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The Node Distribution of the Random Waypoint Mobility Model for Wireless Ad Hoc Networks
, 2003
"... 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 closedform expression of this distribution and an indepth investigation ..."
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Cited by 376 (10 self)
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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 closedform expression of this distribution and an indepth investigation is still missing. This fact impairs the accuracy of the current simulation methodology of ad hoc networks and makes it impossible to relate simulationbased 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.
Geographic random forwarding (GeRaF) for ad hoc and sensor networks: Energy and latency performance
 IEEE TRANSACTIONS ON MOBILE COMPUTING
, 2003
"... In this paper, we study a novel forwarding technique based on geographical location of the nodes involved and random selection of the relaying node via contention among receivers. We provide a detailed description of a MAC scheme based on these concepts and on collision avoidance and report on its e ..."
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Cited by 367 (15 self)
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In this paper, we study a novel forwarding technique based on geographical location of the nodes involved and random selection of the relaying node via contention among receivers. We provide a detailed description of a MAC scheme based on these concepts and on collision avoidance and report on its energy and latency performance. A simplified analysis is given first, some relevant trade offs are highlighted, and parameter optimization is pursued. Further, a semiMarkov model is developed which provides a more accurate performance evaluation. Simulation results supporting the validity of our analytical approach are also provided.
Probability Estimates for Multiclass Classification by Pairwise Coupling
 Journal of Machine Learning Research
, 2003
"... Pairwise coupling is a popular multiclass classification method that combines together all pairwise comparisons for each pair of classes. This paper presents two approaches for obtaining class probabilities. Both methods can be reduced to linear systems and are easy to implement. ..."
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Cited by 301 (2 self)
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Pairwise coupling is a popular multiclass classification method that combines together all pairwise comparisons for each pair of classes. This paper presents two approaches for obtaining class probabilities. Both methods can be reduced to linear systems and are easy to implement.
Connections with Multiple Congested Gateways in PacketSwitched Networks Part 1: Oneway Traffic
 ACM Computer Communication Review
, 1991
"... In this paper we explore the bias in TCP/IP networks against connections with multiple congested gateways. We consider the interaction between the bias against connections with multiple congested gateways, the bias of the TCP window modification algorithm against connections with longer roundtrip ti ..."
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Cited by 299 (14 self)
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In this paper we explore the bias in TCP/IP networks against connections with multiple congested gateways. We consider the interaction between the bias against connections with multiple congested gateways, the bias of the TCP window modification algorithm against connections with longer roundtrip times, and the bias of Drop Tail and Random Drop gateways against bursty traffic. Using simulations and a heuristic analysis, we show that in a network with the window modification algorithm in 4.3 tahoe BSD TCP and with Random Drop or Drop Tail gateways, a longer connection with multiple congested gateways can receive unacceptably low throughput. We show that in a network with no bias against connections with longer roundtrip times and with no bias against bursty traffic, a connection with multiple congested gateways can receive an acceptable level of throughput. We discuss the application of several current measures of fairness to networks with multiple congested gateways, and show that diff...
Stability, queue length and delay of deterministic and stochastic queueing networks
 IEEE Transactions on Automatic Control
, 1994
"... Motivated by recent development in high speed networks, in this paper we study two types of stability problems: (i) conditions for queueing networks that render bounded queue lengths and bounded delay for customers, and (ii) conditions for queueing networks in which the queue length distribution of ..."
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Cited by 231 (21 self)
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Motivated by recent development in high speed networks, in this paper we study two types of stability problems: (i) conditions for queueing networks that render bounded queue lengths and bounded delay for customers, and (ii) conditions for queueing networks in which the queue length distribution of a queue has an exponential tail with rate `. To answer these two types of stability problems, we introduce two new notions of traffic characterization: minimum envelope rate (MER) and minimum envelope rate with respect to `. Based on these two new notions of traffic characterization, we develop a set of rules for network operations such as superposition, inputoutput relation of a single queue, and routing. Specifically, we show that (i) the MER of a superposition process is less than or equal to the sum of the MER of each process, (ii) a queue is stable in the sense of bounded queue length if the MER of the input traffic is smaller than the capacity, (iii) the MER of a departure process from a stable queue is less than or equal to that of the input process (iv) the MER of a routed process from a departure process is less than or equal to the MER of the departure process multiplied by the MER of the routing process. Similar results hold for MER with respect to ` under a further assumption of independence. These rules provide a natural way to analyze feedforward networks with multiple classes of customers. For single class networks with nonfeedforward routing, we provide a new method to show that similar stability results hold for such networks under the FCFS policy. Moreover, when restricting to the family of twostate Markov modulated arrival processes, the notion of MER with respect to ` is shown to be
The FourierSeries Method For Inverting Transforms Of Probability Distributions
, 1991
"... This paper reviews the Fourierseries method for calculating cumulative distribution functions (cdf's) and probability mass functions (pmf's) by numerically inverting characteristic functions, Laplace transforms and generating functions. Some variants of the Fourierseries method are remar ..."
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Cited by 211 (52 self)
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This paper reviews the Fourierseries method for calculating cumulative distribution functions (cdf's) and probability mass functions (pmf's) by numerically inverting characteristic functions, Laplace transforms and generating functions. Some variants of the Fourierseries method are remarkably easy to use, requiring programs of less than fifty lines. The Fourierseries method can be interpreted as numerically integrating a standard inversion integral by means of the trapezoidal rule. The same formula is obtained by using the Fourier series of an associated periodic function constructed by aliasing; this explains the name of the method. This Fourier analysis applies to the inversion problem because the Fourier coefficients are just values of the transform. The mathematical centerpiece of the Fourierseries method is the Poisson summation formula, which identifies the discretization error associated with the trapezoidal rule and thus helps bound it. The greatest difficulty is approximately calculating the infinite series obtained from the inversion integral. Within this framework, lattice cdf's can be calculated from generating functions by finite sums without truncation. For other cdf's, an appropriate truncation of the infinite series can be determined from the transform based on estimates or bounds. For Laplace transforms, the numerical integration can be made to produce a nearly alternating series, so that the convergence can be accelerated by techniques such as Euler summation. Alternatively, the cdf can be perturbed slightly by convolution smoothing or windowing to produce a truncation error bound independent of the original cdf. Although error bounds can be determined, an effective approach is to use two different methods without elaborate error analysis. For this...
User mobility modeling and characterization of mobility patterns
 IEEE Journal on Selected Areas in Communications
, 1997
"... Abstract—A mathematical formulation is developed for systematic tracking of the random movement of a mobile station in a cellular environment. It incorporates mobility parameters under the most generalized conditions, so that the model can be tailored to be applicable in most cellular environments. ..."
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Cited by 202 (0 self)
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Abstract—A mathematical formulation is developed for systematic tracking of the random movement of a mobile station in a cellular environment. It incorporates mobility parameters under the most generalized conditions, so that the model can be tailored to be applicable in most cellular environments. This mobility model is used to characterize different mobilityrelated traffic parameters in cellular systems. These include the distribution of the cell residence time of both new and handover calls, channel holding time, and the average number of handovers. It is shown that the cell resistance time can be described by the generalized gamma distribution. It is also shown that the negative exponential distribution is a good approximation for describing the channel holding time. Index Terms—Mobile communication. I.
A computational model of trust and reputation
 In Proceedings of the 35th Hawaii International Conference on System Science (HICSS
, 2002
"... Despite their many advantages, eBusinesses lag behind brick and mortar businesses in several fundamental respects. This paper concerns one of these: relationships based on trust and reputation. Recent studies on simple reputation systems for eBusinesses such as eBay have pointed to the importance ..."
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Cited by 199 (0 self)
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Despite their many advantages, eBusinesses lag behind brick and mortar businesses in several fundamental respects. This paper concerns one of these: relationships based on trust and reputation. Recent studies on simple reputation systems for eBusinesses such as eBay have pointed to the importance of such rating systems for deterring moral hazard and encouraging trusting interactions. However, despite numerous studies on trust and reputation systems, few have taken studies across disciplines to provide an integrated account of these concepts and their relationships. This paper first surveys existing literatures on trust, reputation and a related concept: reciprocity. Based on sociological and biological understandings of these concepts, a computational model is proposed. This model can be implemented in a real system to consistently calculate agents ’ trust and reputation scores. 1.
Capacity and delay tradeoffs for adhoc mobile networks
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 2005
"... We consider the throughput/delay tradeoffs for scheduling data transmissions in a mobile adhoc network. To reduce delays in the network, each user sends redundant packets along multiple paths to the destination. Assuming the network has a cell partitioned structure and users move according to a s ..."
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Cited by 189 (12 self)
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We consider the throughput/delay tradeoffs for scheduling data transmissions in a mobile adhoc network. To reduce delays in the network, each user sends redundant packets along multiple paths to the destination. Assuming the network has a cell partitioned structure and users move according to a simplified independent and identically distributed (i.i.d.) mobility model, we compute the exact network capacity and the exact endtoend queueing delay when no redundancy is used. The capacity achieving algorithm is a modified version of the GrossglauserTse 2hop relay algorithm and provides O(N) delay (where N is the number of users). We then show that redundancy cannot increase capacity, but can significantly improve delay. The following necessary tradeoff is established: delay/rate ≥ O(N). Two protocols that use redundancy and operate near the boundary of this curve are developed, with delays of O(√ N) and O(log(N)), respectively. Networks with noni.i.d. mobility are also considered and shown through simulation to closely match the performance of i.i.d. systems in the O(√ N) delay regime.