In this paper, we investigate the Pell sequence and the Perrin sequence and we derive some relationships between these sequences and permanents and determinants of one type of Hessenberg matrices.
Commercial transport planning as well as individual intra-city or inter-city traffic in densely populated regions, both in Europe and the US, increasingly suffer from congestion problems, to an extent which e.g. affects predictable transport planning substantially (except - so far - for overnight tours). Due to the highly dynamic character of congestion forming and dissolving, no static approach like shortest path finding, applied globally or individually in car navigators, is adequate here: Its use even makes things worse as can be frequently observed. In this paper we present a completely decentralized multi-agent approach (termed BeeJamA) on multiple layers where car or truck routing are handled through algorithms adapted from the BeeHive algorithms which in turn have been derived from honey bee behavior. We report on extensive distributed simulation experiments in the BeeJamA project which demonstrate a very substantial improvement over traditional congestion handling
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