Stochastic Properties of Mobility Models in Mobile Ad Hoc Networks

The stochastic model assumed to govern the mobility of nodes in a mobile ad hoc network has been shown to significantly affect the network's coverage, maximum throughput, and achievable throughput-delay trade-offs. In this paper, we compare several mobility models, including the random walk, random waypoint, and Manhattan models on the basis of the number of states visited in a fixed time, the time to visit every state in a region, and the effect of the number of wandering nodes on the time to first enter a set of states. These metrics for a mobility model are useful for assessing the achievable event detection rates in surveillance applications where wireless-sensor-equipped vehicles are used to detect events of interest in a city. We also consider mobility models based on Correlated Random Walks, which can account for time dependency, geographical restrictions, and nonzero drift. We demonstrate that these models are analytically tractable by using a matrix-analytic approach to derive new, closed-form results in both the time and transform-domains for the probability that a node is at any location at any time for both semi-infinite and finite 1D lattices. We also derive first entrance time distributions for these walks. We find that a correlated random walk 1) covers more ground in a given amount of time and takes a smaller amount of time to cover an area completely than a random walk with the same average transition rate, 2) has a smaller first entrance time to small sets of states than the random waypoint and random walk models, and 3) leads to a uniform distribution of nodes (except at the boundaries) in steady state.     

无线自组网个体移动模型分析

应用Palm积分分析随机点模型、随机方向模型和随机游走模型的平稳速度分布,证明速度衰减问题源于各个移动周期内速度和持续时间的相关性.应用Palm积分和几何概率分析随机点模型和随机方向模型的平稳节点分布,证明这2种模型具有非均匀节点分布特征.应用中心极限定理证明无边界区域随机游走模型的轨迹端点成正态分布.结果表明时间型随机游走模型是最合理的个体移动模型.     

Contact time in random walk and random waypoint: Dichotomy in tail distribution

Contact time (or link duration) is a fundamental factor that affects performance in Mobile Ad Hoc Networks. Previous research on theoretical analysis of contact time distribution for random walk models (RW) assume that the contact events can be modeled as either consecutive random walks or direct traversals, which are two extreme cases of random walk, thus with two different conclusions. In this paper we conduct a comprehensive research on this topic in the hope of bridging the gap between the two extremes. The conclusions from the two extreme cases will result in a power-law or exponential tail in the contact time distribution, respectively. However, we show that the actual distribution will vary between the two extremes: a power-law-sub-exponential dichotomy, whose transition point depends on the average flight duration. Through simulation results we show that such conclusion also applies to random waypoint.     

Superdiffusive Behavior of Mobile Nodes and Its Impact on Routing Protocol Performance

Mobility is the most important component in mobile ad hoc networks (MANETs) and delay-tolerant networks (DTNs). In this paper, we first investigate numerous GPS mobility traces of human mobile nodes and observe superdiffusive behavior in all GPS traces, which is characterized by a “faster-than-linear” growth rate of the mean square displacement (MSD) of a mobile node. We then investigate a large amount of access point (AP) based traces, and develop a theoretical framework built upon continuous time random walk (CTRW) formalism, in which one can identify the degree of diffusive behavior of mobile nodes even under possibly heavy-tailed pause time distribution, as in the case of reality. We study existing synthetic models and trace-based models in terms of the capability of producing various degrees of diffusive behavior, and use a set of Lévy walk models due to its simplicity and flexibility. In addition, we show that diffusive properties make a huge impact on contact-based metrics and the performance of routing protocols in various scenarios, and that existing models such as random waypoint, random direction model, or Brownian motion lead to overly optimistic or pessimistic results when diffusive properties are not properly captured. Our work in this paper, thus, suggests that the diffusive behavior of mobile nodes should be correctly captured and taken into account for the design and comparison study of network protocols.     

On the stationary distribution of speed and location of random waypoint

In "Stationary distributions for the random waypoint mobility model" (TMC, Vol. 3, No, 1), Navidi and Camp find the stationary distribution of the random waypoint model, with or without pause on a rectangular area. In this short note, we show that, under the stationary regime, speed and location are independent.     

Analysis of Random Mobility Models with Partial Differential Equations

In this paper, we revisit two classes of mobility models which are widely used to represent users' mobility in wireless networks: random waypoint (RWP) and random direction (RD). For both models, we obtain systems of partial differential equations which describe the evolution of the users' distribution. For the RD model, we show how the equations can be solved analytically both in the stationary and transient regime, adopting standard mathematical techniques. Our main contributions are 1) simple expressions which relate the transient duration to the model parameters and 2) the definition of a generalized random direction model whose stationary distribution of mobiles in the physical space corresponds to an assigned distribution.     

The node distribution of the random waypoint mobility model for wireless ad hoc networks

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 closed-form expression of this distribution and an in-depth investigation is still missing. This fact impairs the accuracy of the current simulation methodology of ad hoc networks and makes it impossible to relate simulation-based 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 model's 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.     

A Statistical Analysis of the Long-Run Node Spatial Distribution in Mobile Ad Hoc Networks

In this paper, we analyze the node spatial distribution of mobile wireless ad hoc networks. Characterizing this distribution is of fundamental importance in the analysis of many relevant properties of mobile ad hoc networks, such as connectivity, average route length, and network capacity. In particular, we have investigated under what conditions the node spatial distribution resulting after a large number of mobility steps resembles the uniform distribution. This is motivated by the fact that the existing theoretical results concerning mobile ad hoc networks are based on this assumption. In order to test this hypothesis, we performed extensive simulations using two well-known mobility models: the random waypoint model, which resembles intentional movement, and a Brownian-like model, which resembles non-intentional movement. Our analysis has shown that in Brownian-like motion the uniformity assumption does hold, and that the intensity of the concentration of nodes in the center of the deployment region that occurs in the random waypoint model heavily depends on the choice of some mobility parameters. For extreme values of these parameters, the uniformity assumption is impaired.     

Intelligent actor mobility in wireless sensor and actor networks

In wireless sensor and actor network research, the commonly used mobility models for a mobile actor are random walk model, random waypoint mobility model, or variants thereof. For a fully connected network, the choice of mobility model for the actor is not critical because, there is at least one assured path from the sensor nodes to the actor node. But, for a sparsely connected network where information cannot propagate beyond a cluster, random movement of the actor may not be the best choice to maximize event detection and subsequent action. This paper presents static and dynamic intelligent mobility models that are based on the inherent clusters’ information of a sparsely connected network. Simulation results validate the idea behind the intelligent mobility models and provide insights into the applicability of these mobility models in different application scenarios.     

Epoch, length of the random waypoint model in mobile ad hoc networks

In this paper, we derive the probability distribution of the epoch length for the random waypoint model in mobile ad hoc networks. An epoch here is referred to as the movement between two target locations in the mobility model. Such a study is important as the epoch length distribution may be required for the derivation of the link-duration distribution or node spatial distribution for mobile ad hoc networks. The analytical result is then verified via simulation.     

Spatial node distribution of the random waypoint mobility model with applications

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 one-dimensional integral giving the density up to a normalization constant. This result is also generalized to the case where the waypoints have a nonuniform distribution. As a special case, we study a modified RWP model, where the waypoints are on the perimeter. The analytical results are illustrated through numerical examples. Moreover, the analytical results are applied to study certain performance aspects of ad hoc networks, namely, connectivity and traffic load distribution.     

Bandwidth estimation in high mobility scenarios of IEEE 802.11 infrastructure‐less mobile ad hoc networks

Bandwidth estimation in mobile ad hoc networks (MANET), where each node can move randomly and is capable of frequently changing its link with other nodes, is a challenging task. Motivation of this work is in contrast with TCP new‐reno which decreases the congestion window both in the event of link failure and congestion, which in the case of packet loss due to link failure should be close to available channel bandwidth. The proposed novel approach capture the node's mobility behavior in broadcast and unicast scenarios of IEEE 802.11 standard to efficiently estimate the sender's window size. This proposal introduces a data structure and source‐to‐destination path stability metric to imitate the mobility behavior of network and presents the analytic characterization of steady‐state throughput as a function of packet loss, round trip time, and path stability over IEEE 802.11 infrastructure‐less MANET. The performance is evaluated over random‐walk, random‐waypoint, and Gauss‐Markov mobility models in 2D and 3D environments using QualNet 7.4 network simulator. The proposed analytical model is also evaluated through two‐tailed statistical test. Analytical, statistical, and simulation‐based comparisons demonstrate the effectiveness of proposed method in high‐mobility scenarios.     

The random waypoint mobility model with uniform node spatial distribution

In this paper, we tackle the problem of designing a random mobility model generating a target node spatial distribution. More specifically, we solve a long standing open problem by presenting two versions of the well-known random waypoint (RWP) mobility model in bounded regions generating a uniform steady-state node spatial distribution. In the first version, named temporal-RWP, we exploit the temporal dimension of node mobility and achieve uniformity by continuously changing the speed of a mobile node as a function of its location and of the density function of trajectories in the movement region R. In the second version, named spatial-RWP, we instead exploit the spatial dimension and achieve uniformity by selecting waypoints according to a suitably defined mix of probability density functions. Both proposed models can be easily incorporated in wireless network simulators, and are thus of practical use. The RWP models presented in this paper allow for the first time completely removing the well-known border effect causing possible inaccuracies in mobile network simulation, thus completing the picture of a “perfect” simulation methodology drawn in existing literature.     

Stationary distributions for the random waypoint mobility model

In simulations of mobile ad hoc networks, the probability distribution governing the movement of the nodes typically varies over time and converges to a "steady-state" 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. In addition, implementation of our method for the NS-2 simulator is available.     

Random waypoint mobility model in cellular networks

In this paper we study the so-called random waypoint (RWP) mobility model in the context of cellular networks. In the RWP model the nodes, i.e., mobile users, move along a zigzag path consisting of straight legs from one waypoint to the next. Each waypoint is assumed to be drawn from the uniform distribution over the given convex domain. In this paper we characterise the key performance measures, mean handover rate and mean sojourn time from the point of view of an arbitrary cell, as well as the mean handover rate in the network. To this end, we present an exact analytical formula for the mean arrival rate across an arbitrary curve. This result together with the pdf of the node location, allows us to compute all other interesting measures. The results are illustrated by several numerical examples. For instance, as a straightforward application of these results one can easily adjust the model parameters in a simulation so that the scenario matches well with, e.g., the measured sojourn times in a cell.     

基于不同移动模型的移动自组网多播路由协议性能研究

为了研究移动自组网中多播路由协议在不同移动模型下的性能,选取随机路点移动模型、高斯马尔科夫移动模型和参考点组移动模型,将三种移动模型的移动场景加入到NS2中,对基于部分网络编码的实时多播协议PNCRM进行仿真.结果表明,PNCRM协议在随机路点移动模型和高斯马尔科夫移动模型中的数据包投递率明显高于参考点组移动模型,但是参考点组移动模型的总开销和端到端延时是最优的.这样我们就可以根据不同的性能指标要求选择合适的移动模型.     

Optimal Delay–Throughput Tradeoffs in Mobile Ad Hoc Networks

In this paper, we investigate the delay–throughput tradeoffs in mobile ad-hoc networks. We consider four node mobility models: 1) two-dimensional independent and identically distributed (i.i.d.) mobility, 2) two-dimensional hybrid random walk, 3) one-dimensional i.i.d. mobility, and 4) one-dimensional hybrid random walk. Two mobility time scales are included in this paper. i) Fast mobility, where node mobility is at the same time scale as data transmissions. ii) Slow mobility, where node mobility is assumed to occur at a much slower time scale than data transmissions. Given a delay constraint $D$ , we first characterize the maximum throughput per source–destination (S-D) pair for each of the four mobility models with fast or slow mobiles. We then develop joint coding–scheduling algorithms to achieve the optimal delay–throughput tradeoffs.      

Two-Dimensional Modeling and Analysis of Generalized Random Mobility Models for Wireless Ad Hoc Networks

Most important characteristics of wireless ad hoc networks, such as link distance distribution, connectivity, and network capacity are dependent on the long-run properties of the mobility profiles of communicating terminals. Therefore, the analysis of the mobility models proposed for these networks becomes crucial. The contribution of this paper is to provide an analytical framework that is generalized enough to perform the analysis of realistic random movement models over two-dimensional regions. The synthetic scenarios that can be captured include hotspots where mobiles accumulate with higher probability and spend more time, and take into consideration location and displacement dependent speed distributions. By the utilization of the framework to the random waypoint mobility model, we derive an approximation to the spatial distribution of terminals over rectangular regions. We validate the accuracy of this approximation via simulation, and by comparing the marginals with proven results for one-dimensional regions, we find out that the quality of the approximation is insensitive to the proportion between dimensions of the terrain.     

Gamma random waypoint mobility model for wireless ad hoc networks

Random waypoint (RWP) mobility model is widely used in ad hoc network simulation. The model suffers from speed decay as the simulation progresses and may not reach the steady state in terms of instantaneous average node speed. Furthermore, the convergence of the average speed to its steady state value is delayed. This usually leads to inaccurate results in protocol validation of mobile ad hoc networks modeling. Moreover, the probability distributions of speed vary over the simulation time, such that the node speed distribution at the initial state is different from the corresponding distribution at the end of the simulation. In order to overcome these problems, this paper proposes a modified RWP mobility model with a more precise distribution of the nodes' speed. In the modified model, the speeds of nodes are sampled from gamma distribution. The results obtained from both analysis and simulation experiments of the average speed and the density of nodes' speed indicate that the proposed gamma random waypoint mobility model outperforms the existing RWP mobility models. It is shown that a significant performance improvement in achieving higher steady state speed values that closely model the pre‐assumed average speeds are possible with the proposed model. Additionally, the model allows faster convergence to the steady state, and probability distribution of speed is steady over the simulation time. Copyright © 2012 John Wiley & Sons, Ltd.     

Ensuring strong data guarantees in highly mobile ad hoc networks via quorum systems

Ensuring the consistency and the availability of replicated data in highly mobile ad hoc networks is a challenging task because of the lack of a backbone infrastructure. Previous work provides strong data guarantees by limiting the motion and the speed of the mobile nodes during the entire system lifetime, and by relying on assumptions that are not realistic for most mobile applications. We provide a small set of mobility constraints that are sufficient to ensure strong data guarantees and that can be applied when nodes move along unknown paths and speed, and are sparsely distributed.

In the second part of the paper, we analyze the problem of conserving energy while ensuring strong data guarantees, using quorum system techniques. We devise a condition necessary for a quorum system to guarantee data consistency and data availability under our mobility model. This condition shows the unsuitability of previous quorum systems and is the basis for a novel class of quorum systems suitable for highly mobile networks, called mobile dissemination quorum (MDQ) systems. We also show a MDQ system that is provably optimal in terms of communication cost by proposing an efficient implementation of a read/write atomic shared memory.

The suitability of our mobility model and MDQ systems is validated through simulations using the random waypoint model and the restricted random waypoint on a city section. Finally, we apply our results to assist routing and coordinate the low duty cycle of mobile nodes while maintaining network connectivity.