CROSSING A NON-JACKSON NETWORK
(WITH OR WITHOUT A MAP)
Michael Tortorella
This talk considers for deterministic and stochastic flow networks the problem of computing the cross-network value of a performance parameter that is path-additive and whose values on individual nodes and links are known. We assume the network has Markovian routing but do not otherwise restrict the arrival processes, queueing discipline, or service time distributions. The method relies on generalizing the traffic equation to path-additive functionals of the flow in the network. The results are expressed in matrix form to provide computationally convenient expressions involving the inverse of the matrix I - R where R is the routing matrix of the network.
Telecommunications packet networks, logistics networks, and the like, employ address-based routing in which a packet at a particular node chooses the next node to visit according to its destination address, a lookup table in the node, and the current state of congestion in the network. Markovian routing is mathematically more tractable, so we are led to inquire whether networks using address-based routing may be suitably approximated by Markovian routing. This talk also describes three Markovian routing models for approximating address-based routing.