Space-time large deviations in capacity-constrained relay networks
- Hirsch, Christian
- Jahnel, Benedikt
- Patterson, Robert I. A.
2010 Mathematics Subject Classification
- 60F10 60K35
- large deviation, measure-valued differential equations, entropy, capacity, relay
We consider a single-cell network of random transmitters and fixed relays in a bounded domain of Euclidean space. The transmitters arrive over time and select one relay according to a spatially inhomogeneous preference kernel. Once a transmitter is connected to a relay, the connection remains and the relay is occupied. If an occupied relay is selected by another transmitters with later arrival time, this transmitter becomes frustrated. We derive a large deviation principle for the space-time evolution of frustrated transmitters in the high-density regime.
- ALEA Lat. Am. J. Probab. Math. Stat., 15 (2018), pp. 587--615, DOI 10.30757/ALEA.v15-24 .