Statistics Seminars: A large deviations approximation for the stationary distribution of queuing network.
16 March 2001 14:00 in CM221
"Product form stationary distributions for queueing networks like in the Jackson case are a quite rare occurrence. However, it is quite common for multidimensional processes with large polyhedral state space to admit product form approximations in the vicinity of some of the boundary facets (typically with different exponents near each facet). These exponents may be obtained from the local solutions of a large deviations variational problem, which reduces to solving some algebraic systems in the case of Markovian and renewal ""phase type"" networks. Determining analytically all the local solutions opens the possibility of constructing global approximations for the stationary distribution obtained by taking linear combinations of the local approximations. The determination of the correct asymptotic proportionality coefficients, called ""sharp large deviations"" problem, appears to be very challenging for multidimensional processes. However, some simple numerical approximations for the proportionality coefficients are available."
room CM103 (seminar) 2.15 - 3.00 pm
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