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1、1 MATHEMATICAL MODELLING OF PUBLIC TRANSPORT SYSTEMS; SOME INSIGHTS, EXTENSIONS Some Simple Approximations to Optimization Problems, SIAM J. of Applied Mechanics, 1973* (iii) Optimal Parameters for a Coordinated Rail Wirasinghe 1979 Rail feeder routes Ghoneim, Wirasinghe Extension to “many to many”

2、demand bus routes, incl. passing of stops with no passengers; Zone and skip stop service in commuter rail Schonfeld (Berkeley) Zonal bus service Wirasinghe an increasing unit value of waiting time, as waiting time increases; and also optimal uniform Some Simple Approximations to Optimization Problem

3、s, SIAM J. of Applied Mechanics, 1973 24 INSIGHTS RE “WAREHOUSE LOCATION” PROBLEM IF THE DEMAND FOR “SERVICES” FROM THE “NEAREST” WAREHOUSE IS A SLOWLY VARYING DENSITY IN THE (X,Y) PLANE, AND THE STREET NETWORK IS DENSE, THEN THERE IS A CLOSED FORM SOLUTION FOR THE OPTIMAL DENSITY OF WAREHOUSES THAT

4、 MINIMIZES THE SUM OF THE WAREHOUSE AND TRANSPORT COSTS. THUS THE NUMBER OF WAREHOUSES CAN ALSO BE ESTIMATED BY INTEGRATING THE OPTIMAL DENSITY. THIS PROBLEM IS CONSIDERED A “np-hard” PROBLEM BY DISCRETE MODELERS EVEN WHEN THE NUMBER OF WAREHOUSES IS GIVEN. 25 26 EXTENSIONS OF THE WAREHOUSE LOCATION

5、 PROBLEM THE BUS GARAGE LOCATION PROBLEM IS A ROUGH APPROXIMATION OF THE WAREHOUSE LOCATION PROBLEM, AS THERE ARE ONLY A FEW GARAGES IN MOST CITIES (WIRASINGHE 1982 (2nd Ed.), 303p. (ii) Approximate Stochastic Behavior of n- Server Service Systems with Large n, Springer-Verlag, 1973, 118p. (iii) App

6、roximate Behavior of Tandem Queues, Springer-Verlag, 1979, 410 pages. 28 DETERMINISTIC QUEUEING THEORY THE BOOK “APPLICATIONS OF QUEUEING THEORY” IS ONE OF NEWELLS GREATEST CONTRIBUTIONS DETERMINISTIC QUEUEING THEORY (DQT) AND THE FLUID APPROXIMATION OF A PEAK PERIOD QUEUE ARE KEY THE BASIS FOR THE

7、MEAN WAITING TIME FOR TRANSIT SERVICE BEING HALF A HEADWAY IS BASED ON DQT. USEFUL FOR EXAMPLE IF WE DECIDE TO ASSUME THAT THE COST OF WAITING TIME PER UNIT TIME IS AN INCREASING FUNCTION OF THE ELAPSED WAITING TIME (WIRASINGHE 1990) 29 30 31 32 CONTRIBUTIONS BY NEWELLS STUDENTS/ASSOCIATES TO RELATED FIELDS TRAFFIC SAFETY - HAUER TRANSIT TECHNOLOGY VUCHIC (THREE BOOKS) AIRPORT TERMINAL ANALYSIS - WIRASINGHE (with BANDARA, VANDEBONA, DADA, de BARROS, CORREIA, NANAYAKKARA, LAM, WONG) TRANSPORT, LOGISTICS, PLANNING (NO PROGRESS RE MAN

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