Analytical round-trip time estimation of a three-dimensional elevator system based on exact stopping position identification

Abstract

Two-dimensional (2-D) as well three-dimensional (3-D) elevators are expected to become a vital part of the future building transportation systems. In order to carry out an elevator traffic system design for a 3-D system, it is necessary evaluate the round-trip time. A ‘scanning’ approach has been previously developed to find the value of the round trip time in 2-D and 3-D systems. The 3-D path of scanning could be linearized into a 1-D line as in a conventional elevator system. It was later found that the RTT is insensitive to the exact stopping positions in a 1-D system, but extremely sensitive in a 2-D or 3-D system. Furthermore, in the conventional 1-D traffic analysis, the average number of stops is non-integral because stops are repeatable within trips, causing a great trouble in estimating RTT in a 3-D system. In this article, with the help of order statistics, the method to break down a series of repeatable stops in a 3-D system into several series of non-repeatable stops is described in detail. And the number of stops of all these non-repeatable series becomes integral, making it suitable for analytical calculation. Then, the RTT of each “non-repeatable” series is separately estimated analytically, with the overall RTT with repeatable stops given by the weighted sum of all these “non-repeatable” series. Methods to estimate the average RTT of each non-repeatable series, the probability density function of each series, and the final weighted average are discussed. Finally, the results are verified using the Monte Carlo simulation method. The method described in this article can give designers a much clearer understanding of the overall concept of RTT estimation by calculation in a multi-dimensional system.