@inproceedings{kuhl_damerdji_wilson_1998, title={Least squares estimation of nonhomogeneous Poisson processes}, DOI={10.1109/wsc.1998.745045}, abstractNote={We formulate and evaluate weighted least squares (WLS) and ordinary least squares (OLS) procedures for estimating the parametric mean-value function of a nonhomogeneous Poisson process. We focus the development on processes having an exponential rate function, where the exponent may include a polynomial component or some trigonometric components. Unanticipated problems with the WLS procedure are explained by an analysis of the associated residuals. The OLS procedure is based on a square root transformation of the detrended event (arrival) times - that is, the fitted mean-value function evaluated at the observed event times; and under appropriate conditions, the corresponding residuals are proved to converge weakly to a normal distribution with mean 0 and variance 0.25. The results of a Monte Carlo study indicate the advantages of the OLS procedure with respect to estimation accuracy and computational efficiency.}, booktitle={1998 Winter Simulation Conference: Proceedings: Grand Hotel, Washington, D.C., 13-16 December, 1998}, publisher={Piscataway, New Jersey: IEEE ; New York, New York: Association for Computing Machinery ; San Diego, California: Society for Computer Simulation International}, author={Kuhl, M. E. and Damerdji, H. and Wilson, J. R.}, year={1998}, pages={637–646} }
@article{damerdji_glynn_1998, title={Limit theory for performance modeling of future event set algorithms}, volume={44}, ISSN={["0025-1909"]}, DOI={10.1287/mnsc.44.12.1709}, abstractNote={In a discrete-event simulation, the information related to the events scheduled to occur in the future is kept in a data structure called the future event set (FES). In this paper, we study the interaction hold model, a popular stochastic model for FES performance analysis, corresponding to the superposition of a (fixed) number of renewal processes. The general state-space Markov chain formed by the discrete-time process that keeps track, at event times, of the residual lifetimes is shown here to be recurrent in the sense of Harris, and its stationary distribution is obtained. Linked lists and indexed lists, two popular FESs, are investigated using this model. For the interaction hold model, we make rigorous certain published results as well as introduce new ones. For example, we derive the distribution of the relative position of the event to be inserted in the data structure. In the exponential case, our analytic and empirical results confirm that when events with relatively short lifetimes often get regenerated upon their occurrence, it is better to scan a list (or sublist) from its head rather than tail. In the same context and for indexed lists with sublists with constant sizes, our results suggest that subsequent sublists should be of larger sizes, i.e., the first sublist should contain the smallest number of records, the second sublist the second smallest number of records, etc.}, number={12}, journal={MANAGEMENT SCIENCE}, author={Damerdji, H and Glynn, PW}, year={1998}, month={Dec}, pages={1709–1722} }