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203
The Node Distribution of the Random Waypoint Mobility Model for Wireless Ad Hoc Networks
, 2003
"... The random waypoint model is a commonly used mobility model in the simulation of ad hoc networks. It is known that the spatial distribution of network nodes moving according to this model is, in general, nonuniform. However, a closedform expression of this distribution and an indepth investigation ..."
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Cited by 377 (10 self)
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The random waypoint model is a commonly used mobility model in the simulation of ad hoc networks. It is known that the spatial distribution of network nodes moving according to this model is, in general, nonuniform. However, a closedform expression of this distribution and an indepth investigation is still missing. This fact impairs the accuracy of the current simulation methodology of ad hoc networks and makes it impossible to relate simulationbased performance results to corresponding analytical results. To overcome these problems, we present a detailed analytical study of the spatial node distribution generated by random waypoint mobility. More specifically, we consider a generalization of the model in which the pause time of the mobile nodes is chosen arbitrarily in each waypoint and a fraction of nodes may remain static for the entire simulation time. We show that the structure of the resulting distribution is the weighted sum of three independent components: the static, pause, and mobility component. This division enables us to understand how the models parameters influence the distribution. We derive an exact equation of the asymptotically stationary distribution for movement on a line segment and an accurate approximation for a square area. The good quality of this approximation is validated through simulations using various settings of the mobility parameters. In summary, this article gives a fundamental understanding of the behavior of the random waypoint model.
Stationary Distributions for the Random Waypoint Mobility Model
 IEEE Transactions on Mobile Computing
, 2003
"... In simulations of mobile ad hoc networks, the probability distribution governing the movement of the nodes typically varies over time, and converges to a "steadystate" distribution, known in the probability literature as the stationary distribution. Some published simulation results ig ..."
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Cited by 188 (7 self)
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In simulations of mobile ad hoc networks, the probability distribution governing the movement of the nodes typically varies over time, and converges to a "steadystate" distribution, known in the probability literature as the stationary distribution. Some published simulation results ignore this initialization discrepancy. For those results that attempt to account for this discrepancy, the practice is to discard an initial sequence of observations from a simulation in the hope that the remaining values will closely represent the stationary distribution. This approach is inefficient and not always reliable. However, if the initial locations and speeds of the nodes are chosen from the stationary distribution, convergence is immediate and no data need be discarded. We derive the stationary distributions for location, speed, and pause time for the random waypoint mobility model. We then show how to implement the random waypoint mobility model in order to construct more efficient and reliable simulations for mobile ad hoc networks. Simulation results, which verify the correctness of our method, are included.
Access and Mobility of Wireless PDA Users
"... In this paper, we analyze the mobility patterns of users of wireless handheld PDAs in a campus wireless network using an 11 week trace of wireless network activity. Our study has three goals. First, we characterize the highlevel mobility and access patterns of handheld PDA users and compare these c ..."
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Cited by 142 (4 self)
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In this paper, we analyze the mobility patterns of users of wireless handheld PDAs in a campus wireless network using an 11 week trace of wireless network activity. Our study has three goals. First, we characterize the highlevel mobility and access patterns of handheld PDA users and compare these characteristics to previous workload mobility studies focused on laptop users. Second, we develop two wireless network topology models for use in wireless mobility studies: an evolutionary topology model based on user proximity and a campus waypoint model that serves as a tracebased complement to the random waypoint model. Finally, we use our wireless network topology models as a case study to evaluate adhoc routing algorithms on the network topologies created by the access and mobility patterns of users of modern wireless PDAs.
Singlecopy Routing in Intermittently Connected Mobile Networks
 In IEEE SECON
, 2004
"... Abstract — Intermittently connected mobile networks are wireless networks where most of the time there does not exist a complete path from source to destination, or such a path is highly unstable and may break soon after it has been discovered. In this context, conventional routing schemes would fai ..."
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Cited by 131 (11 self)
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Abstract — Intermittently connected mobile networks are wireless networks where most of the time there does not exist a complete path from source to destination, or such a path is highly unstable and may break soon after it has been discovered. In this context, conventional routing schemes would fail. To deal with such networks we propose the use of an opportunistic hopbyhop routing model. According to the model, a series of independent, local forwarding decisions are made, based on current connectivity and predictions of future connectivity information diffused through nodes’ mobility. The important issue here is how to choose an appropriate next hop. To this end, we propose and analyze via theory and simulations a number of routing algorithms. The champion algorithm turns out to be one that combines the simplicity of a simple random policy, which is efficient in finding good leads towards the destination, with the sophistication of utilitybased policies that efficiently follow good leads. We also state and analyze the performance of an oraclebased optimal algorithm, and compare it to the online approaches. The metrics used in the comparison are the average message delivery delay and the number of transmissions per message delivered. I.
Perfect Simulation and Stationarity of a Class of Mobility Models
 in IEEE Infocom
, 2005
"... Abstract — We define “random trip", a generic mobility model for independent mobiles that contains as special cases: the random waypoint on convex or non convex domains, random walk with reflection or wrapping, city section, space graph and other models. We use Palm calculus to study the model ..."
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Cited by 106 (3 self)
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Abstract — We define “random trip", a generic mobility model for independent mobiles that contains as special cases: the random waypoint on convex or non convex domains, random walk with reflection or wrapping, city section, space graph and other models. We use Palm calculus to study the model and give a necessary and sufficient condition for a stationary regime to exist. When this condition is satisfied, we compute the stationary regime and give an algorithm to start a simulation in steady state (perfect simulation). The algorithm does not require the knowledge of geometric constants. For the special case of random waypoint, we provide for the first time a proof and a sufficient and necessary condition of the existence of a stationary regime. Further, we extend its applicability to a broad class of non convex and multisite examples, and provide a readytouse algorithm for perfect simulation. For the special case of random walks with reflection or wrapping, we show that, in the stationary regime, the mobile location is uniformly distributed and is independent of the speed vector, and that there is no speed decay. Our framework provides a rich set of well understood models that can be used to simulate mobile networks with independent node movements. Our perfect sampling is implemented to use with ns2, and it is freely available to download from
PATHS: Analysis of PATH Duration Statistics and their Impact on Reactive MANET Routing Protocols
 in Proc. of MobiHoc
, 2003
"... We develop a detailed approach to study how mobility impacts the performance of reactive MANET routing protocols. In particular we examine how the statistics of path durations including PDFs vary with the parameters such as the mobility model, relative speed, number of hops, and radio range. We find ..."
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Cited by 78 (4 self)
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We develop a detailed approach to study how mobility impacts the performance of reactive MANET routing protocols. In particular we examine how the statistics of path durations including PDFs vary with the parameters such as the mobility model, relative speed, number of hops, and radio range. We find that at low speeds, certain mobility models may induce multimodal distributions that reflect the characteristics of the spatial map, mobility constraints and the communicating tra#c pattern. However, our study suggests that at moderate and high velocities the exponential distribution with appropriate parameterizations is a good approximation of the path duration distribution for a range of mobility models. The reciprocal of the average path duration is analytically shown to have a strong linear relationship with the throughput and overhead that is confirmed by the simulation results for DSR.
Mobility Models for Ad hoc Network Simulation
, 2004
"... In this paper, we propose a novel general technique, based on renewal theory, for analyzing mobility models in ad hoc networks. Our technique enables an accurate derivation of the steady state distribution functions for node movement parameters such as distance and speed. We first apply our techniqu ..."
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Cited by 70 (1 self)
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In this paper, we propose a novel general technique, based on renewal theory, for analyzing mobility models in ad hoc networks. Our technique enables an accurate derivation of the steady state distribution functions for node movement parameters such as distance and speed. We first apply our technique to the random waypoint model and provide alternative proofs for previous claims about the discrepancy between the steady state average speed and the average speed associated with the simulated distribution [1]. Our main contribution is a new methodology for simulating mobility which guarantees steady state for node movement distributions from the start of the simulation. Our methodology enables the correct and efficient simulation of a desired steady state distribution, and can be implemented in a manner transparent to the user. We support our claims through both formal proofs as well as extensive simulations.
Spatial Node Distribution of the Random Waypoint Mobility Model with Applications
 IEEE TRANSACTIONS ON MOBILE COMPUTING
, 2006
"... The random waypoint model (RWP) is one of the most widely used mobility models in performance analysis of ad hoc networks. We analyze the stationary spatial distribution of a node moving according to the RWP model in a given convex area. For this we give an explicit expression, which is in the fo ..."
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Cited by 62 (11 self)
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The random waypoint model (RWP) is one of the most widely used mobility models in performance analysis of ad hoc networks. We analyze the stationary spatial distribution of a node moving according to the RWP model in a given convex area. For this we give an explicit expression, which is in the form of a onedimensional integral giving the density up to a normalization constant.
Group and swarm mobility models for ad hoc network scenarios using virtual tracks
 In Proceedings of MILCOM
, 2004
"... The mobility model is one of the most important factors in the performance evaluation of a mobile ad hoc network (MANET). Traditionally, the random waypoint mobility model has been used to model the node mobility, where the movement of one node is modeled as independent from all others. However, in ..."
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Cited by 57 (10 self)
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The mobility model is one of the most important factors in the performance evaluation of a mobile ad hoc network (MANET). Traditionally, the random waypoint mobility model has been used to model the node mobility, where the movement of one node is modeled as independent from all others. However, in reality, especially in large scale military scenarios, mobility coherence among nodes is quite common. One typical mobility behavior is group mobility. Thus, to investigate military MANET scenarios, an underlying realistic mobility model is highly desired. In this paper, we propose a “virtual track ” based group mobility model (VT model) which closely approximates the mobility patterns in military MANET scenarios. It models various types of node mobility such as group moving nodes, individually moving nodes as well as static nodes. Moreover, the VT model not only models the group mobility, it also models the dynamics of group mobility such as group merge and split. Simulation experiments show that the choice of mobility model has significant impact on network performance. I.
Modeling Path Duration Distributions in MANETs and their Impact on Reactive Routing Protocols
 IEEE Journal on Selected Areas in Communications
, 2004
"... We develop a detailed approach to study how mobility impacts the performance of reactive MANET routing protocols. In particular we examine how the statistics of path durations including PDFs vary with the parameters such as the mobility model, relative speed, number of hops, and radio range. We find ..."
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Cited by 53 (6 self)
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We develop a detailed approach to study how mobility impacts the performance of reactive MANET routing protocols. In particular we examine how the statistics of path durations including PDFs vary with the parameters such as the mobility model, relative speed, number of hops, and radio range. We find that at low speeds, certain mobility models may induce multimodal distributions that reflect the characteristics of the spatial map, mobility constraints and the communicating traffic pattern. However, our study suggests that at moderate and high velocities the exponential distribution with appropriate parameterizations is a good approximation of the path duration distribution for a range of mobility models.