Evaluation of the potential for energy saving in macrocell and femtocell networks using a heuristic introducing sleep modes in base stations
© Vereecken et al; licensee Springer. 2012
Received: 30 August 2011
Accepted: 15 May 2012
Published: 15 May 2012
In mobile technologies two trends are competing. On the one hand, the mobile access network requires optimisation in energy consumption. On the other hand, data volumes and required bit rates are rapidly increasing. The latter trend requires the deployment of more dense mobile access networks as the higher bit rates are available at shorter distance from the base station. In order to improve the energy efficiency, the introduction of sleep modes is required. We derive a heuristic which allows establishing a baseline of active base station fractions in order to be able to evaluate mobile access network designs. We demonstrate that sleep modes can lead to significant improvements in energy efficiency and act as an enabler for femtocell deployments.
Compared to the different wired access network technologies, mobile access networks are significantly less energy efficient . In light of ICT being estimated to be responsible for about 2-4% of the worldwide carbon emissions [2, 3], this is an important challenge and energy efficiency is a key design parameter for current and future mobile access networks.
On the other hand, in mobile communications the user bit rate demand is ever increasing. In the past, mobile access networks were mainly used for voice and text communication, However, data communications are rapidly increasing and currently responsible for the larger part of the traffic on mobile access networks .
The above trends pose an important challenge for the future mobile access network. On the one hand, it needs to sustain the increasing user demand, which corresponds with deploying an increasing number of base stations, while at the same time it is required to limit carbon emissions and energy consumption.
One solution is the optimisation of the base stations in order to make them more energy efficient. Also, new network technologies like long term evolution (LTE)  are emerging, which will allow higher bit rates as well as higher ranges to provide these bit rates. It is however questionable whether these solutions will suffice since the rising bit rate demand implies a drastic increase in the number of base stations. Thus, solutions that reduce the power consumption of a mobile access network as a whole are required.
When optimising a system for energy efficiency, the introduction of sleep modes is one of the most commonly used approaches and is already well known in other wireless communication systems such as sensor networks . In this article, we will demonstrate the introduction of sleep modes is essential if we want to deploy mobile access networks with a high coverage for large bit rates. Moreover, we will provide a method to establish the best-effort active base station fraction in such a network. We will limit our discussion to LTE implementations as this is the emerging standard designed for high bit rate applications . This can be used as a baseline to evaluate the energy efficiency of practical implementations.
In Section 2, we elaborate on the work related to our study. In Section 3, we discuss the base station behaviour. This is used as an input for a heuristic to find an optimal distribution of active base stations, which is derived in Section 4. We apply the heuristic on a theoretical topology to evaluate the active base station fraction (Section 5) and then evaluate the environmental impact of the different design choices (Section 7). Afterwards, in Section 8 we demonstrate the use of the heuristic in a topology designed for an urban environment. In Section 9 we summarise the main conclusions.
2 Related work
Sleep modes in wireless networks are already used in multiple situations. For example, the requirement of providing a certain coverage while certain nodes can sleep is a well known problem in sensor networks [7, 8]. The authors of  give a good overview of the different techniques that can be used in wireless contexts. Due to the requirement for long battery life times, sleep modes were also introduced in the mobile subscriber devices [9, 10].
In this article, we are focussing on the mobile access network and more specifically the base station. In some studies, it is suggested to reduce the carbon footprint of a base station by using renewable energy sources [11, 12]. Although this effort is viable in itself, it doesn't improve the energy consumption of the mobile access network. Other authors make improvements on the base stations themselves . These efforts are viable but, as we will demonstrate, optimisations in the network as a whole are possible as well.
In terms of introducing sleep modes in base stations, some solutions are already suggested. Some authors make the distinction between micro-sleep where base stations are only shortly suspended and deep-sleep where users need to connect to different base stations in order to maintain connectivity [14, 15]. In this study we do not consider these micro-sleep modes. Also, in , it is demonstrated that sleep modes are an enabler for introducing small cell base stations and low power mobile access networks. In [17, 18], a similar exercises are performed to evaluate the switching off of macrocells in order to limit power consumption of the access network. In the above cited studies, the network optimization is performed without taking into account the user behaviour. However, the authors of  propose an algorithm in which also the requirements of the users are accounted for.
Another approach which is used is the so called cell zooming where during low use periods base stations are turned off and only lower bit rates are fully covered [20, 21]. This technique however only allows a limited fraction of base stations to be switched off and reduces the level of service for the users since the approach does not account for user behaviour.
In the above cited studies, the focus is on the optimization of current network deployments. As such, the performance evaluation of the solution is based on an always-on network. In this study, we would like to investigate the question on the maximum number of sleeping base stations while guaranteeing the required connectivity for the users. This while taking into account the future high bit rate requirement of the users. This question is relevant as the future mobile access network will require a significant increase in energy efficiency.
Based on this result, one can establish a baseline to assess the energy efficiency of future practical implementations. We will demonstrate that for these high bit rate mobile access network, a disruptive approach with large idle base station fractions is possible and necessary. Moreover, we offer a heuristic on the basis of which algorithms and protocols for this future mobile access network can be designed.
3 Characterisation of base stations
When characterising the power consumption of a mobile network, one needs to consider that the power consumption of the base station is more or less constant. This is a direct consequence of the input power of the antenna, which directly defines the power consumption, being kept at a constant level [22, 23]. On the other hand, the range of the base station varies depending on which bit rate is needed. The range and the bit rate are thus strongly correlated. When deploying a mobile network for a certain bit rate, this will have consequences for the base station density and thus for the overall power consumption of a network.
To determine the range of a base station, first the maximum allowable path loss to which a transmitted signal can be subjected while still being detectable at the receiver, is calculated . Therefore, a link budget has to be set up. A link budget takes all the gains and the losses from the transmitter through the medium to the receiver into account. When the maximum allowable path loss is known, the range can be determined by using a propagation model. Different propagation models exist and the propagation model used depends on the design parameters (e.g. indoor vs. outdoor, macrocell vs. femtocell base station, urban vs. suburban vs. rural area, etc.). In this study, we focus on macrocell and femtocell base stations. For the macrocell base station we used the Erceg C model , while for the femtocell base station the ITU-R P.1238 model is used . For both the macrocell and the femtocell we assume a frequency of 2.6 GHz as defined in the LTE standard. We assume the macrocell to transmit at 43 dBm, whereas femtocells transmit at 21 dBm.
When determining the bit rate at which we want to evaluate the range, two parameters are key: the receiver signal-to-noise ratio (SNR) and the channel bandwidth. The receiver SNR represents the SNR at the receiver for a certain bit error rate (BER) and is determined by the used modulation scheme and coding rate.
The modulation scheme provides the translation of a binary bit stream into an analogue signal that can be transmitted through the medium. This is done shifting both amplitude and phase of the signal, a number of distinct modulations result in the modulation scheme. LTE supports three modulation schemes: quadrature phase shifting keying (QPSK) shifting only on phase and allowing 2 bits (4 values) per symbol and 16-QAM and 64-QAM (quadrature amplitude modulation), shifting both amplitude and phase allowing for 4 bits (16 values) and 6 bits (64 values) per symbol, respectively.
The modulation scheme is always accompanied by a coding rate that allows to determine if there are any errors introduced in the signal during transmission. This is done by adding redundant bits to the signal. The coding rate is the number of real information bits divided by the total number of bits. For example, a coding rate of 2/3 implies that for every two information bits one redundant bit is added. In LTE, the following combinations are supported: 1/3 QPSK, 1/2 QPSK, 2/3 QPSK, 1/2 16-QAM, 2/3 16-QAM, 1/2 64-QAM, and 2/3 64-QAM. The higher the coding rate and the higher the modulation, the higher the bit rate, but also the higher the receiver SNR and thus the lower the range becomes. For a macrocell base station in a 5 MHz channel, for example, a range of 1089.9 m is obtained for a bit rate of 2.8 Mbps (1/2 QPSK) and 193.5 m for a bit rate of 16.9 Mbps (2/3 64-QAM).
A second important parameter that influences the bit rate and the range is the channel bandwidth. The channel bandwidth indicates the width of the frequency band used to transmit the data. The higher the channel bandwidth, the higher the bit rate, but the lower the range. For a macrocell base station, the 1/2 QPSK modulation corresponds to a bit rate of 2.8 Mbps and a range of 1089.9 m in a 5 MHz channel, while it corresponds with a bit rate of 11.3 Mbps and a range of 778.7 m in a 20 MHz channel.
Bit rates resulting from modulation schemes, coding rates and channel bandwidths in LTE
4 Heuristic to put base stations in sleep mode
4.1 Determination of the heuristic
In Section 3, we demonstrated that higher bit rates correspond with shorter distances between the user and the base station. Since the bit rate demand is on the rise, mobile networks will be required to provide coverage for these higher bit rates. This implies smaller cell sizes, resulting in a larger number of base stations to cover a certain area and hence larger power consumption. On the other hand, since cell sizes are smaller, there is also a smaller number of users present in a cell and thus the probability of a user requiring the high bit rates in a cell is decreasing. This consideration leads to the opportunity to introduce sleep modes in the network. If all users in a cell can be served by base stations outside the cell, then the base station in the cell is no longer required and can be turned to a sleep mode. Hence, the power consumption of the mobile network can be reduced.
In order to evaluate this opportunity, we designed a heuristic to find a best-effort distribution of base stations to be put to sleep mode in order to minimise power consumption.
This matrix represents the possibilities to provide a user with a suitable connection. In case a row of the matrix P contains only zeroes, this implies that no base station is close enough to the user to provide its demand. Since we can do nothing to serve those users we need to keep them out of the equation.
For the base stations, we assume the capacity limits to be larger than the actual capacity required by the base station. This is a valid assumption since LTE is currently designed providing sufficient resource blocks to cover the expected load. Moreover, this also implies that extending the capacity of base stations is also possible in case our design should require it.
Identify the users with the least potential connections.
Select the base stations to which these users can connect.
Of these base stations, select the base station to which most users can connect and switch it on.
Remove the users that connect to this base station from the heuristic and start over.
By first satisfying the users with the least connections we assure that later on in the algorithm we do not need to switch on an additional base station just to satisfy this one user. On the other hand, by assuring that in each iteration the potential base station satisfying the most users is selected, in each step we maximise the number of users we no longer need to consider. Thus, we simplify the problem and reduce the number of iterations.
In the algorithm, we can implement this by defining an n-dimensional vector S. We initialise this vector on S j = 0 and for each base station that is switched on, we put the value on 1. Since we remove the users that are satisfied at each iteration, the heuristic is stopped once all users are satisfied. The algorithm is denoted in pseudocode in Algorithm 1.
Algorithm 1. Heuristic for a best-effort distribution of sleep modes in a base station topology for minimal power consumption
Z : Z j = Sign (∑i∈IP ij )
C b = C b × Z(*)
Q = P ○ S
for j = 1 → n do
if Q j = 1 then
until ∑ i, j P ij = 0
(*) '×' represents elementwise multiplication.
(**) We select only one base station to be switched on, hence J1.
The heuristic requires information on both the exact location of the base stations and the users, as well as the bit rate requirement of the users. In practical deployments, the user information will not be readily available. Additionally, the user information is only valid at a certain moment in time and is subject to change due to movement and changes in bit rate requirements. Reevaluation on regular intervals for an entire mobile access network could be resource and time intensive.
On the other hand, the heuristic does provide a near-optimal solution for putting deployed base stations in a sleep mode. Hence, it provides a baseline for practical implementations of sleep mode algorithms in mobile access networks to be evaluated against. Also, during the design of a mobile access network, it can provide useful information on the suitability of a topology for the introduction of sleep modes.
4.2 Use of the heuristic in a theoretical case
Next, we define a user density and distribute users randomly in the area covered by the base stations until the required user density is reached. We use a uniform distribution. Since users on the edge of the covered area can reach less base stations than users in the centre, we need to make sure the covered area is large enough to limit this effect.
We have displayed this probability distribution for the different available bit rates for LTE at a channel bandwidth of 5 MHz in Figure 2. One can see how the parameter α defines the distribution. A preference for lower bit rates (α > 0) is typical in a situation where the use of the mobile access network is mainly for voice calls and the use of high bit rate applications like video streaming is limited. Also, cases in which idle users maintain a low bit rate connection with the access network, can be modelled by using a high value for α. Situations where the larger part of the users need to maintain a high bit rate connection with the access network can be modelled with negative values for α.
In Figure 3 we display an example distribution for a user density D U of 500 users/km2 with α = 3 in a femtocell access network operating for a channel bandwidth of 5 MHz. In the access network there are 1951 base stations, covering an area of approximately 1.11 km2. Of these base stations, 42 need to be active in order to provide all users with a connection. This leads to an active base station fraction of 2.15%. In the following discussion, we will denote this as F A expressing the number of active base stations divided by the total number of base stations. Lower values for F A imply more base stations are switched off and thus power consumption is reduced.
5 The active base station fraction F A
5.1 Upper limit for F A
Using the ranges determined in Section 3, in the case of a femtocell network with a 5 MHz channel bandwidth this corresponds with a user density of approximately 1757 users/km2. In comparison, for a macrocell network this limit is already reached at a user density of 10 users/km2.
5.2 Determination of F A through simulation
As one can see in Figure 3, users are not evenly distributed over the surface and some clusters appear. Additionally, the users operating at lower bit rates can connect to base stations at larger distances. Therefore, lower active base station fractions will be possible.
When using femtocells (Figure 4a), even in cases with a large preference for high bit rates (α = -5) the fraction of active base stations is lower than the theoretical maximum. For high values of α, additional savings in the order of 85 to 95% compared to the theoretical maximum are possible. Note however that for α > 3 the probability for a user requiring a high bit rate is so low that the viability of deploying such a dense network is questionable.
It is also important to note the standard deviation on the simulations. Depending on the user distribution the result may vary 2 to 10%. This indicates that the actual fraction of active base stations is difficult to predict.
In the case we use macrocells (Figure 4b), it is also possible to save energy using sleep modes, albeit in the case where lower bit rates are preferred over higher bit rates (α > 0). Active base station fractions of 15-25% for α = 5 can lead to significant reductions in power consumption although the active base station fractions in the order of 50-75% seem more realistic.
6 Evaluation of the heuristic towards optimal solutions
First of all, it is clear that the ILP always provides the optimal solution. Second, for higher base station densities, the heuristic results in a near-optimal solution. For lower densities, there is a significant difference between the heuristic and the ILP. These values are mainly corresponding with α ≥ 4.
This deviation can be explained by the heuristic being designed to first satisfy the users requiring the highest bit rate, and particularly the bit rate defining the base station density. These users are (almost) not present for the high values of α. As such, for every user there is a high number of possible base stations connecting each user and picking one of these base stations will immediately drastically reduce the solution space, possibly excluding the optimal solution.
Although this is a factor to be considered when using the heuristic, it is of little impact to the overall conclusions, as it only marginally impacts the conclusions for very low base station densities. Moreover, this is an extreme case in which it is doubtful whether it is economically viable to roll out an access network capable of these high bit rates when there are almost no users requiring them.
7 Environmental impact of the mobile access network
7.1 Power consumption
One of the purposes of the introduction of sleep modes is reducing the environmental footprint. However, this evaluation is largely dependent on the selected environmental parameter. First we investigate the power consumption. On the one hand we determine the power consumption when the base station is active, or for femtocell base stations or macrocell base stations, respectively. On the other hand, there is the power consumption or when the base stations are in sleep mode.
with or the average active base station fraction of the access network and or the base station density.
If we assume a typical power consumption of 10 W for a femtocell base station and 3 kW for a macrocell base station, in the case of D U = 500 users/km2, α = 3, a channel bandwidth of 5 MHz and assuming the ideal situation where , a macrocell network would consume 10.7 kW/km2, whereas a femtocell network would consume only 0.37 kW/km2 or 3.5% of what the macrocell network would consume. Alternatively, when assuming the base stations cannot be put in sleep mode or F A = 1, the femtocell network would consume 17.6 kW/km2 compared to 30.8 kW/km2 for the macrocell network. As in this case, the femtocell network consumes 57% of the macrocell network, we see that the ability to put base stations in sleep mode is a key enabler to make a femtocell deployment a significant improvement compared to a macrocell deployment.
When comparing deployments with channel bandwidths of 5 MHz (I) and 20 MHz (II), . The proportion of active base station fractions is 45 to 70%. Thus, the 5 MHz deployment is less power consuming, independent of α.
7.2 Life cycle assessment
The use of power consumption as an environmental parameter is closely related to the requirement to reduce carbon emissions. However, when evaluating carbon emissions, the power consumption during the use of a device is only one part of the impact. When assessing carbon emissions, or other environmentally impacting factors, life cycle assessment (LCA) is often used. In LCA, the impacts during material extraction, manufacturing, transport, use and end-of-life are evaluated. In the case of carbon emissions, the use phase impact is directly correlated to the power consumption. By multiplying the average power consumption as given in (13) with the life time l and the carbon emission intensity I, which denotes the amount of CO2 emitted when producing 1 kWh of electrical power, one can calculate the use phase impact. Analysis of the other phases leads to an impact L, expressed in kg CO2 per device. The latter impact cannot be influenced by F A and will be an important factor when evaluating the overall environmental desirability of deploying new mobile access networks.
8 Use of the heuristic in a practical deployment
As explained, when designing a mobile access network providing a large coverage for high bit rates, we need to deploy base stations with a high density. Using femtocells, we can create a more energy efficient access network. This was derived based on a theoretical situation with a hexagonal grid. Therefore, we would like to apply the derived heuristic in a more realistic situation.
We applied a genetic heuristic as used by mobile operators to deploy a set of LTE femtocells in an urban environment (Ghent, Belgium). The target for the heuristic was to provide a 95% coverage at a bit rate of 11.3 Mbps using a channel bandwidth of 5 MHz. On a surface of approximately 56000 m2, 85 femtocells were deployed resulting in a density of 1518 base stations/km2. Compared to a theoretical density of 320 base stations/km2 when using a hexagonal grid, we see the practical deployment needs about 4,7 times more base stations.
In light of the requirement for both increasing bit rates and reduced energy consumption in mobile access networks, the introduction of sleep modes is a key element. As it is difficult to analytically predict the energy saving potential that can be achieved by using sleep modes in mobile access network deployments, we have derived a heuristic that can serve as a design tool for establishing a baseline.
Due to the small cell size, femtocell access networks appear to be better suitable than macrocell networks for introducing sleep modes. At user densities between 100 and 1000 users the optimal active base station fraction for high bit rate networks is below 20%. Thus, covering areas for high bit rates with sleep-enabled femtocells has a high potential for being less power consuming than using macrocells. However, also in macrocell networks there are opportunities for introducing sleep modes, especially when users have a preference for lower bit rates.
In practical deployments, where the distribution of base stations is suboptimal compared to a hexagonal grid deployment, the introduction of sleep modes helps in optimising the use of the base stations and reduces the effects of increased power consumption due to this suboptimal deployment.
The research leading to these results had received funding from the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement n. 257740 (Network of Excellence "TREND") and the IBBT-project Green ICT. W. Joseph was a Post-Doctoral Fellow of FWO-V (Research Foundation Flanders).
- Vereecken W, Van Heddeghem W, Deruyck M, Puype B, Lannoo B, Joseph W, Colle D, Martens L, Demeester P: Power consumption in telecommunication networks: overview and reduction strategies. Communications Magazine, IEEE 2011, 49(6):62-69.View Article
- Malmodin J, Moberg A, Lundn D, Finnveden G, Lövehagen N: Greenhouse Gas Emissions and Operational Electricity Use in the ICT and Entertainment & Media Sectors. Journal of Industrial Ecology 2010, 14(5):770-790. 10.1111/j.1530-9290.2010.00278.xView Article
- Pickavet M, Vereecken W, Demeyer S, Audenaert P, Vermeulen B, Develder C, Colle D, Dhoedt B, Demeester P: Worldwide energy needs for ICT: The rise of power-aware networking. In Advanced Networks and Telecommunication Systems, 2008. ANTS '08. 2nd International Symposium on. Volume 2. [Bombay, India]; 2008:1-3.View Article
- Cisco VNI Mobile: Global Mobile Data Traffic Forecast Update 2010 - 2015. Tech rep Cisco 2011.
- 3GPP: LTE: 3rd Generation Partnership Project: Technical Specification Group Radio Access Network: Evolved Universal Terrestrial Radio Access (E-UTRA): User Equipment (UE) radio transmission and reception (TS 36.101 v9.1.0 Release 9). 2009.
- Jones CE, Sivalingam KM, Agrawal P, Chen JC: A Survey of Energy Efficient Network Protocols for Wireless Networks. Wireless Networks 2001, 7: 343-358. 10.1023/A:1016627727877View Article
- Fusco G, Gupta H: ϵ -Net Approach to Sensor k-Coverage. EURASIP Journal on Wireless Communications and Networking 2010, 2010: 1-12. [Article ID 192752]View Article
- Simon G, Molnar M, Gonczy L, Cousin B: Robust k-Coverage Algorithms for Sensor Networks. Instrumentation and Measurement, IEEE Transactions on 2008, 57(8):1741-1748.View Article
- Xiao Y: Energy saving mechanism in the IEEE 802.16e wireless MAN. Communications Letters, IEEE 2005, 9(7):595-597. 10.1109/LCOMM.2005.1461675View Article
- Zhou J, Jacobsson M, Niemegeers I: Link Quality-Based Transmission Power Adaptation for Reduction of Energy Consumption and Interference. EURASIP Journal on Wireless Communications and Networking 2010, 2010: 1-17. [Article ID 920131]View Article
- Schmitt G: The Green Base Station. In Telecommunication - Energy Special Conference (TELESCON), 2009 4th International Conference on. Volume 4. [Vienna, Austria]; 2009:1-6.
- Valerdi D, Zhu Q, Exadaktylos K, Xia S, Arranz M, Liu R, Xu D: Intelligent energy managed service for green base stations. In GLOBECOM Workshops (GC Wkshps), 2010 IEEE. Volume 29. [Miami, Florida]; 2010:1453-1457.View Article
- Mancuso V, Alouf S: Reducing costs and pollution in cellular networks. Communications Magazine, IEEE 2011, 49(8):63-71.View Article
- Correia L, Zeller D, Blume O, Ferling D, Jading Y, Godor I, Auer G, Van Der Perre L: Challenges and enabling technologies for energy aware mobile radio networks. Communications Magazine, IEEE 2010, 48(11):66-72.View Article
- Saker L, Elayoubi SE, Chahed T: Minimizing Energy Consumption via Sleep Mode in Green Base Station. In Wireless Communications and Networking Conference (WCNC), 2010 IEEE. Volume 12. [Sydney, Australia]; 2010:1-6.View Article
- Ashraf I, Boccardi F, Ho L: Sleep mode techniques for small cell deployments. Communications Magazine, IEEE 2011, 49(8):72-79.View Article
- Marsan M, Chiaraviglio L, Ciullo D, Meo M: Optimal Energy Savings in Cellular Access Networks. In Communications Workshops, 2009. ICC Workshops 2009. IEEE International Conference on. Volume 44. [Dresden, Germany]; 2009:1-5.
- Oh E, Krishnamachari B: Energy Savings through Dynamic Base Station Switching in Cellular Wireless Access Networks. In Global Telecommunications Conference (GLOBECOM 2010), 2010 IEEE. Volume 29. [Miami, Florida]; 2010:1-5.View Article
- Dufkova K, Bjelica M, Moon B, Kencl L, Le Boudec JY: Energy savings for cellular network with evaluation of impact on data traffic performance. Wireless Conference (EW), 2010 European 2010, 916-923.View Article
- Samdanis K, Kutscher D, Brunner M: Self-organized energy efficient cellular networks. In Personal Indoor and Mobile Radio Communications (PIMRC), 2010 IEEE 21st International Symposium on. Volume 21. [Istanbul, Turkey]; 2010:1665-1670.
- Niu Z, Wu Y, Gong J, Yang Z: Cell zooming for cost-efficient green cellular networks. Communications Magazine, IEEE 2010, 48(11):74-79.View Article
- Deruyck M, Tanghe E, Joseph W, Martens L: Modelling and optimization of power consumption in wireless access networks. Elsevier Computer Communications 2010, 34(17):2036-2046.View Article
- Deruyck M, De Vulder D, Joseph W, Martens L: Modelling the Power Consumption in Femtocell Networks. In IEEE Wireless Communications and Networking Conference (WCNC). Volume 14. [Paris, France]; 2012.
- Erceg V, Greenstein LJ, Tjandra SY, Parkoff SR, Gupta A, Kulic B, Julius AA, Bianchi R: An Empirically Based Path Loss Model for Wireless Channels in Suburban Environments. IEEE Journal on Selected Areas in Communications 1999, 7(7):1205-1211.View Article
- Recommendation ITU-R P1238-2: Propagation data and prediction methods for the planning of indoor radiocommunication systems and radio local area networks in the frequency range 900 MHz to 100 GHz. 2001.
- IBM: IBM ILOG CPLEX Optimizer.[http://www-01.ibm.com/software/integration/optimization/cplex-optimizer/]
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.