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AQMD arith xpqe Average Vehicle Ridership AVR target Bartholdi and Platzman Based on Spacefilling Binomial Distribution calculated Canoga Park carpool groups carpooler's home carpoolers and non-carpoolers carpooling system Clustering Analysis clustering procedure commuters created by Bartholdi current carpoolers Current Number deftable dist distance matrix dotplot xpqa employees who live Euclidean distance Euclidean Space expected number form the carpools forming carpools heuristic algorithm heuristic route heuristic was applied implement the incentive incentive measure loopindex lower triangular matrix maxd maxinput minimum distance number of carpoolers number of cars number of current number of employees number of participants number of points number of residences oldx optimal parm problem Projected AVR proposed carpool random numbers random points SAS PROC CLUSTER shown in Figure single linkage single vehicle route sort xpqe spacefilling curve total driving total number travelling salesman heuristic type=int type=real xpqb xpqc xpqd xpqf Zip Code Region