A. Chaintreau, J.-Y. Le Boudec, N. Ristanovic
Proceedings of the eleventh international joint conference on Measurement and modeling of computer systems, pages 109-120, 2009
Used by the Quanticol project
The authors develop a mean field model of movement and data ageing using real data collected from cabs in the San Francisco Bay area. The region is divided into 15 regular patches in a grid with a sixteenth patch representing the rest of the world (although only four patches connect directly to the sixteenth patch due to the geography).
They first develop an ODE model of movement between patches which describes the number of cabs in each patch over time. This is later parameterised by the real data.The system to model how data ages is then described as a set of PDEs with one PDE for each patch. It takes into account movement between patches, the ageing of data, and how each cab can obtain younger data either from a base station or from other cabs. Rates to describe the occurrence of opportunistic contacts between cabs in the same patch, and in neighbouring patches area again derived from the real data. Although the model is expressed as a PDE (due to two variables, time and age), the spatial aspect is treated discretely.
The PDEs have a unique solution defined as a non-linear ODE problem. Analytic results are provided for the single-patch case, and the multi-patch case is approximated by considering low age and high age asymptotics. Validation is performed on the model, and then experiments are performed to investigate different approaches to locating base stations. The output of the model is considered spatially, in the sense that values are provided for each patch rather than averaging across all patches.
The paper is interesting as a patch model, and provides some ideas for parameterisation when detailed GPS data is available.