Regression estimates of inputs to an M(t)/G/\(\infty\) service system (Q1098206)

Three problems are solved: proof of convergence in distribution of a sequence \(\{N^ k(t)\}\) 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 \(E(N^ k(t))\) \((k=1,2,...)\) aside from an additive constant; exploration of \(L_ 1\) and \(L_ 2\) criteria for estimating parameters of the regression models. Presentation of a numerical analysis of a case study involving an M(t)/M/\(\infty\) 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 \(L_ 1\) fitting criterion are analyzed.