Numerical algorithms for dynamic traffic demand estimation between zones in a network

This paper presents numerical methods for dynamic traffic demand estimation between N zones in a network, where the zones are disjoint subsets of nodes of the network. Traffic is assumed to be generated or absorbed only in the zones and nowhere else in the network. Traffic volumes between zones over a fixed period of time are modeled as independent random variables with unknown means which it is desired to estimate. For each zone, the volume of all incoming and outgoing traffic is counted on a regular basis but no information about the origin or destination of the observed traffic is used. Procedures are suggested for a regular update of estimates of the N(N - 1) mean traffic demands between the zones on the basis of an incoming stream of the 2N traffic counts. The procedures are based on an exponential smoothing scheme and are reminiscent of the expectation maximization (EM) algorithm if smoothing is removed. Fast and reliable numerical algorithms, based on the conjugate gradient method, are presented for normal as well as for Poisson traffic demands. The Poisson case is linked with entropy maximization. Computational tests based on simulated data demonstrate both the numerical and statistical efficiency of the procedures.