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.     

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 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.     

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.     

A misdirected route avoidance using random waypoint mobility model in wireless sensor network

Wireless Networks - In this paper, a novel method is proposed to reduce the number of route misdirection to increase network throughput. This method increases the network throughput by accurately...     

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.     

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.     

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.     

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.     

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.     

Delay and capacity in MANETs under random walk mobility model

The closed-form results for delay and capacity in mobile ad hoc networks are important for the performance analysis of different transmission protocols. Most existing works focus on independent and identically distributed mobility model, which is always regarded as an idealized global model. In this paper, we extend the investigation to the random walk model, which characterizes practical situations more accurately. Some local movements cause a series of complicated probabilistic problem, we develop a method to calculate the meeting probability between two randomly selected nodes under random walk mobility model. Targeting at the most commonly used routing schemes which are modeled by 2HR-f algorithm, we obtain the closed-form solutions for delay and capacity, where the wireless interference and medium access contention among nodes are considered. Extensive simulations demonstrate the accuracy of our theoretical results.     

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.     

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.     

An improved electron and hole mobility model for general purposedevice simulation

A new, comprehensive, physically-based, semiempirical, local model for transverse-field dependent electron and hole mobility in MOS transistors is presented. In order to accurately predict the measured relationship between the effective mobility and effective electric field over a wide range of substrate doping and bias, we account for the dependence of surface roughness limited mobility on the inversion charge density, in addition to including the effect of coulomb screening of impurities by charge carriers in the bulk mobility term. The result is a single mobility model applicable throughout a generalized device structure that gives good agreement with measured mobility data and measured MOS I-V characteristics over a wide range of substrate doping, channel length, transverse electric field, substrate bias, and temperature     

A Coxian model for channel holding time distribution forteletraffic mobility modeling

In this letter, we derive an algebraic set of equations that examines the relationships between the cell residence times and the handoff call's channel holding time. When the cell residence times have an Erlang or Hyper-Erlang distribution, the channel holding times can be represented by a Coxian model. An algorithm is presented to compute the parameters of the equivalent Coxian model. The analytical models proposed in this letter provide a flexible framework for further studies into the optimization and performance evaluation aspects of teletraffic mobile systems     

Multicast capacity and delay trade‐offs in ad hoc networks with random iid mobility model

In this paper, multicast capacity and delay trade‐offs of mobile ad hoc networks are considered under random independently and identically distributed (iid) mobility model. Compared with unicast, multicast can reduce the overall network load by a factor with high probability (whp) in static random ad hoc networks, where k is the number of destination nodes in a multicast session. So we firstly discuss whether the law still holds in mobile random ad hoc networks, and in this case what delay should be tolerated. Through the relation between average retransmissions and multicast capacity, we prove that order of multicast capacity is not achievable whp, and delay for multicast capacity is , where is the number of ad hoc nodes in the whole networks, and and c is a positive constant. Then achievable throughput whp is considered. The nearest neighbor transmission strategy is introduced by Grossglauser and Tse to achieve throughput which is so far the highest achievable unicast capacity. So the multicast capacity of mobile ad hoc networks under this strategy is studied. The analysis shows that under any multicast routing scheme based on the nearest neighbor transmission strategy, the upper bound on multicast capacity is whp. Then we propose a multicast routing and scheduling scheme by which mobile ad hoc networks can achieve throughput whp, and must tolerate total network delay. Copyright © 2009 John Wiley & Sons, Ltd.     

Static random access memory using high electron mobility transistors

A 4-bit fully decoded static random access memory (RAM) has been designed and fabricated using high electron mobility transistors (HEMT's) with a direct-coupled FET logic approach. The circuit incorporates approximately 50 logic gates. A fully operating memory circuit was demonstrated with an access time of 1.1 ns and a minimum WRITE-enable pulse of less than 2-ns duration at room temperature. This memory consumes a total power of 14.89 mW and 87.8 µW per memory cell.     

基于时间门方法的随机耦合模型在复杂腔体电磁预测中的应用

利用随机耦合模型(random coupling model,RCM)预测复杂腔体电磁效应时,通常要通过测量辐射阻抗来实现,但实验过程中满足混沌腔体以及耦合通道的腔体加工、实验过程模拟等条件要求较高,且实验步骤繁琐.为了克服上述问题,文中采用时间门方法(time gating method,TGM),通过对散射参数进行...     

The failure time random variable modelling

Construction of adequate probabilistic models is nowadays an important issue in examining the reliability of technical systems. Presented herein is the failure time random variable modelling in applications to real technical systems. A linear regression model is discussed and its role in creating Weibull's proportional hazards model of technical systems is shown.     

Low hitting time random walks in wireless networks

Random walks can be conveniently exploited for implementing probabilistic algorithms to solve many searching problems arised by distributed applications, for example, service discovery, p2p file sharing, etc. In this paper we consider random walks executed on uniform wireless networks and study how to reduce the expected number of walk steps required to reach a target, namely the hitting time. The latter is the main search performance metric of a random walk based algorithm, since it determines the average response to a search as well as its cost; thus, the actual convenience of using random walks compared to other solutions depends on achieving a low hitting time. We show how in uniform wireless networks, the natural implementation of a random walk which selects the next node to visit at random among all neighbors is not a good choice, since it has a strong negative effect on the hitting time. This paper studies such a negative effect analytically and proposes two neighbor selection rules aiming at reducing the hitting time. A simulation study confirms the benefits of the proposed solutions. Copyright © 2008 John Wiley & Sons, Ltd.