Stepwise derivation and verification of a universal elevator round trip time formula for general traffic conditions

Abstract

The evaluation of the round trip time (τ) still forms the basis for the design of elevator traffic systems. The elevator round trip time is the time taken for the elevator to complete a full cycle of the building, picking up passengers from their origin floors and dropping them off at their destination floors. It is assumed that the elevator car transports P passengers from their origins to their destinations during one round trip. By dividing the value of the round trip time by the target interval, the required number of elevators in the group can be found and fed into the overall traffic design. Traditionally, simplified formulae have been used to evaluate the value of the round trip time under a number of simplifying assumptions. This paper develops the formulae for the most general case of mixed traffic conditions, whereby every floor can be an occupant floor and an exit/entrance floor (i.e. every floor can have a percentage population, U(i), and a percentage arrival rate, P_arr(i)). However, the formulae developed make a simplification by assuming a constant passenger arrival model, rather than the widely accepted Poisson passenger arrival model. The new developed set of formulae comprises three parts: the kinematic part (τ_K), the door part (τ_S) and the passenger transfer part (τ_P). The kinematic part in turn comprises six components: the up journey (UJ) time; the down journey (DJ) time; the upper connecting journey (UCJ) time; the lower connecting journey (LCJ) time; the down return journey (DRJ) time; and the up return journey (URJ) time. The derivation process is accompanied by stepwise verification of all the different components of the round trip time using the Monte Carlo simulation (MCS) method. The results of the formulae match those from the MCS to less than 0.0025%.

Practical application: Engineers usually design elevator traffic systems under up-peak traffic conditions, where only incoming traffic is assumed. It is sometimes useful to assess the design under a mixture of traffic conditions (e.g. lunchtime conditions). The formulae developed in this paper can thus be used to allow the designer to evaluate the round trip time under a mixture of traffic conditions. In practice, the formulae would not be evaluated by hand, but implemented as a software programme. Once the designer has evaluated the round trip time under the specified mix of traffic conditions (e.g. 40% incoming traffic; 40% outgoing traffic; 20% inter-floor traffic), then he/she can divide that number by the target interval to find the required number of elevators. This result can then be compared to the required number of elevators under up-peak conditions to assess the adequacy of the design for these mixed traffic conditions.