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.     

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.     

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.     

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.     

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.     

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.     

Evaluating inter-arrival time in general random waypoint mobility model

In the study of wireless ad hoc networks, the Random Waypoint (RWP) mobility model is extensively used to describe the movement pattern of the hosts. In this paper, we extend our discussion to the general RWP mobility model, where the waypoints may not be uniformly distributed, and hosts may use different distributions to generate their waypoints. In particular, we study a useful property, namely the Inter-Arrival Time (IAT) of hosts to a given area in a network, when the mobility of such hosts is modeled using the random waypoint mobility model. We derive the value of IAT analytically. Three schemes are used to estimate its value. The correctness of our analysis and estimations are verified through simulations. Case studies are also carried out in this paper to show how IAT could be used in the study and applications of mobile wireless networks.     

Network connectivity of one-dimensional MANETs with random waypoint movement

An analysis of network connectivity of one-dimensional mobile ad hoc networks with a particular mobility scheme is presented, focusing on the random waypoint mobility scheme. The numerical results are verified using simulation to show their accuracy under practical network conditions. Observations on RWP properties further lead to approximations and an eventual simple network connectivity formula.     

Capacity Scaling in Ad Hoc Networks With Heterogeneous Mobile Nodes: The Super-Critical Regime

We analyze the capacity scaling laws of mobile ad hoc networks comprising heterogeneous nodes and spatial inhomogeneities. Most of previous work relies on the assumption that nodes are identical and uniformly visit the entire network space. Experimental data, however, show that the mobility pattern of individual nodes is usually restricted over the area, while the overall node density is often largely inhomogeneous due to the presence of node concentration points. In this paper we introduce a general class of mobile networks which incorporates both restricted mobility and inhomogeneous node density, and describe a methodology to compute the asymptotic throughput achievable in these networks by the store-carry-forward communication paradigm. We show how the analysis can be mapped, under mild assumptions, into a Maximum Concurrent Flow (MCF) problem over an associated Generalized Random Geometric Graph (GRGG). Moreover, we propose an asymptotically optimal scheduling and routing scheme that achieves the maximum network capacity.     

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.     

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.     

The diameter of mobile ad hoc networks

With the prevalence of mobile devices, it is of much interest to study the properties of mobile ad hoc networks. In this paper, we extend the concept of diameter from static ad hoc network to mobile ad hoc network, which is the expected number of rounds for one node to transmit a message to all other nodes in the network, reflecting the worst end‐to‐end delay between any two node. Specifically, we investigate the diameter of identically and independently mobility model in cell‐partitioned network and random walk mobility model in two‐dimensional torus network, achieving the boundary , when (k=Ω(n)), and O(k log2k), respectively, where n is the number of nodes and k is the number of cells of network and especially under random walk mobility model . A comparison is made among the diameter of mobile ad hoc networks under identically and independently mobility model, random walk mobility model and static ad hoc network, showing that mobility dramatically decreases the diameter of the network and speed is an essential and decisive factor of diameter. Copyright © 2016 John Wiley & Sons, Ltd.     

The critical transmitting range for connectivity in mobile ad hoc networks

In this paper, we have investigated the critical transmitting range for connectivity in mobile ad hoc networks. We have proven that, in the presence of bounded and obstacle free mobility, the CTR in the mobile case is at least as large as the CTR in the case of uniformly distributed points (asymptotically). For the case of RWP mobility, we have proven a more accurate characterization of the CTR and shown that, if the pause time is 0, there is an asymptotic gap between the mobile and uniform scenario. We have verified the quality of our results through simulation. We have also presented a formula that, given the value of the CTR in the uniform case, provides a good approximation of the CTR in the most extreme case of RWP mobility, i.e., when the pause time is set to 0. We want to remark that the approach presented in this paper can be easily extended to other mobility models: If the expression of the pdf f/sub m/ that resembles the long-term node distribution is known and satisfies certain properties, it is sufficient to compute the minimum value of f/sub m/ on R to determine the value of the critical range for connectivity. We believe that the results presented in this paper provide a better understanding of the behavior of a fundamental network parameter in the presence of mobility and, in particular, of RWP mobility. From a practical point of view, our results can be used to improve the accuracy of RWP mobile ad hoc networks simulation, which is commonly used to evaluate the performance of ad hoc networking protocols.     

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.     

Integrated Routing and Storage for Messaging Applications in Mobile Ad Hoc Networks

This paper is motivated by the observation that traditional ad hoc routing protocols are not an adequate solution for messaging applications (e.g., e-mail) in mobile ad hoc networks. Routing in ad hoc mobile networks is challenging mainly because of node mobility – the more rapid the rate of movement, the greater the fraction of bad routes and undelivered messages. For applications that can tolerate delays beyond conventional forwarding delays, we advocate a relay-based approach to be used in conjunction with traditional ad hoc routing protocols. This approach takes advantage of node mobility to disseminate messages to mobile nodes. The result is the Mobile Relay Protocol (MRP), which integrates message routing and storage in the network; the basic idea is that if a route to a destination is unavailable, a node performs a controlled local broadcast (a relay) to its immediate neighbors. In a network with sufficient mobility – precisely the situation when conventional routes are likely to be non-existent or broken – it is quite likely that one of the relay nodes to which the packet has been relayed will encounter a node that has a valid, short (conventional) route to the eventual destination, thereby increasing the likelihood that the message will be successfully delivered. Our simulation results under a variety of node movement models demonstrate that this idea can work well for applications that prefer reliability over latency.     

Modeling human mobility in obstacle-constrained ad hoc networks

In this paper we present a mobility model for ad hoc networks consisting of human-operated nodes that are deployed in obstacle-constrained environments. According to this model, the network nodes move around the obstacles in a way that resembles how humans bypass physical obstructions. A recursive procedure is executed by each node at its current position to determine the next intermediate destination point until the final destination point is reached. The proposed mobility model is validated using real-life trace data and studied using both mathematical analysis and simulations. Furthermore, the model is extended to incorporate several operational aspects of ad hoc networks in mission critical scenarios, where it is best applicable. These extensions include hierarchical node organization, distinct modes of node activity, event-based destination selection and impact of the physical obstacles on signal propagation. The model is implemented as an add-on module in Network Simulator (ns-2).     

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.     

Futuristic speed prediction using auto‐regression and neural networks for mobile ad hoc networks

In this paper, we propose a speed prediction model using auto‐regressive integrated moving average (ARIMA) and neural networks for estimating the futuristic speed of the nodes in mobile ad hoc networks (MANETs). The speed prediction promotes the route discovery process for the selection of moderate mobility nodes to provide reliable routing. The ARIMA is a time‐series forecasting approach, which uses autocorrelations to predict the future speed of nodes. In the paper, the ARIMA model and recurrent neural network (RNN) trains the random waypoint mobility (RWM) dataset to forecast the mobility of the nodes. The proposed ARIMA model designs the prediction models through varying the delay terms and changing the numbers of hidden neuron in RNN. The Akaike information criterion (AIC), Bayesian information criterion (BIC), auto‐correlation function (ACF), and partial auto‐correlation function (PACF) parameters evaluate the predicted mobility dataset to estimate the model quality and reliability. The different scenarios of changing node speed evaluate the performance of prediction models. Performance results indicate that the ARIMA forecasted speed values almost match with the RWM observed speed values than RNN values. The graphs exhibit that the ARIMA predicted mobility values have lower error metrics such as mean square error (MSE), root MSE (RMSE), and mean absolute error (MAE) than RNN predictions. It yields higher futuristic speed prediction precision rate of 17% to 24% throughout the time series as compared with RNN. Further, the proposed model extensively compares with the existing works.     

Distributed Mobility Management for Target Tracking in Mobile Sensor Networks

Mobility management is a major challenge in mobile ad hoc networks (MANETs) due in part to the dynamically changing network topologies. For mobile sensor networks that are deployed for surveillance applications, it is important to use a mobility management scheme that can empower nodes to make better decisions regarding their positions such that strategic tasks such as target tracking can benefit from node movement. In this paper, we describe a distributed mobility management scheme for mobile sensor networks. The proposed scheme considers node movement decisions as part of a distributed optimization problem which integrates mobility-enhanced improvement in the quality of target tracking data with the associated negative consequences of increased energy consumption due to locomotion, potential loss of network connectivity, and loss of sensing coverage.