

Lina Al-Kanj received her B.E.

degree in Electrical and Com-

munications Engineering from

the Lebanese University in

2005, and her ME degree in

Computer and Communications

Engineering from the American

University of Beirut (AUB) in

2007. Since 2007, she has been

enrolled as a PhD student at

AUB. During her PhD studies,

she spent two semesters (Fall

2009 and Spring 2010) as a

visiting PhD student at the

University of Texas at Austin,

Texas, United States. Her research interests include cooperative

communications and radio network planning and optimization.

Zaher Dawy received his B.E.

degree in Computer and Commu-

nications Engineering from the

American University of Beirut

(AUB) in 1998. He received his

masters and doctoral degrees

in Communications Engineering

from Munich University of Tech-

nology (TUM) in 2000 and 2004,

respectively. Between 1999 and

2000, he worked as a part-time

engineer at Siemens AG research

labs in Munich focusing on the

development of enhancement

techniques for UMTS. At TUM,

between 2000 and 2003 he managed and developed a research project with

Siemens AG where he designed advanced multiuser receiver structures for

UMTS base stations. He joined the Department of Electrical and Computer

Engineering at AUB in September 2004 where he is currently an Associate

Professor. Dr. Dawy is the recipient of AUB 2008 teaching excellence

award, best graduate award from TUM in 2000, youth and knowledge

Siemens scholarship for distinguished students in 1999, and distinguished

graduate medal of excellence from Harriri foundation in 1998. He is a

senior member of the IEEE, Chair of the IEEE Communications Society

Lebanon Chapter, and a member of the Lebanese Order of Engineers. His

research interests are in the general areas of wireless communication net-

works, cellular technologies, and computational biology.

520 Wireless Netw (2012) 18:507–521

123

George Turkiyyah is a Profes-

sor and Chair of the Computer

Science department at the

American University of Beirut

(AUB). He obtained his MS and

PhD from Carnegie Mellon

University and his BE from

AUB. Prior to joining AUB, he

was an Assistant and then Asso-

ciate Professor at the University

of Washington. His research

interests are in high-performance

computing, geometric modeling,

physically-based simulation,

numerical optimization, and

large-scale Web-enabled data repositories. Prof Turkiyyah is the author

of more than 50 refereed publications, holds 3 patents on geometric

representation technologies, has graduated 6 PhD students, co-founded

a software startup, and published a number of widely-used software

systems. He has won a number of awards including the 2003 Trans-

portation Research Board K.B. Woods award for best paper in Design

and Construction, best presentation/poster awards in the 2007 ACM

Solid and Physical Modeling and the 2006 Medicine Meets Virtual

reality conferences. He chaired the 2003 ASCE Engineering Mechanics

Conference and co-chaired SPM 03, the eighth ACM Symposium on

Solid Modeling and Applications. Prof Turkiyyah serves on the pro-

gram committees of a number of conferences including the ACM/SIAM

SPM Solid and Physical Modeling Symposium and Computer-Aided

Design. He is a member of ACM and SIAM.

Wireless Netw (2012) 18:507–521 521

123

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