Christian Bettstetter

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 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.

On the minimum node degree and connectivity of a wireless multihop network

This paper investigates two fundamental characteristics of a wireless multi -hop network: its minimum node degree and its k--connectivity. Both topology attributes depend on the spatial distribution of the nodes and their transmission range. Using typical modeling assumptions :--- :a random uniform distribution of the nodes and a simple link model :--- :we derive an analytical expression that enables the determination of the required range r0 that creates, for a given node density ρ, an almost surely k--connected network. Equivalently, if the maximum r0 of the nodes is given, we can find out how many nodes are needed to cover a certain area with a k--connected network. We also investigate these questions by various simulations and thereby verify our analytical expressions. Finally, the impact of mobility is discussed.The results of this paper are of practical value for researchers in this area, e.g., if they set the parameters in a network--level simulation of a mobile ad hoc network or if they design a wireless sensor network.

Connectivity of wireless multihop networks in a shadow fading environment

This article analyzes the connectivity of multihop radio networks in a log-normal shadow fading environment. Assuming the nodes have equal transmission capabilities and are randomly distributed according to a homogeneous Poisson process, we give a tight lower bound for the minimum node density that is necessary to obtain an almost surely connected subnetwork on a bounded area of given size. We derive an explicit expression for this bound, compute it in a variety of scenarios, and verify its tightness by simulation. The numerical results can be used for the practical design and simulation of wireless sensor and ad hoc networks. In addition, they give insight into how fading affects the topology of multihop networks. It is explained why a high fading variance helps the network to become connected.

Self-organization in communication networks: principles and design paradigms

The trend toward ubiquitous wireless communication demands for a higher level of self-organization in networks. This article gives an introduction and overview on this topic and investigates the fundamental question: What are design paradigms for developing a self-organized network function? We propose four paradigms and show how they are reflected in current protocols: design local interactions that achieve global properties, exploit implicit coordination, minimize the maintained state, and design protocols that adapt to changes. Finally, we suggest a general design process for self-organized network functions.

On the Connectivity of Ad Hoc Networks

This paper presents a framework for the calculation of stochastic connectivity properties of wireless multihop networks. Assuming that n nodes, each node with transmission range r0, are distributed according to some spatial probability density function, we study the level of connectivity of the resulting network topology from three viewpoints. First, we analyze the number of neighbors of a given node. Second, we study the probability that there is a communication path between two given nodes. Third, we investigate the probability that the entire network is connected, i.e. each node can communicate with every other node via a multihop path. For the last-mentioned issue, we compute a tight approximation for the critical (r0 ,n )pairs that are required to keep the network connected with a probability close to one. In fact, the problem is solved for the general case of a k-connected network, accounting for the robustness against node failures. These issues are studied for uniformly distributed nodes (with and without ‘border effects’), Gaussian distributed nodes, and nodes that move according to the commonly used random waypoint mobility model. The results are of practical value for the design and simulation of wireless sensor and mobile ad hoc networks.

GSM phase 2+ general packet radio service GPRS: Architecture, protocols, and air interface

The general packet radio service (GPRS) is a new bearer service for GSM that greatly improves and simplifies wireless access to packet data networks, e.g., to the Internet. It applies a packet radio principle to transfer user data packets in an efficient way between mobile stations and external packet data networks. This tutorial gives an introduction to GPRS. The article discusses the system architecture and its basic functionality. It explains the offered services, the session and mobility management, the routing, the GPRS air interface including channel coding, and the GPRS protocol architecture. Finally, an interworking example between GPRS and IP networks is shown.

On the connectivity of wireless multihop networks with homogeneous and inhomogeneous range assignment

This paper investigates the connectivity of wireless multihop networks with uniformly randomly distributed nodes. We analyze the required transmission range that creates, for a given node density, an almost surely k-connected topology. Besides scenarios in which each node has the same range, we discuss inhomogeneous range assignments. Our results are of practical value for the task of setting parameters in network-level simulations of ad hoc networks and in the design of wireless sensor networks.

Hop distances in homogeneous ad hoc networks

Given is the network-level view of a wireless multi-hop network with n uniformly distributed nodes, each of them with radio transmission range r/sub 0/, on a rectangular area. This paper investigates the discrete probability distribution of the minimum number of wireless hops H between a random source and destination node. This topology attribute has significant impact on the network performance, e.g., on route discovery delay and message delivery. We derive closed form expressions for the probability that two nodes can communicate within H = 1 hop (i.e., via a direct link) or H = 2 hops (i.e., over one relay node). Connection paths with H > 2 hops and the expected hop distance E{H} are studied by analytical bounds and extensive simulations.

Code construction and decoding of parallel concatenated tail-biting codes

Based on the two-dimensional (2-D) weight distribution of tail-biting codes we give guidelines on how to choose tail biting component codes that are especially suited for parallel concatenated coding schemes. Employing these guidelines, we tabulate tail-biting codes of different rate, length, and complexity. The performance of parallel concatenated block codes (PCBCs) using iterative (turbo) decoding is evaluated by simulation and bounds are calculated in order to study their asymptotic performance.

How to achieve a connected ad hoc network with homogeneous range assignment: an analytical study with consideration of border effects

The paper presents an analytical investigation of the connectivity of wireless ad hoc networks with randomly uniformly distributed nodes and homogeneous transmission range assignment The probability that a network is connected depends on the number of nodes, n, per area, A, and their transmission ranges, r/sub 0/. We derive an analytical expression that enables the determination of critical (r/sub 0/, n)-pairs that achieve, with high probability, a connected network in an area A. As opposed to prior analytical work on this topic (see Bettstetter, C., Proc. ACM Symp. on Mobile Ad Hoc Networks and Comp.-MobiHoc, 2002), we now consider border effects, which have significant impact on the obtained results. Furthermore, we calculate the expected node degree and the probability that the network has no isolated node. All three results are of practical value in simulation and system design of ad hoc and wireless sensor networks. While the paper considers a circular system area, the methods can also be applied to other shapes.