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13 Simulation of Wireless Network Systems This chapter deals with simulation of wireless network systems. We introduce the basics of discrete-event simulation as it is the simulation technique that is used for simulating wireless networks. We then review the main characteristics of the commonly used stochastic distribu- tions used for the simulation of wireless networks. The techniques used to generate and test random number sequences are investigated. Then, we introduce the techniques used to generate random variates followed by performance metrics considerations. The chapter concludes with cases studies on the simulation of some wireless network systems. 13.1 Basics of Discrete-Event Simulation Simulation is a general term that is used in many disciplines including performance evalua- tion of computer and telecommunications systems. It is the process of designing a model of a real system and conducting experiments with this model for the purpose of understanding its behavior, or of evaluating various strategies of its operation. Others defined simulation as the process of experimenting with a model of the system under study using computer program- ming. It measures a model of the system rather than the system itself. A model is a description of a system by symbolic language or theory to be seen as a system with which the world of objects can be expressed. Thus, a model is a system interpretation or realization of a theory that is true. Shannon defined a model as ‘the process of designing a computerized model of a system (or a process) and conducting experiments with this model for the purpose either of understanding the behavior of the system or of evaluating various strategies for the operation of the system.’ Based on the above definition of a model, we can redefine simulation as the use of a model, which may be a computer model, to conduct experiments which, by inference, convey an understanding of the behavior of the system under study. Simulation experiments are impor- tant aspect of any simulation study since they help to: † discover something unknown or test an assumption † find candidate solutions, and provide a mean for evaluating them. Basically, modeling and simulation of any system involve three types of entities: (a) real system; (b) model; and (c) simulator. These entities are to be understood in their interrelation Wireless Networks. P. Nicopolitidis, M. S. Obaidat, G. I. Papadimitriou and A. S. Pomportsis Copyright ¶ 2003 John Wiley & Sons, Ltd. ISBN: 0-470-84529-5 to one another as they are related and dependent on each other. The real system is a source of raw data while the model is a set of instructions for data generating. The simulator is a device for carrying out model instructions. We need to validate and verify any simulation model in order to make sure that the assumptions, distributions, inputs, outputs, results and conclu- sions, as well as the simulation program (simulator), are correct [1–10]. Systems in general can be classified into stochastic and deterministic types [1–3]: † Stochastic systems. In this case, the system contains a certain amount of randomness in its transitions from one state to another. A stochastic system can enter more than one possible state in response to an activity or stimulus. Clearly, a stochastic system is nondeterministic in the sense that the next state cannot be unequivocally predicted if the present state and the stimulus are known. † Deterministic systems. Here, the new state of the system is completely determined by the previous state and by the activity or input. Among the reasons that make simulation attractive in predicting the performance of systems are [1–3]: † Simulation can foster a creative attitude for trying new ideas. Many organizations or companies have underutilized resources, which if fully employed, can bring about dramatic improvements in quality and productivity. Simulation can be a cost-effective way to express, experiment with, and evaluate such proposed solutions, strategies, schemes, or ideas. † Simulation can predict outcomes for possible courses of action in a speedy way. † Simulation can account for the effect of variances occurring in a process or a system. It is important to note that performance computations based solely on mean values neglect the effect of variances. This may lead to erroneous conclusions. † Simulation promotes total solutions. † Simulation brings expertise, knowledge and information together. † Simulation can be cost effective in terms of time. In order to conduct a systematic and effective simulation study and analysis, the following phases should be followed [1,4,5]. Figure 13.1 summarizes these major steps. † Planning. In the planning phase, the following tasks have to be defined and identified: – Problem formulation. If a problem statement is being developed by the analyst, it is important that policymakers understand and agree with the formulation. – Resource estimation. Here, an estimate of the resources required to collect data and analyze the system should be conducted. Resources including time, money, personnel and equipment, must be considered. It is better to modify goals of the simulation study at an early stage rather than to fall short due to lack of critical resources. – System and data analysis. This includes a thorough search in the literature of previous approaches, methodologies and algorithms for the same problem. Many projects have failed due to misunderstanding of the problem at hand. Also, identifying parameters, variables, initial conditions, and performance metrics is performed at these stages. Furthermore, the level of detail of the model must be established. Wireless Networks342 † Modeling phase. In this phase, the analyst constructs a system model, which is a repre- sentation of the real system. – Model building. This includes abstraction of the system into a mathematical relation- ship with the problem formulation. – Data acquisition. This involves identification, specification, and collection of data. – Model translation. Preparation and debugging of the model for computer processing. Models in general can be of different types. Among these are: (a) descriptive models; (b) physical models such as the ones used in aircraft and buildings; (c) mathematical models such as Newton’s law of motion; (d) flowcharts; (e) schematics; and (f) computer pseudo code. The major steps in model building include: (a) preliminary simulation model diagram; (b) construction and development of flow diagrams; (c) review model diagram with team; (d) initiation of data collection; (e) modify the top-down design, test and validate for the required degree of granularity; (f) complete data collection; (g) iterate through steps (e) and (g) until the final granularity has been reached; and (h) final system diagram, transformation and verification. In the context of this phase, it is important to point out two concepts: † Model scooping. This is the process of determining what process, operation, equipment, etc., within the system should be included in the simulation model, and at what level of detail. † Level of detail. This is determined based on the component’s effect on the stability of the Simulation of Wireless Network Systems 343 Figure 13.1 Overview of the simulation methodology [1–5] analysis. The appropriate level of detail will vary depending on the modeling and simula- tion goals. 13.1.1 Subsystem Modeling When the system under simulation study is very large, a subsystem modeling is performed. All subsystem models are later linked appropriately. In order to define/identify subsystems, there are three general schemes: † Flow scheme. This scheme has been used to analyze systems that are characterized by the flow of physical or information items through the system, such as pipeline computers. † Functional scheme. This scheme is useful when there are no directly observable flowing entities in the system, such as manufacturing processes that do not use assembly lines. † State-change scheme. This scheme is useful in systems that are characterized by a large number of interdependent relationships and that must be examined at regular intervals in order to detect state changes. 13.1.2 Variable and Parameter Estimation This is usually done by collecting data over some period of time and then computing a frequency distribution for the desired variables. Such an analysis may help the analyst to find a well-known distribution that can represent the behavior of the system or subsystem. 13.1.3 Selection of a Programming Language/Package Here, the analyst should decide whether to use a general-purpose programming language, a simulation language or a simulation package. In general, using a simulation package such as NS2 or Opnet may save money and time, however, it may not be flexible and effective to use simulation packages as they may not contain capabilities to do the task such as modules to simulate the protocols or features of the network under study. 13.1.4 Verification and Validation (V&V) Verification and validation are two important tasks that should be carried out for any simula- tion study. They are often called V&V and many simulation journals and conferences have special sections and tracks that deal with these tasks, respectively. Verification is the process of finding out whether the model implements the assumptions correctly. It is basically debugging the computer program (simulator) that implements the model. A verified computer program can in fact represent an invalid model; a valid model can also represent an unverified simulator. Validation, on the other hand, refers to ensuring that the assumptions used in developing the model are reasonable in that, if correctly implemented, the model would produce results close to these observed in real systems. The process of model validation consists of validating assumptions, input parameters and distributions, and output values and conclusions. Valida- tion can be performed by one of the following techniques: (a) comparing the results of the Wireless Networks344 simulation model with results historically produced by the real system operating under the same conditions; (b) expert intuition; (c) theoretical (analytic) results using queuing theory or other analytic methods; (d) another simulation model; and (e) artificial intelligence and expert systems. 13.1.5 Applications and Experimentation After the model has been validated and verified, it can be applied to solve the problem under investigation. Various simulation experiments should be conducted to reveal the behavior of the system under study. Keep in mind that it is through experimentation that the analyst can understand the system and make recommendations about the system design and optimum operation. The extent of experiments depends on cost to estimate performance metrics, the sensitivity of performance metrics to specific variables and the interdependencies between control variables [1,4,5]. The implementation of simulation findings into practice is an important task that is carried out after experimentation. Documentation is very important and should include a full record of the entire project activity, not just a user’s guide. The main factors that should be considered in any simulation study are: (a) Random Number Generators (RNGs); (b) Random Variates or observations (RVs); (c) programming errors; (d) specification errors; (e) length of simulation; (f) sensitivity to key parameters; (g) data collection errors in simulation; (h) optimization parameter errors; (i) incorrect design; and (j) influence of initial conditions. The main advantages of simulation are [4,5]: † Flexibility. Simulation permits controlled experimentation with the system model. Some experiments cannot be performed on the real physical system due to inconvenience, risk and cost. † Speed. Using simulation allows us to find results of experiments in a speedy manner. Simulation permits time compression of a system over an extended period of time. † Simulation modeling permits sensitivity analysis by manipulating input variables. It allows us to find the parameters that influence the simulation results. It is important to find out which simulation parameters influence performance metrics more than others as proper selection of their operating values is essential for stable operation. † Simulation modeling involves programming, mathematics, queuing theory, statistics, system engineering and science as well as technical documentation. Clearly, it is an excellent training tool. The main drawbacks of simulation are [4,5]: † It may become expensive and time-consuming especially for large simulation models. This will consume long computer simulation time and manpower. † In simulation modeling, we usually make assumptions about input variables and para- meters, and distributions, and if these assumptions are not reasonable, this may affect the credibility of the analysis and the conclusions. † When simulating large networks or systems, the time to develop the simulator (simulation program) may become long. Simulation of Wireless Network Systems 345 † It is usually difficult to initialize simulation model parameters properly and not doing so may affect the credibility of the model as well as require longer simulation time. 13.2 Simulation Models In general, simulation models can be classified in three different dimensions [3]: (a) a static versus dynamic simulation model, where a static model is representation of a system at a particular time, or one that may be used to represent a system in which time plays no role, such as Monte Carlo models, and a dynamic simulation model represents a system as it evolves over time; (b) deterministic versus stochastic models where a deterministic model does not contain any probabilistic components while a stochastic model has at least some random input components; (c) continuous versus discrete simulation models where a discrete- event simulation is concerned with modeling of a system as it evolves over time by repre- sentation in which the state variables change instantaneously at separate points in time, usually called events. On the other hand, continuous simulation is concerned with modeling a system by a representation in which the state variables change continuously with respect to time. In order to keep track with the current value of simulation time during any simulation study, we need a mechanism to advance simulation time from one value to another. The variable that gives the current value of simulation time is called the simulation clock. The schemes that can be used to advance the simulation clock are [1]: † Next-event time advance. In this scheme, simulation clock is initialized to zero and the times of occurrences of future events are found out. Then simulation clock is advanced to the time of occurrence of the most imminent event in the future event list, then the state of the system is updated accordingly. Other future events are determined in a similar manner. This method is repeated until the stopping condition/criterion is satisfied. Figure 13.2 summarizes the next-event time advance scheme. † Fixed-increment time advance. Here, simulation clock is advanced in fixed increments. After each update of the clock, a clock is made to determine if any events should have occurred during the previous fixed interval. If some events were scheduled to have occurred during this interval, then they are treated as if they occurred the end of the interval and the system state is updated accordingly. A fixed-increment time advance scheme is not used in discrete-event simulation. This is due to the following drawbacks: (a) errors are introduced due to processing events at the end of the interval in which they occur; and (b) it is difficult to decide which event to process first when events that are not simultaneous in reality are treated as such in this scheme. The main components that are found in most discrete-event simulation models using the next-event time advance scheme are [1–5]: (a) system state which is the collections of state variables necessary to describe the system at a particular time; (b) simulation clock which is a variable giving the current value of simulated time; (c) statistical counters which are the variables used for storing statistical information about system performance; (d) an initializing routine which is a procedure used to initialize the simulation model at time zero; (e) a timing routine which is a procedure that determines the next event from the event list and then Wireless Networks346 advances the simulation clock to the time when that event is to occur; (f) an event routine which is a procedure that updates the system state when a particular type of event occurs; (g) library routines that are a set of subprograms used to generate random observations from probability distributions; (h) a report generator which is a procedure that computes estimates of the desired measures of performance and produces a report when the simulation ends; and (i) the main program which is a procedure that invokes the timing routine in order to determine the next event and then transfers control to the corresponding event routine to Simulation of Wireless Network Systems 347 Figure 13.2 Summary of next-event time advance scheme [1–5] properly update the system state, checks for termination and invokes the report generator when the conditions for terminating the simulation are satisfied. Simulation begins at time 0 with the main program invoking the initialization routine, where the simulation clock is initialized to zero, the system state and statistical counters are initialized, as well as the event list. After control has been returned to the main program, it invokes the timing routine to find out the most eminent routine. If event i is the most eminent one, then simulation clock is advanced to the time that this event will occur and control is returned to the main program. The available programming languages/packages for simulating computers and network systems are: † General purpose languages such as C, C11, Java, Fortran, and Visual Basic. † Special simulation languages such as Simscript II.5, GPSS, GASP IV, CSIM, Modsim III. † Special simulation packages such as Comnet III, Network II.5, OPNet, QNAP, Network Simulation 2 (NS-2). 13.3 Common Probability Distributions Used in Simulation The basic logic used for extracting random values from probability distribution is based on a Cumulative Distribution Function (CDF) and a Random Number Generator (RNG). The CDF has Y values that range from 0 to 1. RNGs produce a set of numbers which are uniformly distributed across this interval. For every Y value there exists a unique random variate value, X, that can be calculated. All commercial simulation packages do not require the simulationist to write a program to generate random variates or observations. The coding is already contained in the package using special statements. In such a case, a model builder simply: (a) selects a probability distribution from which he desires random variates; (b) specifies the input parameters for the distribution; and (c) designates a random number stream to be used with the distribu- tion. Standard probability distributions are usually perceived in terms of the forms produced by their Probability Density Functions (pdf). Many probability density functions have para- meters that control their shape and scale characteristics. There are several standard contin- uous and discrete probability distributions that are frequently used with simulation. Examples of these are: the exponential, gamma, normal, uniform continuous and discrete, triangular, Erlang, Poisson, binomial, Weibull, etc. Standard probability distributions are used to repre- sent empirical data distributions. The use of one standard distribution over the other is dependent on the empirical data that it is representing, or the type of stochastic process that is being modeled. It is essential to understand the key characteristics and typical applica- tions of the standard probability distributions as this helps analysts to find a representative distribution for empirical data and for processes where no historical data are available. Next is a brief review of the main characteristics of the most often used probability distributions for simulation [1–4]. † Bernoulli distribution. This is considered the simplest discrete distribution. A Bernoulli variate can take only two values, which are denoted as failure and success, or x ¼ 0 and Wireless Networks348 x ¼ 1, respectively. If p represents the probability of success, then q ¼ 1 2 p is the prob- ability of failure. The experiments to generate a Bernoulli variate are called Bernoulli trials. This distribution is used to model the probability of an outcome having a desired class or characteristic; for example, a packet in a computer network reaches or does not reach the destination, and a bit in a packet is affected by noise and arrives in error. The Bernoulli distribution and its derivative can be used only if the trials are independent and identical. † Discrete uniform. This distribution can be used to represent random occurrence with several possible outcomes. A Bernoulli (1/2) and Discrete Uniform (DU) ð0; 1Þ are the same. † Uniform distribution (continuous). This distribution is also called the rectangular distribu- tion. It is considered one of the simplest distributions to use. It is commonly used if a random variable is bounded and no further information is available. Examples include: distance between source and destination of message on a network, and seek time on a disk. In order to generate a continuous uniform distribution, Uða; bÞ, you need to: generate u , Uð0; 1Þ and return a ¼ðb 2 aÞu. The key parameters are: a ¼ lower limit and b ¼ upper limit, where b . a. The continuous uniform distribution is used as a ‘first’ model for a quantity that is felt to be randomly varying between two bonds a and b, but about which little else is known. † Exponential distribution. This is considered the only continuous distribution with memoryless property. It is very popular among performance evaluation analysts who work in simulation of computer systems and networks as well as telecommunications. It is often used to model the time interval between events that occur according to the Poisson process. † Geometric distribution. This is the discrete analog of the exponential distribution and is usually used to represent the number of failures before the first success in a sequence of Bernoulli trials such as the number of items inspected before finding the first defective item. † Poisson distribution. This is a very popular distribution in queuing, including telephone systems. It can be used to model the number of arrivals over a given interval such as the number of queries to a database system over a duration, t, or the number of requests to a server in a given duration of time, t. This distribution has a special relation with the exponential distribution. † Binomial distribution. This distribution can be used to represent the number of successes in t independent Bernoulli trials with probability p of success on each trial. Examples include the number of nodes in a multiprocessor computer system that are active (up), the number of bits in a packet or cell that are not affected by noise or distortion, and the number of packets that reach the destination node with no loss. † Negative binomial. It is used to model the number of failures in a system before reaching the kth success such as the number of retransmissions of a message that consists of k packets or cells and the number of error-free bytes received on a noisy channel before the k in-error bytes. † Gamma distribution. Similar to the exponential distribution, this is used in queuing model- ing of all kinds, such as modeling service times of devices in a network. † Weibull Distribution. In general, this distribution is used to model lifetimes of components such as memory or microprocessor chips used in computer and telecommunications Simulation of Wireless Network Systems 349 systems. It can also be used to model fatigue failure and ball bearing failure. It is consid- ered the most widely used distribution to represent failure of all types. It is interesting to point out that the exponential distribution is a special case of the Weibull distribution when the shape parameter a is equal to 1. † Normal or Gaussian distribution. This is also called the bell distribution. It is used to model errors of any type including modeling errors and instrumentation errors. Also, it has been found that during the wearout phase, component lifetime follows a normal distribu- tion. A normal distribution with zero mean and a standard deviation of 1 is called standard normal distribution or a unit normal distribution. It is interesting to note that the sum of large uniform variates has a normal distribution. This latter characteristic is used to generate the normal variate, among other techniques such as the rejection and Polar techniques. This distribution is very important in statistical applications due to the central limit theorem, which states that under general assumptions, the mean of a sample of n mutually independent random variables, that have distribution with finite mean and variance, is normally distributed in the limit n ! 1. † Lognormal distribution: The log of a normal variate has a distribution called lognormal distribution. This distribution is used to model errors that are a product of effects of a large number of factors. The product of a large number of positive random variates tends to have a distribution that can be approximated by lognormal. † Triangle distribution. As the name indicates, the pdf of this distribution is specified by three parameters (a, b, c) that define the coordinates of the vertices of a triangle. It can be used as a rough model in the absence of data. † Erlang distribution. This distribution is usually used in queuing models. It is used to model service times in a queuing network system as well as to model the time to repair and time between failures. † Beta distribution. This distribution is used when there is no data about the system under study. Examples include the fraction of packets or cells that need to be retransmitted. † Chi-square distribution. This was discovered by Karl Pearson in 1900 who used the symbol x 2 for the sum. Since then statisticians have referred to it as the chi-square distribution. In general, it is used whenever a sum of squares of normal variables is involved. Examples include modeling the sample variances. † Student’s distribution. This was derived by Gosset who was working for a winery whose owner did not appreciate his research. In order not to let his supervisor know about his discovery, he published his findings in a paper under the pseudonym student. He used the symbol t to represent the variable and hence the distribution was called the ‘student’s t distribution’. It can be used whenever a ratio of normal variate and the square root of chi- square variable is involved and is commonly used in setting confidence intervals and in t- tests in statistics. † F-Distribution. This distribution is used in hypothesis testing. It can be generated from the ratio of two chi-square variates. Among its applications is to model the ratio of sample variances as in the F-test for regression and analysis of variances. † Pareto distribution. This is also called the double-exponential distribution, the hyperbolic distribution, and the power-law distribution. It can be used to model the amount of CPU time consumed by an arbitrary process, the web file size on an Internet server, and the number of data bytes in File Transfer Protocol (FTP) bursts [8]. Wireless Networks350