建模与仿真课件：L09-Output Analysis 2.pdfVIP

Lecture 9 of Modeling Simulation 曹晖 caohui@tsinghua.edu.cn Department of Industrial Engineering Tsinghua University  Much more difficult problem than analysis for terminating simulations  Want to estimate (e.g. for discrete- and continuous-time processes) D = delay in queue of lim E (D ) i  i i the ith customer   lim E (Q(t )) Q(t) = number in queue t   at time t 2012/12/3 Output Analysis for a Single System (2) 2 2012/12/3 Output Analysis for a Single System (2) 3  If steady-state is the goal, initial conditions will generally bias the results of the simulation for some period of time  lim E(Y ) E[Y (m)]  i i  Most common technique is to warm up the model, also called initial data deletion  Identify index l (for discrete-time processes) or time t0 (for continuous-time processes) beyond which the output appears not to be drifting any more  Clear statistical accumulators at that time  Start over with data collection, and count only data observed past that point 2012/12/3 Output Analysis for a Single System (2) 4  Given the observations Y , Y ,……, Y 1 2 m  An estimator of  m Y i Y (m, l)  il 1 m l  Less biased than Y (m)  After warm up period, observations will still have variance, s