 
Summary: A IIYDI~ODYNAMIC LIMIT FOR, A LATTICE CAI~ICATUI~E OF
DYNAMIC ROUTINC IN CII~CUIT SWITCHED NETWOI~KS
V. Anantharam *
School of Electrical Engineering
Cornell University, Ithaca, NY 14853
ABSTR, ACT
In simulations circuit switched networks with dynamic alternate routing exhibit
hysteresis phenomena, which suggest that under dynamic routing there may be more
than one stable regime of operation for the same offered traffic. This possibility also
shows up in some analytical models of dynamic routing : one can write ODE limits
for network occupancy probabilities which admit multiple equilibrium points for ccrta.in
ranges of parameters. These ODE limits average out the spatial variation of the network.
We attempt to preserve the spatial characteristics by considering a lattice model of
dynamic routing. We derive a hydrodynamic equation for this lattice model. This is
an integrodifferential equation which describes how the spatial occupancy profile of the
network evolves over time, and it admits multiple spatially homogeneous equilibrium
solutions for certain ranges of the parameters. These solutions may be loosely thought
of as the different operating regimes. Using this equation one can study questions like
"for what parameter values is a hot spot of heavy loading in the system likely to take
over the whole network by knockon effects ?"
