Automatic planning of 3G UMTS all-IP release 4 networks with realistic traffic

Computers & Operations Research 40 (2013) 1991–2003

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Automatic planning of 3G UMTS all-IP release 4 networks with realistic traffic Mohammad Reza Pasandideh, Marc St-Hilaire n Department of Systems and Computer Engineering, Carleton University, Ottawa (Ontario), Canada

a r t i c l e i n f o

abstract

Available online 4 March 2013

Most Universal Mobile Telecommunications Systems (UMTS) service providers are switching to an allIP (also called flat-IP) architecture. Using an all-IP architecture within 3G networks provides a costeffective transport network since the same infrastructure can be used for both voice and data services. However, planning and designing such an architecture is very complex especially if realistic traffic profiles are taken into consideration. As a result, this paper first provides a mathematical formulation (presented in Appendix for readability reasons) for the global planning problem of 3G UMTS all-IP Release 4 networks with realistic traffic profile. Due to the complexity of the problem, heuristics based on local search and tabu search are also proposed. Finally, a comparative study is performed to evaluate how good the heuristics are with respect to a reference model. Results show that the tabu search is able to provide solutions that are close to optimal solutions in a much shorter computation time. & 2013 Elsevier Ltd. All rights reserved.

Keywords: Third Generation (3G) mobile networks Universal Mobile Telecommunications System (UMTS) Network planning Heuristics All-IP Mixed Integer Programming (MIP) Optimization

1. Introduction Backward compatibility of 3G UMTS networks with widely deployed GSM networks is an advantage which has made them popular in the world. The other benefit was incorporating IP technology as a new solution in the transport network of UMTS networks. As a result, costly Asynchronous Transfer Mode (ATM) based transmission devices were replaced with low cost Internet Protocol (IP) solutions. Mixing flat-IP or all-IP architecture with 3G UMTS networks had a remarkable impact on establishment of flexible and economical transport networks, where the same bearer was used for both voice and data services. Consequently, cellular operators became so interested in 3G UMTS networks with all-IP architecture. In the competitive market of cellular networks, operators have to invest a huge portion of their budget on their network infrastructure to maintain new services with market demands. Consequently, design and upgrade of networks with a minimum cost become a high priority and challenging for network operators. As a result, operators demand for efficient planning tools which can accommodate new technologies and services. Such a need has motivated researches in academia and industry to study and develop planning tools, algorithms and software. The planning products are used to assist network planners to design a cost minimum network while observing several considerations.

n

Corresponding author. E-mail addresses: [email protected] (M.R. Pasandideh), [email protected] (M. St-Hilaire). 0305-0548/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.cor.2013.02.017

The basic architecture of 3G UMTS all-IP Release 4 networks is illustrated in Fig. 1. UMTS networks are composed of the Radio Access Network (RAN), also known as Universal Terrestrial Radio Access Network (UTRAN) and the Core Network (CN). UTRAN is the coverage area of the mobile users and includes Radio Network Controller (RNC) and series of Node B planted in cells. Node Bs and RNCs respectively perform almost similar duties as Base Station (BS) and Base Station Controller (BSC) in 2G networks, but support advanced features like soft handover. RNC provides connectivity between one or more Node Bs, UTRAN and CN, mobility and radio resource management [1]. The CN is the central part of the network and comprises of Circuit Switch (CS) and Packet Switch (PS) domains. In the former version of Release 4 networks (i.e. Release 99), voice and signaling traffics were handled by the same Network Elements (NEs). This in turn endures some design limitations. In Release 4 networks, voice and signaling traffics are handled by separate NEs to promote scalable, reliable, and cost-effective architecture with respect to Release 99 [2]. The legacy Mobile Switching Center (MSC) is split into an MSC Server (MSS) and a Media Gateway (MGW). MSS is responsible for control plane data, including application protocols, mobility management and call control logic, while MGW handles user plane data like voice stream. One MSS is capable to support multiple MGWs and in case of MGW failure, MSS can re-route traffic through another MGW and there will be no service interruption [3]. For the PS domain, the main components are the Serving GPRS Support Node (SGSN) and the Gateway GPRS Support Node (GGSN) for packet switching between mobile users and external Packet Data Network (PDN) like Internet. A common node among the CS and PS networks is the Home Location Register (HLR). The HLR in 3G networks is an evolved version from the HLR in 2G networks and stores subscriber profiles, authentication

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Fig. 1. 3G UMTS all-IP Release 4 network architecture.

information, and equipment identity. In all-IP architecture, user plane and control plane data are transmitted in form of packets over IP. The facilitators are edge routers and core routers which are respectively installed in UTRAN and core sites for packet routing purposes. UMTS networks offer parallel CS (e.g. speech, circuit data, SMS) and PS (e.g. data, MMS, VoIP, video call, etc.) services. Based on service precedence, reliability, delay, and throughput, UMTS networks define four Quality of Service (QoS) classes: conversational, streaming, interactive, and background. Each class is differentiated by parameters like maximum bit rate, guaranteed bit rate, bit error rate, and transfer delay. QoS is managed per subscriber and can be different for each requested service. Services like voice and streaming video need a real-time traffic support defined in the conversational and streaming classes. On the other hand, services like web browsing and email do not need a real-time traffic support and have lower priority compared to services like CS voice [4]. The QoS parameters assigned to the requested service are negotiated between the subscriber, GGSN and the external PDN and are set in the Packet Data Protocol (PDP) context. The PDP context is a set of data structure defined on SGSN and GGSN, which contains the subscriber session information when the subscriber has an active session. In UMTS networks, a subscriber should first perform a ‘‘network attach’’ procedure to start using a CS (PS) service. During this procedure, the subscriber is authenticated and authorized by the MSS (SGSN) through enquires to the HLR. To use a CS service like a voice call, a subscriber first sends a connection request to the RNC. After exchanging a few messages, a connection between the subscriber and the RNC is established. Then, the subscriber sends another connection request destined to the MSS in the core network. The MSS starts the authentication procedure through enquires from the HLR and exchange of encryption keys with the subscriber. If the authentication is successfully done, the subscriber send a call control setup request to the MSS and a radio bearer is established by the RNC between the subscriber and the MSS. The early steps for using a PS service are similar to those in the CS service. When a connection is setup between the RNC and the subscriber, similar authentication procedure is performed by the

SGSN. Then, the subscriber initiates a PDP context activation procedure, by requesting an Access Point Name (APN), from the APN lists defined in HLR. The APN is used as a reference to an external PDN which supports the services to be accessed by the subscriber [4]. The SGSN negotiates with UTRAN to allocate the radio bearer bandwidth for the data session. The SGSN assigns a GGSN to serve the data call considering some criteria like APN and subsequently creates a tunnel based on GPRS Tunneling Protocol (GTP) to the GGSN. The GGSN assigns an IP address to the subscriber and similar to SGSN, creates a PDP context for the data call. Finally, the SGSN sends a PDP context activation accept message to the subscriber and the subscriber starts using the PS service [5]. As a first contribution, this paper provides a mathematical formulation1 for the global planning problem of 3G UMTS all-IP Release 4 networks with realistic traffic profile. More formally, the problem simultaneously finds the location and the type of all network elements, the number and the type of links and the network topology while minimizing the cost and respecting a set of constraints. Due to the complexity of the problem, heuristics based on local search and tabu search are also proposed. Finally, a comparative study is performed to evaluate how good the heuristics are with respect to a reference model. The rest of this paper is organized as follows. Section 2 provides a summary of the related works on UMTS network planning. The mathematical model and the two heuristics are introduced in Sections 3 and 4 respectively. Then, Section 5 presents an illustrative example followed by the design experiments and the results in Section 6. Finally, the paper is concluded in Section 7.

2. Related work on UMTS network planning Network planning is a well known field in operation research. In fact, most of the tools proposed in the literature will involve operation research techniques such as discrete optimization and heuristics. 1 Due to the large number of equations, the mathematical model is presented in Appendix to enhance readability.

M.R. Pasandideh, M. St-Hilaire / Computers & Operations Research 40 (2013) 1991–2003

The primary goal of UMTS network planning tools is to provide an optimum topology for the network. Many parameters and factors are involved to select the optimum node locations, node and link types, topology, and so on. Several models and algorithms (both from the fields of network/telecommunication and operation research) have been proposed to solve the planning problem of UMTS networks. However, due to the high complexity of the problem, most of the proposals only focus on a portion of the network. In fact, the entire planning problem is decomposed into three sub-problems: (i) the cell planning sub-problem, (ii) the access network planning sub-problem, and (iii) the core network planning sub-problem. These sub-problems are either considered individually and solved separately or combined and solved jointly. The following sections describe these subproblems. 2.1. The cell planning sub-problem The UMTS air interface is based on W-CDMA. As a result, the usual coverage and frequency assignment problems faced in 2G networks do not apply in UMTS networks. The objective of the cell planning sub-problem can be summarized as: Minimizing network cost or electromagnetic field and maximizing capacity, coverage and signal quality. Different profit maximization models have been proposed in the literature. For example, Kalvenes et al. [6] considered the trade-off between the revenue generated per served customer and the cost of constructing new towers. Similarly, authors in [7], present a stochastic revenue optimization model for CDMA networks inspired by bid pricing models from the airline industry. A linear combination of different objectives such as cost, interference, coverage, balanced traffic and so on is introduced in Theil et al. [8]. They propose an algorithm based on simulated annealing to solve the site selection problem. Similarly, some multi-objective cell planning problems can be found in Jamaa et al. [9] and Choi et al. [10]. Minimizing electromagnetic field level as an objective for the cell planning problem has been tackled by Crainic et al. [11]. They considered radio protection constraints, handover and downlink capacity constraints and formulated five objective functions, scaling five functions of electrical field levels. Chen and Yuan, in [12], present integer linear models and a tabu search algorithm to deal with cell coverage at minimum cost in terms of the power usage. Overlap between adjacent cells is considered to support handover requirements. Finally, other relevant work on the cell planning sub-problem is listed below:

 Air interface power control: Amaldi et al. [13] and Yang et al. [14].  Cell planning algorithms: Zdunek and Ignor [15], Galota et al. [16], Eisenblatter et al. [17], Amaldi et al. [13,18–23], Jamma et al. [24], Sohn and Jo [25], Mathar and Schmeink [26].

2.2. The access network planning sub-problem The objective of the access planning sub-problem is usually cost minimization, but other objectives such as reliability or combination of cost and reliability could be considered. Here are the most relevant papers:

 Cost-effective access networks: Harmatos et al. [27,28], Lauther 

et al. [29], Krendzel et al. [30], Juttner et al. [31], Wu and Pierre [32]. Reliable access networks: Tripper et al. [33], Charnsripinyo and Tipper [34], Szlovencsak et al. [35], Harmatos et al. [27,28] and Krendzel et al. [36].

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2.3. The core network planning sub-problem The objective of the core planning sub-problem is usually cost minimization. However, other objectives like reliability could be considered. There are few research literatures on the core network planning sub-problem due to the similarity of this subproblem to the wired network planning problem. Here are some related papers: Shalak et al. [37], Ricciato et al. [38], Harmatos et al. [39] and Ouyang and Fallah [40]. 2.4. Combination of sub-problems When the previous sub-problems are tackled separately, the problem complexity is reduced, but as the interactions between sub-problems are neglected, solution optimality is sacrificed. On the other hand, combining more than one sub-problem has the advantage of providing a solution closer to the global optimal, but at the expense of increasing problem complexity. Such an approach is known as integrated or global approach. The objective of the global approach is similar to those of each sub-problem mentioned before. Cost minimization is the main objective, while considering network quality. Some related work considering a global approach include: Zhang et al. [41], Chamberland and Pierre [42], Chamberland [43], St-Hilaire et al. [44–47]. Finally, the authors in [48] proposed a new hybrid method combining the sequential approach and the global approach to reduce execution time and eventually solve larger problems. In a previous paper [49], we formulated the planning problem of 3G UMTS Release 4 networks and incorporated a realistic traffic profile as a single integrated Mixed-Integer linear Program (MIP). The realistic traffic profile was taken from live networks which could capture all aspects of the voice and data traffics (e.g. Busy Hour Call Attempt (BHCA), simultaneous calls, bandwidth, signaling traffic, etc.). The integrated (global) planning problem entailed simultaneous consideration of the access and the core network sub-problems and was solved by a MIP solver. Since the problem is NP-hard, the CPU time required to find a solution is growing exponentially with respect to the problem size. Up to a certain point, even the memory might not be sufficient to store the exploration tree of the branch and bound. As a result, only small size problems were considered. 2.5. Problem statement and contributions Most UMTS network models proposed in the literature [42–46] deal with older releases (such as Release 99). Since then, new releases such as Release 4, have been standardized. While MSC was the only node to handle both user plane and control plane in Release 99, MGW and MSS were introduced in Release 4 to deal with user plane and control plane respectively. Moreover, IP transport technology was also introduced as an alternative for ATM. Although the model formulation in this paper may have similarities to the other papers (such as [45]), there are many differences due to introducing new nodes with separate functioning roles, new links and interfaces, IP as a new transport media, as well as a more complex/realistic traffic model. Finally, most planning tools [42–46] consider a very simple traffic model. In fact, they do not consider CS-data traffic and most of the time, only one type of PS-data traffic is used. Finally, most of the traffic parameters used in this paper (see Table 10) are not even considered in other papers. These parameters are important because they consider almost all aspects of the voice and data traffic. Finally, the advantage of using IP technology within Release 4 networks, makes it more cost-optimized and flexible.

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3. Model formulation In order to formulate the model and define the planning problem of 3G UMTS all-IP Release 4 networks, we suppose the following information is known:

 The location of Node Bs.  The potential locations of all NEs (i.e. RNCs, MGWs, MSSs,

portion of these subscribers have PDP context. Columns 7 and 8 show BH attached subscribers and simultaneous PDP context. If a subscriber decides to use packet data services, it must first attach and then activate a PDP context. Finally, the last column gives the signaling load for the CS traffic. Once the traffic records are calculated, we need to design a network which can fulfill these traffic requirements for the subscribers.

SGSNs, GGSNs, edge routers/CS routers/PS routers).

 The different types of NEs and links, their capacities and    

their costs. The installation cost for given types of facilities (including for instance: floor space, cables, racks, electric installations, labor, etc.). The subscriber traffic profile. The planning parameters. The number of subscribers for each Node B.

In this paper, our focus is on the development of automatic planning tools for the design of 3G UMTS all-IP Release networks. In other words, we want to develop a computer based programming tool which is able to perform network planning tasks with minimum human intervention and effort. The planning tool will jointly provide the following as output:

 The number, the location and the type of NEs (i.e. RNCs,  

MGWs, MSSs, SGSNs, GGSNs, edge routers/CS routers/PS routers) to be installed. The number and the type of links and interfaces. The design of the network topology.

In this paper, we consider each Node B as a ‘‘traffic node’’ or ‘‘test point’’. All-IP Release 4 networks involve different NEs for voice and data services in which every NE deals with specific aspects of the traffic. Therefore, to consider all aspects of the traffic, we need to produce a traffic record for each Node B. 3.1. Node B traffic record

3.2. The model The proposed model simultaneously finds the number, the location and type of all network elements (i.e. RNC, MSS, SGSN, router, etc.). Moreover, it also determines the necessary number and type of links and interfaces in order to design the network topology. In this paper, a tree topology is considered and IP is used as the technology model for node interconnections. The model for the 3G UMTS all-IP Release 4 networks planning problem, denoted as ALLIPR4PP, is shown in Fig. 2. Due to the complexity of the model, only a summarized version is presented. Interested readers may consult the Appendix for more details about the mathematical model formulation. The objective of the model is to minimize the total cost of the network while respecting a set of constraints. The network cost (as shown in Eq. (A3) from the Appendix) includes the cost for the links, interfaces and the nodes. Uniqueness constraints limit the number of equipment that can be installed at a given site. This makes an analogy to the amount of available rack space at a given location. Although this can be changed, our formulation enforces only one equipment per given site. Assignment constraints impose that a lower layer node will be connected to at least one upper layer node. In the proposed formulation, a tree topology was used to connect all network elements (other topologies can also be used by replacing a few of these constraints). Capacity constraints make sure that the amount of traffic going through a piece of equipment will never exceed the capacity of that equipment. For example, a given type of router has a fixed number of ports and, as a result, can only accommodate a limited number of links. For every network element, the traffic flow conservation constraints state that the incoming traffic should be equal to the outgoing traffic. Finally, additional constraints make sure

Node B traffic record is a set of different aspects for voice and data traffics. Considering Node B’s subscribers, such record is calculated using the subscriber traffic profile and different planning parameters. This information is usually given by the operator and might vary subject to traffic forecast and planning strategies. Example values are discussed later in Section 6. Examples of traffic record for two Node Bs are shown in Table 1. The number of subscribers covered by the Node B is randomly generated and tabulated in column 2. Busy Hour Call Attempts, in column three, show the number of calls made by Node B subscribes at Busy Hour (BH). The number of CS traffic channels and the associated CS traffic bandwidth are shown in columns 4 and 5 respectively. PS traffic bandwidth in column 6, represents the bandwidth required for data services of the Node B subscribers. We suppose that a specific ratio of subscribers use data services (attached subscribers) in BH, and furthermore, a

Fig. 2. Summarized version of the mathematical model.

Table 1 Examples of traffic record. Node B index

Subscriber (c0)

BHCA (c1)

CS channels (c2)

CS BW (Mbps) (c3)

PS BW (Mbps) (c4)

Attached subscribers (c5)

Simultaneous PDP context (c6)

Signaling (Mbps) (c7)

1 2

11,180 8089

7090 5130

257 191

6 5

2 1

2236 1617

280 203

0.56 0.40

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all variables are connected and non-negativity and integrality constraints limit the domain of the variables. Since the exact mathematical model (summarized in Fig. 2 and fully described in Appendix) is NP-hard, approximate algorithms are required.

4. Heuristics for the design problem Due to its complexity, the exact model will only work for small instances of the problem. As a result, heuristic algorithms are used such that a trade-off can be made between solution quality and execution time. In practice, a mobile network planner would use the heuristic algorithm instead of the exact model for complexity reasons. Different heuristics such as simulated annealing, genetic algorithm, and tabu search have already been tested to solve UMTS (Release 99) network planning problem in [47]. The authors found that tabu search outperforms the other two heuristics. As a result, this section proposes a local search (LS) and a tabu search (TS) heuristics. 4.1. Local Search heuristic The proposed local search, as shown in Fig. 3, starts with an initial solution in which all NEs (i.e. RNCs, MGWs, MSSs, SGSNs, GGSNs, edge routers/CS routers/PS routers) are installed with their most powerful type. To design interconnecting links, we split the global problem into eight assignment sub-problems: the Node B to edge router, the edge router to RNC, the edge router to CS router, the edge router to PS router, the CS router to MGW, the CS router to MSS, the PS router to SGSN and the PS router to GGSN. Any of these assignment sub-problems is NP-hard and to solve them, we use shortest augmentation path algorithm LAPJV [50] as proposed in [43]. The objective of all these sub-problems is to minimize the cost of the interconnecting links between the lower and the higher level nodes. The number and type of the interconnecting links and interfaces for a node are proportional to the volume of traffic going through the node. LAPJV starts from the first sub-problem, uses the cost matrix of the interconnection links among the lower layer to

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the upper layer node and finds the cost-optimal interconnections. A similar procedure is applied over the rest of the sub-problems. As a result, an initial solution is found. If the initial solution does not respect all constraints, it is unfeasible and the program is terminated. Otherwise, the solution is feasible and its cost is calculated and stored as the best-cost found so far. This solution is also stored as the current solution. The second step is to explore the neighborhood of the current solution which is formed by applying any of the following transformation operations over the current solution:

1. Removing a NE (i.e. RNCs, MGWs, MSSs, SGSNs, GGSNs, edge routers/CS routers/PS routers) that is already installed. 2. Changing the type of a NE (i.e. RNCs, MGWs, MSSs, SGSNs, GGSNs, edge routers/CS routers/PS routers) that is already installed. At each iteration, LS determines the best move. If the best move results in a cost that is lower than the best cost found so far, then the move is performed and a new solution is reached. Otherwise, a local minimum is found and the best solution stored in memory is returned. Local search will keep exploring the neighborhood of the current solution as long as improvement can be made. 4.2. Tabu search heuristic The first step in TS, as shown in Fig. 4, is to find a feasible initial solution. One clever way to do this consists to use the final solution produced by the local search. This solution (i.e. current solution) and its cost (i.e. best-cost) are kept in memory for further improvements. The next step is to determine the best move in the neighborhood of the current solution. The following types of move can be made from a current solution:

1. Remove a NE (i.e. RNCs, MGWs, MSSs, SGSNs, GGSNs, edge routers/CS routers/PS routers) that is already installed.

Fig. 3. Local search algorithm.

Fig. 4. Tabu search algorithm.

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Fig. 5. Potential locations for the illustrated example.

2. Add a NE (i.e. RNCs, MGWs, MSSs, SGSNs, GGSNs, edge routers/CS routers/PS routers) of type t. 3. Change the type of a NE (i.e. RNCs, MGWs, MSSs, SGSNs, GGSNs, edge routers/CS routers/PS routers) that is already installed. At each iteration, TS determines the best move while considering the tabu list and the aspiration criteria. TS configuration parameters are problem specific and are acquired through multiple tests. Selecting a proper duration for tabu conditions is important. It was shown that assigning a very small number to tabu life time, causes cycling, but as this number is increased, the probability of visiting several good solutions increases. However, the tabu life time should not be a very large number, because it then becomes less probable to find good local minimum for lack of available moves [51]. It is also shown that randomly selecting the tabu life time can direct the search towards good solutions [52]. To that end, the number of iterations is randomly chosen between a lower bound (L) and an upper bound (U). Due to this randomness, running the algorithm for multiple times can yield different solutions. As a result, this paper uses a multi-start TS algorithm as proposed in [46].

5. Illustrative example In this section, we solve a sample problem using the local search, tabu search, and the integer programming methods. An illustrative example is given in Fig. 5, comprising of 45 installed Node Bs, five potential sites to install the edge routers (RNCs), five potential sites to install the CS routers (MGWs/MSSs) and five potential sites to install the PS routers (SGSNs/GGSNs) (i.e. 9S1 9 ¼ 5, 9S2 9 ¼ 5 and 9S3 9 ¼ 5) within an area of 400 km2. Three types of NEs (i.e. RNCs, MGWs, MSSs, SGSNs, GGSNs, edge routers, CS routers, PS routers) and four types of links (interfaces) are available with the features presented in Tables 2–7. These values are considered based on practical work experience of the first author with different mobile operators. The upto-date values for these parameters in real market might vary in time with respect to what is presented in this paper.

Table 2 Features of the RNC types. Design Factor

Type A

Type B

Type C

Capacity (channels) Capacity (BHCA) Capacity (Mbps) No. of edge router interfaces Cost ($)

181,000 147,000 1950 12 100,000

284,000 231,000 2800 16 150,000

463,000 443,000 3600 32 250,000

Table 3 Features of the MGW types. Design Factor

Type A

Type B

Type C

Capacity (channels) Capacity (BHCA) No. of CS router interfaces Cost ($)

4048 200,000 12 200,000

12,600 600,000 16 350,000

22,000 900,000 32 500,000

Table 4 Features of the MSS types. Design Factor

Type A

Type B

Type C

Capacity (Mbps) Capacity (channels) Capacity (BHCA) Capacity (subscribers) No. of CS router interfaces Cost ($)

500 15,000 400,000 400,000 12 300,000

1000 20,000 600,000 600,000 16 500,000

2000 41,500 1,000,000 1,000,000 32 600,000

We used the integer programming method to implement the exact algorithm. In order to do this, CPLEX 12.1 [53] was used with all the default settings. It was seen that CPLEX spent 16,319 s to provide an optimal solution. The returned objective value is $2,833,406 after 44,538,161 iterations and the exploration of 1,078,504 nodes. Fig. 6 is the output from the CPLEX, showing the topology and configuration with two RNCs (one of type A and one of type C), one MGW (of type C), one MSS (of type B), one SGSN (of type A), one GGSN (of type A), two edge routers (one of

M.R. Pasandideh, M. St-Hilaire / Computers & Operations Research 40 (2013) 1991–2003

type A and one of type B), one CS router (of type A) and one PS router (of type A). In the second step, we used local search heuristic to implement approximate algorithm. The designed network with this method is shown in Fig. 7. The network includes: two RNCs (one of type B and one of type C), one MGW (of type C), one MSS (of type B), one SGSN (of type A), one GGSN (of type A), two edge routers (both of type B), one CS routers (of type A) and one PS

Table 5 Features of the SGSN types. Design Factor

Type A

Type B

Type C

Capacity (Mbps) Capacity (PDP context) Capacity (subscribers) No. of PS router interfaces Cost ($)

500 480,000 500,000 12 200,000

750 720,000 750,000 16 300,000

1000 960,000 1,000,000 32 400,000

Table 6 Features of the GGSN types. Design Factor

Type A

Type B

Type C

Capacity (Mbps) Capacity (PDP context) No. of PS router interfaces Cost ($)

333 333,000 12 300,000

666 666,000 16 400,000

1000 960,000 32 500,000

Table 7 Costs of the link and interface types. Type

Interface cost ($)

Link cost ($/km)

DS-1 DS-3 FE GE

300 1500 300 1500

700 1500 700 1500

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routers (of type A). It was calculated that the network cost and CPU time are $2,975,949 and 743 s respectively. In the last step, we used tabu search heuristic to implement an advanced approximate algorithm. As shown in Fig. 8, the network designed by tabu search includes two RNCs (one of type A and one of type C), one MGW (of type C), one MSS (of type B), one SGSN (of type A), one GGSN (of type A), three edge routers (all of type A), one CS router (of type A) and one PS router (of type A). The network cost and CPU time are $2,862,127 and 2427 s respectively. The designed network with TS has an optimized topology with lower cost compared to LS. As a result, we found that the gap of the solution provided by local search is 5.03% from the solution provided by CPLEX, while the solution provided by tabu search has a gap of 1.01% from the optimal solution. Local search and tabu search provide such solutions with much less CPU time compared to CPLEX.

6. Simulations and results We supposed that Node Bs are already installed and their number and locations are known. We also assume that the potential locations for all other NEs (i.e. RNCs, MGWs, MSSs, SGSNs, GGSNs, edge routers, CS routers, PS routers) are known. For traffic modeling, we suppose that the subscriber traffic profile and the planning parameters are known. This information is usually provided by the operator and might vary subject to traffic forecast and planning strategies. The subscriber traffic profile and the traffic planning parameters used in this paper are respectively presented in Tables 9 and 10. These values are considered based on practical work experience of the author with mobile operators and might vary subject to traffic forecast and planning strategies. The Adaptive Multi Rate (AMR) codec is used by voice users. The activity factor of a traffic channel is defined as the percentage of time, where traffic is present in the channel. We suppose that the activity factor for voice is 0.5 (and 0.5 silence), while for CSdata and PS-data traffic the activity factor is 1 and 0.4 respectively. It is supposed that network operators define a monthly limited amount for voice and data traffic per subscriber. The network is supposed to be designed to deliver the required capacity for the

Fig. 6. Solution for the illustrated problem obtained with CPLEX.

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Fig. 7. Solution for the illustrated problem obtained with local search.

Fig. 8. Solution for the illustrated problem obtained with tabu search.

specific number of subscribers. We first started with the subscriber allocation for each Node B. We assigned a random number of subscribers to each Node B in a range of 5000 to 20,000 subscribers. Then, using the subscriber traffic profile and traffic planning parameters, we created a traffic record for each Node B. We supposed that three types are available for each NE (type A, B, and C) and four different types of links/interfaces can be used. It is also supposed that the specifications such as the processing capacity, the interface capacity and cost are given for each type of equipment. Similarly, we assumed that the capacity and cost for all types of the links/interfaces are provided. The cost includes all related costs such as floor space, cables, racks, electric installations, labor, etc. The specifications for the nodes, links and interfaces used in this paper are shown in Tables 2–8. The

up-to-date values for these parameters in real market might vary in time with what is presented in this paper. 6.1. Implementation of the exact algorithm We used the linear programming method for the implementation of the exact algorithm to solve the planning problem of 3G UMTS all-IP Release 4 networks. For this purpose, we developed a Cþþ based program to convert the cost function (i.e. Eq. A3 from the Appendix) and all constraints (i.e. Eqs. A4–A83 from the Appendix) into a linear programming (.lp) file format which can be read by the CPLEX solver. We used CPLEX solver 12.1 with all default setting to solve the problem, under a Linux server with one 2.39 GHZ CPU (AMD

M.R. Pasandideh, M. St-Hilaire / Computers & Operations Research 40 (2013) 1991–2003

Table 8 Features of the router types. Design Factor

Type A

Type B

Type C

Capacity (Mbps) No. of interfaces Cost ($)

2000 32 80,000

4000 48 120,000

8000 64 160,000

Table 9 The subscriber traffic profile. Call type Circuit services Voice Average rate Monthly usage Activity factor

CS Data PS Data

AMR 12.2 Kbps 16 Kbps 64 Kbps 144 Kbps 384 Kbps 300 min 10 min 200 Mbps 100 Mbps 50 Mbps 0.5 1 0.4 0.4 0.4

Table 10 The planning parameters. AMR rate in active mode AMR rate in silent mode Mean holding time Soft handover ratio IP over head Attached subscriber ratio Active BH PDP ratio Average PDP duration Retransmission factor Iub interface blocking factor Iub utilization factor Busy days per month Busy days call ratio Busy hour call ratio

18.9 Kbps 4.5 Kbps 120 s 0.4 0.38 0.2 0.5 900 s 0.25 0.02 0.75 22 0.9 0.1

Opteron Processor 250 family) and 16 GB RAM. Considering the nature of the problem and the high number of constraints, we expected a long computation time. As a result, we set up a Time Limit (TL) of 24 h (86,400 s). This means that after 24 h of computation time, CPLEX will return the best solution found so far. If the problem can be solved within the time limit, then the output of the CPLEX solver is the optimal solution. The solution consists of the number, the location and the type of all NEs, links, interfaces, as well as the topology of access and core networks. The solution also provides the cost and the CPU time for the problem. These costs will be used as benchmark for comparison with the results from the approximate algorithms. 6.2. Implementation of approximate algorithms Among different heuristics, local search and tabu search were implemented to solve the planning problem of 3G UMTS all-IP Release 4 networks. We decided to use the local optimum solution found by LS as the initial solution for TS. For this purpose, we implemented LS and TS both in the same Cþþ based program, such that, a local minimum is first found by LS. Then, the quality of such solution is improved by TS with the hope of finding a global optimum. The program aims to minimize the cost function as presented in Eq. (A3) of the Appendix. We start from the initial solution in which all NEs are installed in all their potential locations with their most powerful type. To design the interconnecting links, we break down the ALLIPR4PP into eight sub-problems: the Node B to edge router, the edge

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router to RNC, the edge router to CS router, the edge router to PS router, the CS router to MGW, the CS router to MSS, the PS router to SGSN and the PS router to GGSN.

6.2.1. Local search Beside the number, type and location of NEs, we require to find the cost-optimal interconnecting topology as a part of the initial solution. We started from the first sub-problem. The link type and capacity between each Node B and edge router is determined based on amount of Node B traffic. Node B’s traffic is ultimately accumulated on the selected edge routers. Knowing the number and types of the links, a cost matrix of interconnection links between the Node Bs and the edge routers is constructed, while considering corresponding constraints. The cost matrix contains several possible assignment combinations and is used as input for LAPJV function to find the costoptimal interconnections between all Node Bs and the edge routers. Once the solution of the first sub-problem is found, the upcoming sub-problems are similarly tackled. Once the eight subproblems are solved, the obtained solution will be the current solution. The cost of the current solution is then calculated and is stored as the best cost found so far. The second step consists of exploring the neighborhood of the current solution. For this purpose, a move is made and is accepted, if it has a lower cost than the best cost found so far. Otherwise, LS will suppose that no further improvement can be made and will stop. At this point a local minimum is found and ultimately, the current solution will be the final solution. To execute LS, we used Linux gþþ compiler with the same platform as before.

6.2.2. Tabu search The local minimum found by LS is used as the initial (current) solution for TS. The current solution and its cost are respectively known as the best solution and the best cost. For further improvement, TS determines the best move in the neighborhood of the current solution. The best move is chosen based on tabu list and aspiration criteria. TS performs three types of moves: (i) remove a NE, (ii) add a NE and (iii) change the type of a NE. We configured TS with the following parameters:

 Tabu life time in tabu list randomly chosen between 5 and 9.  Maximum number of iterations (max_iter)¼100.  Maximum number of start (max_start) ¼2. To chose the tabu life time, different values are tested and the optimum results were obtained with a random number between 5 and 9. To fix a value for the number of iterations, we repeated the search for several times. In fact, the main improvement was happened in the early iterations. We set an upper bound of 100 iterations to fit for all set of problems. It was also seen that, with running the tabu program for more than two times, minor quality improvement is achieved over some problems, in the expense of longer CPU time. TS performs 100 iterations for two times. At each iteration, the current solution is compared with the best solution found so far. When the whole search is completed, the best solution is returned as the final solution. The solution consists of the number, the location and the type of all NEs, type and number of the links and interfaces, as well as the topology of access and core networks. The solution also includes the cost and the CPU time for the solution. Similar to LS, we used Linux gþþ compiler with the same platform as before.

2000

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6.3. Numerical analysis To the best of our knowledge, the global planning problem of UMTS Release 4 considering an all-IP infrastructure and a realistic traffic has not been considered so far. As a result, there is no other work to compare with. However, for the sake of comparison, we used the reference model (CPLEX) in order to evaluate the performance of the proposed heuristics. For this purpose, 30 different problem sizes were randomly generated within an area of 100 km2 or 400 km2, representing small and large scale problems. Table 11 shows the numerical results where the first three columns represent respectively the problem number, the size of the area, and the number of Node Bs that are already installed. 9S1 9 is the number of potential locations for the edge router (RNC) and is presented in column 4. Similarly, 9S2 9 and 9S3 9 in the 5th and 6th columns show respectively the potential locations for CS router (MGW/MSS) and PS router (SGSN/GGSN). The following two columns provide the results obtained by the MIP solver (CPLEX). Then, the three subsequent columns show the best solution, the corresponding CPU time, and the gap obtained with the local search respectively. Similarly, the last three columns show the best solution, the corresponding CPU time, and the gap obtained with the tabu search respectively. By comparing the three methods, we can see that CPLEX always find the solutions with the lowest cost even when the time limit is reached. In fact, LS was never able to find the lowest cost while TS found the lowest cost at four different times. In terms of CPU time, we can see that the values from CPLEX are much more spreaded than the other two methods. To that end, LS and TS seem a lot more predictable. On average, LS is the fastest one followed by TS and then CPLEX. We can also notice that for

relatively small problem sizes, CPLEX is very fast, even faster than LS and TS. However, as we increase the problem size, we can clearly see that the execution time from CPLEX is almost growing exponentially. In fact, CPLEX was not able to optimally solve the last five problems within the time limit. As a result, CPLEX does not seem suitable for larger instances of the problem. To further study the results from Table 11, Fig. 9 shows a pair of box and whisker plots, one for the cost and one for the CPU time. These plots show, for each of the three methods, the range of values, the 25th percentile, the median (shown by the dividing line in the box), and the 75th percentile. From the figure, it is clear that the local search is not as competitive in terms of cost with an average cost of $2,971,063 versus $2,789,407 for CPLEX and $2,890,064 for TS. In terms of CPU time, the CPLEX method is definitely not practical as shown by the wide range of values. It is also important to remember that a time limit of 86,400 s was set so without this limit, we could expect to have even larger values. We can also notice that the median is slightly closer to the lower part of the box indicating that lower ratio counts are more concentrated. This also means that the distribution is slightly skewed towards higher values. Fig. 9(b) also shows that the outliers can be very large, especially with CPLEX, even when the medians are not much different. 6.4. Statistical analysis In order to generate better statistics, we randomly generated four instances of each problem size (shown in Table 11) for a total of 120 different problems. Out of these 120 problems, CPLEX and tabu search were able to provide the optimal solution for 92 (77%) and 19 (16%) problems respectively, while no optimal solution was found by the local search.

Table 11 Numerical results. CPLEX 2

9S1 9

Local search

9S2 9

9S3 9

Cost ($)

5 5 5 5 5

5 5 5 5 5

5 5 5 5 5

1,462,335 1,499,105 1,760,827 1,850,368 2,100,229

152 54 1,435 945 1,893

1,499,944 1,520,426 1,776,100 1,974,095 2,221,985

35 40 45 50 55

5 5 5 5 5

5 5 5 5 5

5 5 5 5 5

2,444,225 2,514,815 2,788,062 2,877,196 3,133,179

4026 434 650 898 3,839

400 400 400 400 400

60 65 70 75 80

5 5 5 5 5

5 5 5 5 5

5 5 5 5 5

3,233,417 3,274,512 3,320,597 3,576,809 3,551,323

16 17 18 19 20

100 100 100 100 400

10 15 20 25 30

10 10 10 10 10

5 5 5 5 5

5 5 5 5 5

21 22 23 24 25

400 400 400 400 400

35 40 45 50 55

10 10 10 10 10

5 5 5 5 5

26 27 28 29 30

400 400 400 400 400

60 65 70 75 80

10 10 10 10 10

5 5 5 5 5

Area (km )

Node B

1 2 3 4 5

100 100 100 100 400

10 15 20 25 30

6 7 8 9 10

400 400 400 400 400

11 12 13 14 15

Problem

CPU (s)

Gap (%)

Cost ($)

200 285 373 458 540

2.58 1.43 0.87 6.69 5.80

1,462,335 1,500,627 1,760,827 1,944,718 2,145,767

220 322 462 743 1014

0 0.11 0 5.10 2.17

2,596,044 2,599,864 2,975,949 3,007,039 3,354,674

605 715 743 858 934

6.22 3.39 6.74 4.52 7.07

2,472,978 2,574,839 2,862,127 2,931,825 3,295,990

1196 1955 2427 2134 3732

1.18 2.39 2.66 1.90 5.20

48,275 13,291 30,260 45,666 78,102

3,441,074 3,498,771 3,551,861 3,819,732 3,771,826

938 1093 1137 1241 1174

6.43 6.85 6.97 6.80 6.21

3,413,646 3,440,937 3,479,220 3,791,646 3,737,246

4333 3535 4064 7094 6299

5.58 5.09 4.78 6.01 5.24

1,455,778 1,498,893 1,744,211 1,851,255 2,083,141

507 3,069 869 19,165 832

1,469,132 1,518,248 1,792,572 1,962,585 2,218,899

1356 2015 2724 3250 3844

0.92 1.30 2.78 6.02 6.52

1,456,191 1,498,893 1,744,211 1,945,253 2,123,207

1391 2071 2849 3638 4463

0.03 0 0 5.08 1.93

5 5 5 5 5

2,406,642 2,458,280 2,790,753 2,861,354 3,089,932

32,327 2,713 1,424 1,550 3,284

2,505,148 2,627,218 3,050,053 2,966,178 3,321,133

4506 5035 5524 6083 7987

4.10 6.88 9.30 3.67 7.49

2,431,723 2,572,914 2,918,001 2,923,737 3,286,329

5004 6046 7066 7650 11,775

1.05 4.67 4.56 2.19 6.36

5 5 5 5 5

3,146,851 3,195,625 3,408,300 3,405,885 3,517,579

86,400 86,400 86,400 86,400 86,400

3,430,440 3,376,065 3,592,251 3,557,004 3,737,430

7458 7935 8360 8768 9206

– – – – –

3,260,640 3,339,825 3,528,878 3,549,322 3,714,285

11,239 11,236 13,904 18,321 18,649

– – – – –

(TL) (TL) (TL) (TL) (TL)

Cost ($)

Tabu search CPU (s)

CPU (s)

Gap (%)

M.R. Pasandideh, M. St-Hilaire / Computers & Operations Research 40 (2013) 1991–2003

2001

Fig. 9. Box and whisker plots for (a) the cost and (b) the CPU time.

Table 12 Solution gap comparison for the total simulations. Algorithm

Min. gap (%)

Max. gap (%)

Ave. gap (%)

Standard deviation (%)

95% Confidence interval (%)

Local search Tabu search

0.27 0.00

11.31 7.51

4.98 2.82

2.73 2.20

4.98 7 0.56 2.82 7 0.45

Table 13 CPU time comparison for the total simulations.

Algorithm

Min. CPU (s)

Max. CPU (s)

Ave. CPU (s)

Standard deviation (s)

95% Confidence interval (s)

Local search Tabu search CPLEX

196 216 31

8108 11,775 85,242

2032 3256 15,515

2042 2631 21,925

20327 417 3256 7538 15,515 74480

The statistical cost analysis is presented in Table 12. In this analysis, we have just considered the problems which CPLEX was able to find the optimal solutions. We can state that with 95% confidence, local search provides a solution which its true mean gap is within the interval [4.42, 5.54]. Similarly, tabu search has 95% confidence that the true mean solution gap is within the interval [2.37, 3.27]. We can summarize that TS provides a better solution quality compared to LS. In fact, TS is able to provide the average gap of 2.82% on network cost which shows 43% improvement compared to LS (4.98%). We also performed statistical CPU time analysis as shown in Table 13. We can state that with 95% confidence, tabu search provides a better solution with a mean CPU time within the interval [2,718, 3,794] s. We can also conclude that CPLEX will require a lot more time to solve some of the problems which faced time limit and were stopped before optimal solution. For example, consider a complex planning problem for which the solution is obtained in 2 days by using CPLEX. If the planner decides to optimize the solution by examining 10 different settings, it will require 20 days to find the best solution with CPLEX. Instead, by using approximate algorithms (local search and tabu search in this paper), the best solution will be reached in much shorter time which justifies the use of approximate algorithms for large problem sizes.

profile. The aim of the model is to design the network topology which can provide a satisfactory level of service to the subscribers with minimum network cost. More precisely, the model selects the location and the type of the NEs (i.e. RNCs, MGWs, MSSs, SGSNs, GGSNs, edge routers, CS routers, PS routers), their links and interfaces, as well as the access and core topologies. As a second contribution, we proposed metaheuristics to solve the design problem of the model. In fact, we adapted the local search and the tabu search metaheuristics to our specific problem and developed planning tools to solve the design problem. These algorithms use the global approach and consider the access and core network planning subproblems simultaneously. During the simulations, 120 problems were randomly generated and solved with the proposed algorithms. In order to assess the performance of those algorithms, we compared the results with the optimal solutions obtained from a MIP solver (CPLEX). The results demonstrated that the local search is able to find solutions that, with 95% confidence, the true mean gap is within the interval of [4.42%, 5.54%] from the optimal solutions. Further improvement was achieved by employing the tabu search. With 95% confidence interval, tabu search provided solutions where the true mean gap lies within the interval of [2.37%, 3.27%] from the optimal solutions. Comparing results from the local search and tabu search with the exact algorithm, we realized that the main advantage of such metaheuristics is the low CPU time. Therefore, larger problem sizes can be tackled.

7.1. Limitations To the best of our knowledge, the cost optimization method discussed in this paper has not been implemented in industry yet. As listed below, several issues could potentially prevent the approach from being applied

 Although the model is already quite complex, it is still a

 7. Conclusion In this paper, we introduced a new mathematical model in order to plan 3G UMTS all-IP Release 4 networks with realistic traffic

simplified model of a real life network. For example, the model is based on traffic prediction and a given wave propagation model. This could be an issue if predictions are not good, or if wave do not behaves as predicted, and could result in sporadic network quality problems at different places in the network. Other issues that are not considered in the planning model are the notions of survivability, quality of service, etc. Due to the high cost of equipment, most service providers will deploy their network in a progressive manner and will try to reuse as much as possible from their previous network. In fact, green field deployments only occur sporadically. As a result, models dealing with the expansion/update of the network are

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also required. However, it is important to note that an expansion model is a generalization of the planning problem. Finally, another limitation concerns the structural organization of service providers. Usually, service providers will have different departments dealing with different parts of the network. For example, they will have a department focusing on the radio part (i.e. positioning and configuring the base stations) and different departments will take care of deploying/managing the access and core networks. Since our model is dealing simultaneously with all aspects, it would require a lot of interaction between the departments which is not always possible.

7.2. Future work Nowadays, network updates are much more frequent that designing a green field network. A potential future work can include the adaptation of the model to cover update problems by modifying the search procedure. Investigating different heuristics such as simulated annealing, genetic algorithm and other hybridmetaheuristics to solve the planning problem may be another potential research direction. Finally, we are also planning to adapt the current model to higher releases. In fact, UMTS Release 4 is the base model for higher 3GPP network releases through accommodating new multimedia servers in the core network. This means that the proposed model can be easily adopted to support new releases. In fact, the support of voice services in Long Term Evolution (LTE) can benefit from the architecture of Release 4. In the method known as CS fallback, LTE voice traffic is routed to the existing CS network (via UMTS for example) and there is no need to implement the IP Multimedia Subsystem (IMS). Voice in LTE can also be implemented through IMS, Voice Over LTE via Generic Access (VOLGA2) or a proprietary solution. There are evidences in the market that some operators are reluctant to spend money and deploy IMS, while they can use their existing CS infrastructure. Moreover, all UMTS releases keep the general topology architecture of GPRS for their packet switch network. From a topology point of view, the packet core of LTE, known as Evolved Packet Core (EPC), has similarities to the architecture of the PS domain in the proposed model. For example, SGSN and GGSN have been replaced by Mobility Management Entity (MME) and Serving Gateway (SGW) in LTE. For these reasons, the proposed model is adaptable to higher UMTS releases.

Appendix A. Supplementary data Supplementary data associated with this article can be found in the online version at http://dx.doi.org.10.1016/j.cor.2013.02.017.

References [1] Mishra AR, editor. Fundamentals of cellular network planning and optimisation 2G/2.5G/3Gy evolution to 4G. John Wiley & Sons Ltd; 2004. [2] 3GPP, Universal mobile telecommunication system (UMTS): QoS concept and architecture. 3GPP. Technical Report 23.107 v5.5.0. [3] Dixit S, Prasad R, editors. Wireless IP and building the mobile Internet. Artech House; 2002. [4] Chen Y-K, bing Lin Y. IP connectivity for gateway GPRS support node. IEEE Wireless Communications 2005;12(February (1)):37–46. [5] Castro JP. The UMTS development platform. John Wiley & Sons, Ltd; 2001 p. 41–82. [6] Kalvenes J, Kennington J, Olinick E. Base station location and service assignments in W-CDMA networks. INFORMS Journal on Computing 2006;18: 366–76.

2

http://www.volga-forum.com/.

[7] Olinick EV, Rosenberger JM. Optimizing revenue in CDMA networks under demand uncertainty. European Journal of Operational Research 2008;186(2):812–25. [8] Thiel SU, Giuliani P, Ibbetson LJ, Lister D. An automated UMTS site selection tool. In: Proceedings of the third international conference on 3G mobile communication technologies; May 8–10, 2002. p. 69–73. [9] Jamaa SB, Altman Z, Picard JM, Fourestie B. Multi-objective strategies for automatic cell planning of UMTS networks. In: Proceedings of the VTC 2004spring vehicular technology conference 2004 IEEE 59th, vol. 4; May 17–19, 2004. p. 2420–4. [10] Choi Y, Kim K, Kim N. The positioning of base station in wireless communication with genetic approach. In: Bestak R, Simak B, Kozlowska E, editors. Personal wireless communications, ser. IFIP international federation for information processing, vol. 245. Boston: Springer; 2007. p. 217–29. [11] Crainic TG, Chiara BD, Nonato M, Tarricone L. Tackling electrosmog in completely configured 3G networks by parallel cooperative metaheuristics. Wireless Communications, IEEE 2006;13(6):34–41. [12] Chen L, Yuan D. Solving a minimum-power covering problem with overlap constraint for cellular network design. European Journal of Operational Research 2010;203(3):714–23. [13] Amaldi E, Capone A, Malucelli F. Planning UMTS base station location: optimization models with power control and algorithms. IEEE Transactions on wireless Communications 2003;2(September (5)):939–52. [14] Yang J, Aydin M, Zhang J, Maple C. UMTS base station location planning: a mathematical model and heuristic optimisation algorithms. Communications, IET 2007;1(5):1007–14. [15] Zdunek R, Ignor T. UMTS base station location planning with invasive weed optimization. In: Proceedings of the 10th international conference on artifical intelligence and soft computing: part II. Berlin, Heidelberg: Springer-Verlag; 2010. p. 698–705. [16] Galota M, Glaber C, Reith S, Vollmer H. A polynomial-time approximation scheme for base station positioning in UMTS networks. In: Proceedings of the 5th international workshop on discrete algorithms and methods for mobile computing and communications. New York, NY, USA: ACM; 2001. p. 52–9. ¨ ¨ [17] Eisenblatter A, Fugenschuh A, Koch T, Koster A, Martin A, Pfender T, Wegel O, ¨ R. Modelling feasible network configurations for UMTS. In: AnandaWessaly lingam G, Raghavan S, editors. Telecommunications network design and management. Kluwer; 2002. p. 1–24. [18] Amaldi E, Capone A, Malucelli F. Discrete models and algorithms for the capacitated location problems arising in UMTS network planning. In: Proceedings of the 5th international workshop on discrete algorithms and methods for mobile computing and communications. New York, NY, USA: ACM; 2001. p. 1–8. [19] Amaldi E, Capone A, Malucelli F. Improved models and algorithms for UMTS radio planning. In: Proceedings of the VTC 2001 fall vehicular technology conference IEEE VTS 54th, vol. 2; October 7–11, 2001. p. 920–4. [20] Amaldi E, Capone A, Malucelli F, Signori F. UMTS radio planning: optimizing base station configuration. In: Proceedings of the VTC 2002-fall vehicular technology conference 2002 IEEE 56th, vol. 2; September 24–28, 2002. p. 768–72. [21] Amaldi E, Capone A, Malucelli F, Signori F. Optimization models and algorithms for downlink UMTS radio planning. In: Proceedings of the IEEE wireless communications and networking WCNC 2003, vol. 2; March 16–20, 2003. p. 827–31. [22] Amaldi E, Capone A, Malucelli F, Signori F. A mathematical programming approach for W-CDMA radio planning with uplink and downlink constraints. In: Fall vehicular technology conference (VTC 2003), vol. 2. October 6–9, 2003. p. 806–10. [23] Amaldi E, Capone A, Malucelli F, Signori F. Radio planning and optimization of W-CDMA systems. In: Personal wireless communications, ser. Lecture notes in computer science. Springer Berlin Heidelberg, vol. 2775; 2003. p. 437–47. [24] Jamaa SB, Altman Z, Picard J-M, Fouresti B, Mourlon J. Manual and automatic design for UMTS networks. Mobile Networks and Applications 2004;9:619–26. [25] Sohn S, Jo G-S. Optimization of base stations positioning in mobile networks. In: Gavrilova M, Gervasi O, Kumar V, Tan C, Taniar D, Lagan A, Mun Y, Choo H, editors. Computational science and its applications—ICCSA 2006, ser. Lecture notes in computer science, vol. 3981. Berlin, Heidelberg: Springer; 2006. p. 779–87. [26] Mathar R, Schmeink M. Optimal base station positioning and channel assignment for 3G mobile networks by integer programming. Annals of Operations Research 2001;107:225–36. [27] Harmatos J, Juttner A, Szentesi A. Cost based UMTS transport network topology optimization. In: Proceedings of the international conference on computer communication ICCC 1999; 1999. [28] Harmatos J, Szentesi A, Godor I. Planning of tree-topology UMTS terrestrial access networks. In: Proceedings of the 11th IEEE international symposium on personal, indoor and mobile radio communications PIMRC 2000, vol. 1; September 18–21, 2000. p. 353–7. [29] Lauther U, Winter T, Ziegelmann M. Proximity graph based clustering algorithms for optimized planning of UMTS access network topologies. In: Proceedings of the 10th international conference telecommunications ICT 2003, vol. 2; 2003. p. 1329–34. [30] Krendzel A, Koucheryavy Y, Harju J. Radio access network topology planning for the 4G networks. In: Proceedings of the 5th European wireless conference, Barcelona, Spain; 2004.

M.R. Pasandideh, M. St-Hilaire / Computers & Operations Research 40 (2013) 1991–2003

[31] Juttner A, Orban A, Fiala Z. Two new algorithms for UMTS access network topology design. European Journal of Operational Research 2005;164: 456–74. [32] Wu Y, Pierre S. A new hybrid constraint-based approach for 3G network planning. IEEE Communications Letters 2004;8(May (5)):277–9. [33] Tipper D, Dahlberg T, Shin H, Charnsripinyo C. Providing fault tolerance in wireless access networks. IEEE Communications Magazine 2002;40(January (1)):58–64. [34] Charnsripinyo C, Tipper D. Topological design of 3G wireless backhaul networks for service assurance. In: Proceedings of the 5th international workshop on design of reliable communication networks (DRCN 2005); October 16–19, 2005. p. 9. [35] Szlovencsak A, Godor I, Harmatos J, Cinkler T. Planning reliable UMTS terrestrial access networks. IEEE Communications Magazine 2002;40(January (1)):66–72. [36] Krendzel A, Koucheryavy Y, Harju J. Cost and reliability estimation of radio access network structures for 4G systems. In: Proceedings of the VTC 2003fall vehicular technology conference 2003 IEEE 58th, vol. 4; October 6–9, 2003. p. 2297–2301. [37] Shalak R, Sandrasegaran K, Agbinya J, Subenthiran S. UMTS core network planning model and comparison of vendor product performance. In: The 6th international conference on advanced communication technology, vol. 2; 2004, p. 685–9. [38] Ricciato F, Pilz R, Hasenleithner E. Measurement-based optimization of a 3G core network: a case study. In: Koucheryavy Y, Harju J, Iversen V, editors. Next generation teletraffic and wired/wireless advanced networking, ser., Lecture notes in computer science, vol. 4003. Berlin, Heidelberg: Springer; 2006. p. 70–82. [39] Harmatos J. Planning of UMTS core networks. In: Proceedings of the 13th IEEE international symposium on personal, indoor and mobile radio communications, vol. 2; September 15–18, 2002. p. 740–4. [40] Ouyang Y, Fallah MH. Evolving core networks from GSM to UMTS R4 version. International Journal of Mobile Network Design and Innovation 2009;3(January): 93–102.

2003

[41] Zhang J, Guo L, Wu J. An integrated approach for UTRAN planning and optimization. In: Vehicular technology conference; 2004. VTC 2004-Spring. 2004 IEEE 59th, vol. 4; May 2004. p. 2360–4. [42] Chamberland S, Pierre S. On the design problem of cellular wireless networks. Wireless networks 2005;11(July):489–96. [43] Chamberland S. An efficient heuristic for the expansion problem of cellular wireless networks. Computers & Operations Research 2004;31(October): 1769–91. [44] St-Hilaire M, Chamberland S, Pierre S. Global expansion model for mobile networks. IEEE Communication Letters 2006;10(June (6)):453–5. [45] St-Hilaire M, Chamberland S, Pierre S. Uplink UMTS network design—an integrated approach. Computer Networks 2006;50:2747–61. [46] St-Hilaire M, Chamberland S, Pierre S. A tabu search algorithm for the global planning problem of third generation mobile networks. Computers & Electrical Engineering 2008;34(November):470–87. [47] St-Hilaire M, Liu S. Comparison of different meta-heuristics to solve the global planning problem of UMTS networks. Computer Networks 2011;55(12): 2705–16. [48] St-Hilaire M, Chinneck JW, Chamberland S, Pierre S. Efficient solution of the 3G network planning problem. Computers and Industrial Engineering 2012;63(4):819–30. [49] Pasandideh MR, St-Hilaire M. Automatic planning of UMTS Release 4.0 networks using realistic traffic. In: IEEE international world of wireless mobile and multimedia networks (WoWMoM); 2010. p. 1–9. [50] Jonker R, Volgenant A. A shortest augmenting path algorithm for dense and sparse linear assignment problems. Computing 1987;38(November):325–40. [51] Dro J, Siarry P, Ptrowski A, Taillard E, Jamaa S, Altman Z, et al. Tabu search. In: Metaheuristics for hard optimization. Springer, Berlin Heidelberg; 2006. p. 47–73. [52] Blum C, Aguilera MJB, Roli A, Sampels M. Hybrid metaheuristics: an emerging approach to optimization. 1st ed.Springer Publishing Company, Incorporated; 2008. [53] IBM, ILOG CPLEX v12.1, User Manual for CPLEX, IBM, Inc.; 2009.