356 research outputs found
Restricted Mobility Improves Delay-Throughput Trade-offs in Mobile Ad-Hoc Networks
In this paper we revisit two classes of mobility models which are widely used to repre-sent 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 i) simple expressions which relate the transient dura-tion to the model parameters; ii) the definition of a generalized random direction model whose stationary distribution of mobiles in the physical space corresponds to an assigned distribution
On the well-posedness of weakly hyperbolic equations with time-dependent coefficients
AbstractIn this paper we analyse the Gevrey well-posedness of the Cauchy problem for weakly hyperbolic equations of general form with time-dependent coefficients. The results involve the order of lower order terms and the number of multiple roots. We also derive the corresponding well-posedness results in the space of Gevrey Beurling ultradistributions
Generalized Fourier Integral Operators on spaces of Colombeau type
Generalized Fourier integral operators (FIOs) acting on Colombeau algebras
are defined. This is based on a theory of generalized oscillatory integrals
(OIs) whose phase functions as well as amplitudes may be generalized functions
of Colombeau type. The mapping properties of these FIOs are studied as the
composition with a generalized pseudodifferential operator. Finally, the
microlocal Colombeau regularity for OIs and the influence of the FIO action on
generalized wave front sets are investigated. This theory of generalized FIOs
is motivated by the need of a general framework for partial differential
operators with non-smooth coefficients and distributional data
User Interaction with Online Advertisements: Temporal Modeling and Optimization of Ads Placement
A time-modulated Hawkes process to model the spread of COVID-19 and the impact of countermeasures
Impact of Correlated Mobility on Delay-Throughput Performance in Mobile Ad-Hoc Networks
Abstract—We extend the analysis of the scaling laws of wireless ad hoc networks to the case of correlated nodes movements, which are commonly found in real mobility processes. We consider a simple version of the Reference Point Group Mobility model, in which nodes belonging to the same group are constrained to lie in a disc area, whose center moves uniformly across the network according to the i.i.d. model. We assume fast mobility conditions, and take as primary goal the maximization of pernode throughput. We discover that correlated node movements have huge impact on asymptotic throughput and delay, and can sometimes lead to better performance than the one achievable under independent nodes movements. I. INTRODUCTION AND RELATED WORK In the last few years the store-carry-forward communication paradigm, which allows nodes to physically carry buffered dat
Classes of generalized functions with finite type regularities
We introduce and analyze spaces and algebras of generalized functions which correspond to Hölder, Zygmund, and Sobolev spaces of functions. The main scope of the paper is the characterization of the regularity of distributions that are embedded into the corresponding space or algebra of generalized functions with finite type regularities
Hyperbolic systems with non-diagonalisable principal part and variable multiplicities, II: Microlocal analysis
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