Regression estimates of inputs to an M(t)/G/[infinity] service system

Abstract

Three problems are solved: proof of convergence in distribution of a sequence {Nk(t)} of nonhomogeneous Poisson random variables to a nonhomogeneous Poisson random variable N(t); construction of a sequence of multiple linear regression models whose conditional expectations equal E(Nk(t)) (k = 1,2, ...) aside from an additive constant; exploration of L1 and L2 criteria for estimating parameters of the regression models. Presentation of a numerical analysis of a case study involving a M(t)/M/[infinity] system of reproduction (arrivals) and mortality (services) within a biological population concludes the paper. Potential problems of interpreting parameter estimates obtained from linear programming implementations of the L1 fitting criterion are analyzed.