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Unformatted text preview:  p. 1/30 ARTA  AutoRegressive To Anything A Review Santanu Chakraborty santanu@purdue.edu Department of Industrial Engineering Purdue University p. 2/30 Organization 1. Motivation 2. Problem Statement 3. Introduction to ARTA 4. Numerical Recipe and Algorithm 5. Algorithm for Simulation 6. Available Software 7. References p. 3/30 Motivation Dependent TimeSeries Input Process Demand in an inventory system in successive periods. p. 3/30 Motivation Dependent TimeSeries Input Process Demand in an inventory system in successive periods. Time between file access in a compute network shows burstiness ( ref. Ware et al.). p. 3/30 Motivation Dependent TimeSeries Input Process Demand in an inventory system in successive periods. Time between file access in a compute network shows burstiness ( ref. Ware et al.). Sequence of compressed video frame bitrates ( ref. Melamed et al.). p. 3/30 Motivation Dependent TimeSeries Input Process Demand in an inventory system in successive periods. Time between file access in a compute network shows burstiness ( ref. Ware et al.). Sequence of compressed video frame bitrates ( ref. Melamed et al.). Generally in simulation practice these processes are considered as independent random variable. p. 4/30 Effect of Autocorrelation in Queuing System Assumptions ( ref. Livny et al.) A FIFO queue with one server. Arrival process is lag1 autocorrelated ( a ) . Service is lag1 autocorrelated ( s ) . Both arrival and service distributions are exponential. Studied at utilization of 25%, 50%, 66.6% and 80%. p. 4/30 Effect of Autocorrelation in Queuing System Assumptions ( ref. Livny et al.) A FIFO queue with one server. Arrival process is lag1 autocorrelated ( a ) . Service is lag1 autocorrelated ( s ) . Both arrival and service distributions are exponential. Studied at utilization of 25%, 50%, 66.6% and 80%. Some Results(Utilization = 50%) If a = s = 0 , Waiting time = 1 time unit. s = 0 , a = . 25 , Waiting time reduces by 29%. s = 0 , a = . 25 , Waiting time increases by 80%. s = 0 , a = . 85 , Waiting time is 200 times larger. p. 5/30 Problem Statement Objective To represent a stationary time series input process { Y t ; t = 1 , 2 ,... } , with, An arbitrary marginal distribution F Y . Any feasible autocorrelation structure specified through lag p . p. 5/30 Problem Statement Objective To represent a stationary time series input process { Y t ; t = 1 , 2 ,... } , with, An arbitrary marginal distribution F Y . Any feasible autocorrelation structure specified through lag p . Problem Statement The goal is to define a stationary time series { Y t } with the properties 1. Y t F Y ,t = 1 , 2 ,... , where F Y is an arbitrary CDF 2. ( Corr [ Y t ,Y t +1 ] , Corr [ Y t ,Y t +2 ] ,... , Corr [ Y t ,Y t + p ]) prime = ( 1 , 2 ,... , prime p ) =  p. 6/30 Problem Statement(contd..)Problem Statement(contd....
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 Spring '10
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