# Bounds on the performance of dynamic routing schemes
for highly connected networks

**
F.P. Kelly
**

**
Mathematics of Operations Research 19 (1994) 1-20. **

## Abstract

We describe a procedure for bounding the performance of
dynamic routing schemes for loss or queueing networks. The bound
is developed from a network flow synthesis of a collection of Markov
decision processes, one for each resource of the network. The bound
emerges as a solution to a dual pair of convex programming problems,
where the primal problem describes mean flows through the network and
the dual problem describes implied costs and surplus values at
resources of the network. The bound is particularly appropriate for
large highly connected networks, where it may be approached by simple trunk
reservation or threshold routing schemes.

Keywords: Network flow, dynamic routing, optimization, trunk
reservation, threshold, loss network, queueing network
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