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Probabilistic results for a mobile service scenario

Part of: Stochastic processes Geometric probability and stochastic geometry Inference from stochastic processes

Published online by Cambridge University Press:  01 July 2016

Jesper Møller  and
Man Lung Yiu
Jesper Møller*
Affiliation:
Aalborg University
Man Lung Yiu*
Affiliation:
Hong Kong Polytechnic University
*
∗ Postal address: Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7G, DK-9220 Aalborg, Denmark. Email address: jm@math.aau.dk
∗∗ Postal address: Department of Computing, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong. Email address: csmlyiu@comp.polyu.edu.hk
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Abstract

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We consider the following stochastic model for a mobile service scenario. Consider a stationary Poisson process in Rd, with its points radially ordered with respect to the origin (the anchor); if d = 2, the points may correspond to locations of, e.g. restaurants. A user, with a location different from the origin, asks for the location of the first Poisson point and keeps asking for the location of the next Poisson point until the first time that he/she can be completely certain that he/she knows which Poisson point is his/her nearest neighbour. This waiting time is the communication cost, while the inferred privacy region is a random set obtained by an adversary who only knows the anchor and the points received from the server, where the adversary ‘does the best’ to infer the possible locations of the user. Probabilistic results related to the communication cost and the inferred privacy region are established for any dimension d ≥ 1. Furthermore, special results when d = 1 and particularly when d = 2 are derived.

Keywords

Communication costnearest-neighbour searchPoisson processprivacy regionradial simulation algorithmVoronoi tessellation

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry 60G55: Point processes 62M30: Spatial processes
Secondary: 68U20: Simulation
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 43 , Issue 2 , June 2011 , pp. 322 - 334
Copyright
Copyright © Applied Probability Trust 2011 

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