A Gibbsian model for message routeing in highly dense multihop networks
| Autor: | András Tóbiás, Wolfgang König |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Statistics and Probability
Probability (math.PR) ComputerSystemsOrganization_COMPUTER-COMMUNICATIONNETWORKS Statistical model 02 engineering and technology Topology Interference (wave propagation) Empirical measure 01 natural sciences Exponential function 60F10 60G55 60K30 82B21 90B15 010104 statistics & probability symbols.namesake FOS: Mathematics 0202 electrical engineering electronic engineering information engineering symbols Entropy (information theory) 020201 artificial intelligence & image processing Large deviations theory Limit (mathematics) 0101 mathematics Gibbs measure Mathematics - Probability Mathematics Computer Science::Information Theory |
| Popis: | We investigate a probabilistic model for routeing of messages in relay-augmented multihop ad-hoc networks, where each transmitter sends one message to the origin. Given the (random) transmitter locations, we weight the family of random, uniformly distributed message trajectories by an exponential probability weight, favouring trajectories with low interference (measured in terms of signal-to-interference ratio) and trajectory families with little congestion (measured in terms of the number of pairs of hops using the same relay). Under the resulting Gibbs measure, the system targets the best compromise between entropy, interference and congestion for a common welfare, instead of an optimization of the individual trajectories. In the limit of high spatial density of users, we describe the totality of all the message trajectories in terms of empirical measures. Employing large deviations arguments, we derive a characteristic variational formula for the limiting free energy and analyse the minimizer(s) of the formula, which describe the most likely shapes of the trajectory flow. The empirical measures of the message trajectories well describe the interference, but not the congestion; the latter requires introducing an additional empirical measure. Our results remain valid under replacing the two penalization terms by more general functionals of these two empirical measures. 40 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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