Many wireless network protocols lead to Markov chain models with a transition matrix depending on some parameters. From this the steady state distribution can be computed, and then performance measures such as the throughput of the protocol. To optimise performance efficiently we wish to have gradients with respect to the protocol parameters. What are the appropriate numerical techniques?

The Study Group showed that in general the techniques of sparse linear algebra and preconditioning should be used. For a particular example of interest (the Bianchi chain) these methods were applied and shown to be very efficient, and the same can be expected for any chain with a similar 'escalator' structure.

Problem presented by
Keith Briggs, BT

Study Group contributors
David Allwright (Industrial Mathematics KTN)
Paul Dellar (Imperial College)
Jens Gravesen (Technical University of Denmark)
Jan Van Lent (University of Bath)
Rob Scheichl (University of Bath)
Maxim Zyskin (University of Bristol)