Modelling of Elevator Traffic Systems Using Queuing Theory

It has been long known that the elevator traffic system can be modelled as a multi-server queuing system. Each elevator can be represented as a server. The aim of this paper is to analyse the queue lengths and the average waiting times for elevator traffic systems using queuing theory. A discrete event simulation queuing theory model for an elevator traffic system was built using the SimEvents blocks within Simulink. A large number of simulations were carried out on the SimEvents software to find the average passenger waiting time and the average passenger queue length for a simulation period length of 900 seconds. It has been assumed that the passenger arrival process follows a Poisson distribution, and that the server inter-service time follows an exponential distribution (the average time taken to ‘process’ each passenger). A plot has been made of the average passenger waiting time and average passenger queue length against the system loading. The system loading is defined as the ratio of the actual arrival rate to the design arrival rate (λ divided by µ). In order to verify the results from the queuing modelling, the average passenger waiting time and the average passenger queue length were also extracted from a MATLAB simulation model. Good agreement has been found between the two methods.