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.     

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.     

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.     

Predictability of Aggregated Traffic of Gateways in Wireless Mesh Network with AODV and DSDV Routing Protocols and RWP Mobility Model

When evaluating the performance of routing protocols in wireless mesh network (WMN), we need deeper analysis from the aspect of network traffic complexity to show how traffic characteristics are influenced by routing protocols and node mobility. The predictability of network traffic can be used as one metric of complexity and can be analyzed by multi-scale entropy (MSE) method. With 20 different random waypoint (RWP) mobility scenarios and with destination sequenced distance vector (DSDV), a typical proactive protocol, and Ad hoc on-demand distance vector (AODV), a typical reactive protocol, the predictabilities of aggregated traffic of gateway in WMN are analyzed using MSE method to show how different routing protocols bear different mobility scenarios. The MSE results show that the aggregated traffic of gateway with DSDV is more difficult to be predicted than that with AODV for different mobility scenarios. The maxspeed parameter of RWP dominates the traffic predictability for AODV. Both of the pause time and the maxspeed parameters, have great influence on the traffic predictability for DSDV. The reasons lie in the behaviors of routing protocols, i.e., AODV has up-to-date paths while DSDV does not.     

Distance Reduction in Mobile Wireless Communication: Lower Bound Analysis and Practical Attainment

The transmission energy required for a wireless communication increases superlinearly with the communication distance. In a mobile wireless network, nodal movement can be exploited to greatly reduce the energy required by postponing communication until the sender moves close to a target receiver, subject to application deadline constraints. In this paper, we characterize the fundamental performance limit, namely the lower bound expected communication distance, achievable by any postponement algorithm within given deadline constraints. Our analytical results concern mainly the random waypoint (RWP) model. Specifically, we develop a tight analytical lower bound of the achievable expected communication distance under the model. In addition, we define a more general map-based movement model, and characterize its lower bound distance by simulations. We also address the practical attainment of distance reduction through movement-predicted communication. Specifically, whereas prior work has experimentally demonstrated the effectiveness a least distance (LD) algorithm, we provide an absolute performance measure of how closely LD can match the theoretical optimum. We show that LD achieves an average reduction in the expected communication distance within 62% to 94% of the optimal, over a realistic range of nodal speeds, for both the RWP and map-based models.     

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.     

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.     

Nonlinearities compensator based on SORBFNN in ultra-long-haul high-capacity CO-OFDM systems

The ultraviolet (UV) scattering communication can be applied in military networked on-the-move and unattended ground sensor networks. This paper focuses on the connectivity properties of unmanned aerial vehicles (UAVs) network based on UV communication that ensures the secret communications between UAVs. UAVs network is consisting of a group of UAVs, each of which moving according to a particular mobility model. We discuss random waypoint (RWP) mobility model and circle movement based model (CMBM), which can describe the actual movement of UAVs, respectively. In this paper, the approximations of the probability that the network is k-connected are provided with consideration of transmission using on–off keying and pulse position modulation. More precisely, we evaluate the effects of node density, transmission power, and data rate on k-connectivity. The numerical examples show that the mobility degrades the connectivity probability. When the numbers of nodes \(n=500\) and data rate \(R_b =10\,\hbox {kbps}\), the required transmission power for nodes moving according to RWP is lower than CMBM in order to achieve 2-connectivity of the UAVs network, but it is about twice that for uniformly distributed nodes.     

The Random Trip Model: Stability, Stationary Regime, and Perfect Simulation

We define "random trip", a generic mobility model for random, independent node motions, which contains as special cases: the random waypoint on convex or nonconvex domains, random walk on torus, billiards, city section, space graph, intercity and other models. We show that, for this model, a necessary and sufficient condition for a time-stationary regime to exist is that the mean trip duration (sampled at trip endpoints) is finite. When this holds, we show that the distribution of node mobility state converges to the time-stationary distribution, starting from the origin of an arbitrary trip. 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, thus closing a long standing issue. We show that random walk on torus and billiards belong to the random trip class of models, and establish that the time-limit distribution of node location for these two models is uniform, for any initial distribution, even in cases where the speed vector does not have circular symmetry. Using Palm calculus, we establish properties of the time-stationary regime, when the condition for its existence holds. We provide an algorithm to sample the simulation state from a time-stationary distribution at time 0 ("perfect simulation"), without computing geometric constants. For random waypoint on the sphere, random walk on torus and billiards, we show that, in the time-stationary regime, the node location is uniform. Our perfect sampling algorithm is implemented to use with ns-2, and is available to download from http://ica1www.epfl.ch/RandomTrip     

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.     

Mobility model of vehicle-borne terminals in urban cellular systems

This paper presents a new model describing the mobility of vehicle-borne terminals under realistic urban traffic conditions. The model accounts for arbitrary urban street patterns and realistic terminal movements by a limited number of parameters that can be easily measured or derived from a city map. It introduces distribution functions of street length, direction changes at crossroads, and terminal velocity to find an analytical formulation. For validation, we show by simulation that the model yields cell sojourn time and remaining sojourn time distributions in agreement with previous results. Further independent validation by measurements and by a street pattern tracing software tool prove the model's accuracy.     

Large intelligent surfaces: Random waypoint mobility and two‐way relaying

In this paper, we first investigate the effect of mobility via the random waypoint (RWP) mobility model on the performance of nonaccess point (non‐AP) or AP large intelligent surfaces (LISs). The theoretical average bit error probability (ABEP) for each of these LISs under mobility is formulated. The presented formulation is complicated to solve; hence, the trapezoidal approximation is employed. Simulation results serve to validate the ABEP. Second, we investigate a two‐way relaying (TWR) network assisted by non‐AP or AP LISs. A network with two source/destination nodes with a single relay node employing decode‐and‐forward placed between these nodes is considered. The transmission interval is broken into two transmission phases. In the first phase, the two source nodes transmit information blocks to the relay node assisted by LISs. On receiving these information blocks, the relay node decodes the two information blocks and encodes these into a single information block via the use of network coding. In the second phase, the relay node forwards the network‐coded information block to the destination nodes assisted by LISs, where the intended information block is decoded via network coding. The theoretical ABEP is formulated for the proposed non‐AP and AP LIS‐assisted TWR schemes and is validated by simulation results. RWP mobility is also demonstrated for the proposed TWR schemes.     

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.     

Network lifetime maximization for time‐sensitive data gathering in wireless sensor networks with a mobile sink

With the advances of more and more mobile sink deployments (e.g., robots and unmanned aerial vehicles), mobile sinks have been demonstrated to play an important role in the prolongation of network lifetime. In this paper, we consider the network lifetime maximization problem for time‐sensitive data gathering, which requires sensing data to be sent to the sink as soon as possible, subject to several constraints on the mobile sink. Because the mobile sink is powered by petrol or electricity, its maximum travel distance per tour is bounded. The mobile sink's maximum moving distance from its current location to the next must also be bounded to minimize data loss. As building a new routing tree rooted at each new location will incur an overhead on energy consumption, the mobile sink must sojourn at each chosen location at least for a certain amount of time. The problem, thus, is to find an optimal sojourn tour for the mobile sink such that the network lifetime is maximized, which is subject to a set of constraints on the mobile sink: its maximum travel distance, the maximum distance of each movement, and the minimum sojourn time at each sojourn location. In this paper, we first formulate this novel multiple‐constrained optimization problem as the distance‐constrained mobile sink problem for time‐sensitive data gathering. We then devise a novel heuristic for it. We finally conduct extensive experiments by simulation to evaluate the performance of the proposed algorithm. The experimental results demonstrate that the performance of the proposed algorithm is very promising, and the solution obtained is fractional of the optimal one. Copyright © 2011 John Wiley & Sons, Ltd.     

A lower bound on filtering error with application to phase demodulation

A new lower bound on nonlinear filtering mean square error (MSE) based on rate distortion theory is derived for message and observation models described by state space equations. Unlike previous contributions, the present bound is general in applicability: it can be used in beth the continuous and discrete time cases; it is applicable during the transient (e.g., acquisition) as well as steady state phases; vector-valued processes of arbitrary dimension can be treated; stationary as well as nonstationary processes can be considered; and essentially no restrictions are placed on the nonlinearities. Two easily implemented approaches to the evaluation of the new lower bound are given: one is analytical in nature while the other uses Monte Carlo simulation techniques. The theory is extended to filtering with distortion measures other then MSE. The MSE lower bound is applied to a phase demodulation problem and compared to other lower bounds which are based on rate distortion theory and the Cramacute{e}r-Rao inequality. Results for this problem show the new lower bound to be tighter than the others in the nonlinear, high noise-to-signal ratio region of receiver operation.     

Blocking in Wavelength-Routed Optical Networks With Heterogeneous Traffic

In this paper, we present a new analytical model that can give an accurate estimation of the blocking probabilities in wavelength-routed optical networks with heterogeneous traffic. By heterogeneous, we mean that each session offered to the network has its own traffic intensity and burstiness. In such cases, the blocking probability of a session is determined by the busy-wavelength distributions of the links seen at the arrival points of its calls. Thus, we first present two single-link models to estimate the arrival-point busy-wavelength distribution of a link with heterogeneous traffic: the full-population (FP) model and the reduced-population (RP) model. Both models are based on the BPP/M/W/W model, where the first two moments of an arbitrary session are matched by those of a birth–death process whose arrival rate linearly varies with the average number of busy wavelengths occupied by its own calls. We show that different sessions have different arrival-point busy-wavelength distributions depending on the burstiness of their traffic, i.e., a bursty session observes the link more congested than a smooth session. Next, we provide two extensions of the single-link models, the FP-full-load link-correlation model and the RP-reduced-load link-correlation model, to estimate the blocking probabilities of optical networks with heterogeneous traffic and sparse wavelength conversion. Both models employ the existing link-correlation models to take into account the occupied-wavelength-index correlation between two adjacent links. By comparing the results from the models with simulation results, we demonstrate that both models well approximate the blocking probabilities of individual sessions, as well as the network-wide blocking probability, for a wide range of traffic intensity, burstiness, and heterogeneity.     

Cost analysis of mobility protocols

Increasing demand for mobility in wireless data network has given rise to various mobility management schemes. Most of the analysis on mobility protocols used Random Waypoint mobility model However, the analysis done earlier ignored some major costs, resulting in an incomplete estimation and used random waypoint model which fails to represent realistic movement pattern. In this paper, we have developed an analytical cost model considering all possible costs related to mobility management, and have used city section mobility model, a realistic mobility model, to compute the total costs of two mobility protocols: HIMPv6 and SIGMA. We have defined two novel performance metrics, normalized overhead and efficiency, for mobility protocols based on the signaling costs and used them to evaluate the performance of SIGMA and HMIPv6 protocols varying network size, mobility rate and traffic rate. Results show that the total cost of SIGMA is much less than HMIPv6 due to the higher cost of packet tunneling, even though the mobility signaling cost of SIGMA is higher than HMIPv6. Moreover, mobility signaling costs of both the protocols using city model and random waypoint model are found to be much different, demonstrating the fact that random waypoint model cannot be used as an approximation to a realistic scenario. The analytical framework presented in this paper can be used by the network professionals to estimate amount of load on the network due to mobility protocols and compare them based on the proposed performance metrics to select the best protocol.     

Performance Analysis of a Discrete‐Time Two‐Phase Queueing System

This paper introduces the modeling and analysis of a discrete‐time, two‐phase queueing system for both exhaustive batch service and gated batch service. Packets arrive at the system according to a Bernoulli process and receive batch service in the first phase and individual services in the second phase. We derive the probability generating function (PGF) of the system size and show that it is decomposed into two PGFs, one of which is the PGF of the system size in the standard discrete‐time Geo/G/1 queue without vacations. We also present the PGF of the sojourn time. Based on these PGFs, we present useful performance measures, such as the mean number of packets in the system and the mean sojourn time of a packet.     

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.     

On the capacity of spatially correlated MIMO Rayleigh-fading channels

In this paper, we investigate the capacity distribution of spatially correlated, multiple-input-multiple-output (MIMO) channels. In particular, we derive a concise closed-form expression for the characteristic function (c.f.) of MIMO system capacity with arbitrary correlation among the transmitting antennas or among the receiving antennas in frequency-flat Rayleigh-fading environments. Using the exact expression of the c.f., the probability density function (pdf) and the cumulative distribution function (CDF) can be easily obtained, thus enabling the exact evaluation of the outage and mean capacity of spatially correlated MIMO channels. Our results are valid for scenarios with the number of transmitting antennas greater than or equal to that of receiving antennas with arbitrary correlation among them. Moreover, the results are valid for an arbitrary number of transmitting and receiving antennas in uncorrelated MIMO channels. It is shown that the capacity loss is negligible even with a correlation coefficient between two adjacent antennas as large as 0.5 for exponential correlation model. Finally, we derive an exact expression for the mean value of the capacity for arbitrary correlation matrices.