Wireless Network Design: Optimization Models and Solution ...

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12 Simulation-Based Methods for Network Design 275 operate together. Link-level simulation generally focuses on single transmitter-toreceiver link performance. The results from the link-level simulation are usually adopted as inputs to the system-level simulation. System-level simulation has been widely used to evaluate system performance with incorporation of link-level simulation curves. In order to reduce the simulation complexity, the effects of link-level technologies are abstracted into several curves that are used in a system-level simulation. An example of this mapping is covered in the WiMAX case study in Section 12.5.2. After identifying which type of simulation is most suitable or available to solve the specific problem, the next step is to choose the specific modeling and simulation tool. It is always possible to build one’s own simulation tool but normally in-house development is more time consuming than using commercially available tools. When using a commercial tool, it is necessary to first make a comprehensive reading of the main limitations and assumptions of the simulation framework and the specific model to be used in the simulation. After analyzing specific model features, it is good practice to test model limitations and verify major assumptions. Often a specific tool is chosen because it has a mature simulation model for the specific communication technology that is the subject of the simulation study. This is the case in the Host Identity Protocol (HIP) case study introduced in Section 12.5.4 in this chapter. To summarize, Figure 12.2 groups the different available simulation tools in accordance with the OSI layer they cover [10]. Fig. 12.2 Simulation Tools
276 Marina Aguado, Jasone Astorga, Nerea Toledo and Jon Matias 12.3 Validating Discrete Event Simulations: the Random Number Seed and the Confidence Interval A simulation process is a statistical experiment. In order to represent a behavior that is not known for a specific element, the simulation environment makes use of stochastic modeling with random number streams to introduce changes in the element’s operating environment (i.e., its input). However, it is impossible for a computer program, by its very nature, to generate truly random numbers. Thus, the simulation framework relies on starting a pseudo-random number generator in different states to exhibit unpredictable behavior. The initial state of the generator is known as the random number seed. Each particular simulation run with a specific random number seed value will produce a different behavior and yield new and different results. To account for all statistical behavior that the system might exhibit, the simulation model must be run multiple times with different seed values. As more seeds are chosen, standard behavior should be observed more frequently than anomalous behavior. Intuitively, the more simulation runs performed, the more confidence we have in the results obtained from the study. In other words, the goal is to ensure that a simulation system produces valid statistical behavior by making a sufficient number of runs, each with a different random seed value. One of the important tasks a simulation designer must carry out is that of deciding how many separately seeded trials to run in a simulation experiment so that there will be enough data to make a strong statement about the system’s typical behavior. Suppose that a number of simulations of a system have been run with different random number seeds to obtain n samples of the statistic X, (x1, x2, x3, ..., xi, ..., xn). Statistic X may take on many values and its precise distribution is unknown. In order to calculate, µ, the true mean of the random variable X, which represents the typical behavior of the modeled system with regard to the statistic X, we should run a large number of simulations (theoretically, an infinite number would be required). However, since it is not usually possible to run a very large number of simulations to determine µ, it is interesting to determine the degree of precision with which the mean value, x, of an n-sample set approximates µ. This determines whether the value can be used with confidence to make statements about the typical behavior of the modeled system. Consider an experiment consisting of a collection of samples of X, each of size n, where x is the average value of the n samples corresponding to one trial of the experiment. If the experiment is performed many times with different seed values, then the resulting average value of x, which we denote by X, has its own distribution. In accordance with the central limit theorem, regardless of X’s actual distribution, as the number of samples grows large, the random variable X has a distribution that approaches that of a normal random variable with mean µ, the same mean as the random variable X itself. The theorem further states that if the true variance of X is σ 2 , the variance for statistic X is σ 2 n . To conclude, if sufficient sample size n has been chosen, normally n > 30, it is possible to work with a normal distribution which has known properties instead of working with an unknown distribution.
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International Series in Operations
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Editors Jeff Kennington Eli Olinick
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vi Preface assistance. The work of
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viii Contents 3.4.1 Experiments to
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x Contents 8.3.2 The Solution Proce
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xii Contents References . . . . . .
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List of Contributors Khaldoun Al Ag
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List of Contributors xvii Nitin Sal
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Chapter 1 Introduction to Optimizat
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1 Introduction to Optimization in W
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1 Introduction to Optimization in W
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Part I Background
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10 Dinesh Rajan The goal of this ch
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12 Dinesh Rajan The source encoder
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14 Dinesh Rajan ping (FH) CDMA, and
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16 Dinesh Rajan of SNR is given in
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18 Dinesh Rajan 2.3 Information The
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20 Dinesh Rajan Perror ≤ e −nE
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22 Dinesh Rajan For instance, for t
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24 Dinesh Rajan 2.4.1 Block Codes I
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26 Dinesh Rajan B(z) = 1 � (1 + z
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28 Dinesh Rajan layers. Two of the
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30 Dinesh Rajan nel can support a p
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32 Dinesh Rajan 2.5.2 Physical laye
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34 Dinesh Rajan matched filter for
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36 Dinesh Rajan codes) leads to bet
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38 Dinesh Rajan a length N Inverse
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40 Dinesh Rajan the transmission of
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42 Dinesh Rajan setting, a node may
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44 Dinesh Rajan weighting of the si
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46 Dinesh Rajan 29. Oestges, C., Cl
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48 K. V. S. Hari terrain of operati
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50 K. V. S. Hari fading is calculat
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52 K. V. S. Hari terms have been pr
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54 K. V. S. Hari Fig. 3.1 Normalize
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56 K. V. S. Hari Table 3.3 Impulse
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58 K. V. S. Hari where m antennas a
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60 K. V. S. Hari 3.5.2.4 Dominant R
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62 K. V. S. Hari March, 1984-13 Sep
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64 K. V. S. Hari 47. Van Rees, J.:
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66 J. Cole Smith and Sibel B. Sonuc
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Part II Optimization Problems for N
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102 Eli Olinick carrying capacity.
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104 Eli Olinick 93 85 160 16 38 21
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106 Eli Olinick Amaldi et al. [7] p
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108 Eli Olinick levels (possibly le
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110 Eli Olinick gmℓ ∑ ∑ m∈M
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112 Eli Olinick Using bk to denote
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114 Eli Olinick 5.3.5 Additional De
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116 Eli Olinick capacity, provide n
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118 Eli Olinick ficult optimization
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120 Eli Olinick and-bound so that t
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Chapter 6 Optimization Based WLAN M
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6 Optimization Based WLAN Modeling
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Chapter 7 Spectrum Auctions Karla H
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7 Spectrum Auctions 149 full value.
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7 Spectrum Auctions 151 also decide
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7 Spectrum Auctions 153 disclosed t
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7 Spectrum Auctions 157 bidders to
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7 Spectrum Auctions 159 in the regi
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7 Spectrum Auctions 163 pays, since
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7 Spectrum Auctions 167 and constra
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7 Spectrum Auctions 169 lem has sup
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7 Spectrum Auctions 171 bidder on a
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7 Spectrum Auctions 175 21. Dunford
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Chapter 8 The Design of Partially S
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8 The Design of Partially Survivabl
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200 Khaldoun Al Agha and Steven Mar
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Chapter 10 Compact Integer Programm
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10 Integer Programming Models for P
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Chapter 15 Major Trends in Cellular
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15 Major Trends in Cellular Network
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