Evaluating the elevator round trip time for multiple entrances and incoming traffic conditions using Markov chain Monte Carlo

摘要

The round trip time is the basis for designing elevator systems. There are a number of different methods for calculating the round trip time, whether analytical or numerical. As the building and the conditions of the traffic become more complicated, analytical methods become intractable. Numerical methods offer an attractive alternative for calculating the round trip time. Monte Carlo simulation has been used to find the value of the round trip time. The use of the Markov chain Monte Carlo method is a viable alternative. This paper derives the formulae necessary to build the transition probability matrix for the elevator during a round trip under incoming traffic conditions and multiple entrances. A numerical example is then solved by finding the round trip time using the Markov chain Monte Carlo method and then cross verified by the use of Monte Carlo simulation and the analytical equation based method. Excellent agreement has been found between the three methods, with differences smaller than 0.01%.