The design of vertical transportation systems still heavily relies on the calculation of the round trip time (). The round trip time () is defined as the average time taken by an elevator to complete a full trip around a building. There are currently two methods for calculating the round trip time: the conventional analytical calculation method and the Monte Carlo simulation method. The conventional analytical method is based on calculating the expected number of stops and the expected highest reversal floor and then substituting the values in the main formula for the round trip time. This method makes some assumptions as to the existence of some special conditions (such as equal floor heights and a single entrance). Where these assumptions are not true in a building, this invalidates the use of the analytical formula the use of which will lead to errors in the result. The conventional analytical equation can be further developed to cover some of the special conditions in the building, but they do not cover all these special conditions and also do not cover combinations of these special conditions. The simplest round trip time equation makes the following assumptions: equal floor heights, a single entrance, equal floor populations and that the rated speed is attained in one floor jump. The case of unequal floor populations can be accounted for by amending the values of the probable number of stops and the highest reversal by using the formulae for the unequal floor population case. The work presented in this piece of work identifies the most important four special conditions (out a total of nine conditions) that are assumed in the classical round trip time analytical equation. It then develops analytical formulae for calculating the round trip time equation for any of the four special conditions or any combination of these conditions under incoming traffic conditions. A numerical example is given and verified using Monte Carlo simulation. Practical application: This piece of work presents new equations that allow the designer to evaluate the value of the round trip time. The equations can deal with special cases such as top speed not attained in one floor journey, multiple entrances, unequal floor heights and unequal floor populations. Once the value of the round trip time is obtained, the elevator system can be designed, providing the required number of elevators, their speed and capacity.

The design of an elevator system heavily relies on the calculation of the round-trip time under up-peak (incoming) traffic conditions. The round-trip time can either be calculated analytically or by the use of Monte Carlo simulation. However, the calculation of the round-trip time is only part of the design methodology. This paper does not discuss the round-trip time calculation methodology as this has been addressed in detail elsewhere. This paper presents a step-by-step automated design methodology which gives the optimum number of elevators in very specific, constrained arrival situations. A range of situations can be considered and a judgement can be made as to what is the best cost–performance tradeoff. It uses the round trip value calculated by the use of other tools to automatically arrive at an optimal elevator design for a building. It employs rules and graphical methods. The methodology starts from the user requirements in the form of three parameters: the target interval; the expected passenger arrival rate (AR%) which is the passenger arrival in the busiest 5 min expressed as a percentage of the building population; and the total building population. Using these requirements, the expected number of passengers boarding an elevator car is calculated. Then, the round-trip time is calculated (using other tools) and the optimum number of elevators is calculated. Further iterations are carried out to refine the actual number of passengers boarding the elevator and the actual achieved target. The optimal car capacity is then calculated based on the final expected passengers boarding the car. The HARint plane is presented as a graphical tool that allows the designer to visualise the solution. Three different rated speeds are suggested and used in order to explore the possibility of reducing the number of elevator cars. Moreover, the average passenger travel time is used to indicate the need for zoning of buildings. Practical application: This paper has an important application in allowing the designer to arrive at the optimum design for the elevator system using a clearly defined methodology. This ensures that the number of elevators, their speed and their capacity are optimised, thus ensuring that the cost of the elevator system and the space it occupies within the building are minimised. The method also employs a graphical method (the HARint) in order to allow the designer to visualise the optimality and the feasibility of the different design options.

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, Parr(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 (τK), the door part (τS) and the passenger transfer part (τP). 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.

A previous paper introduced the concept of the HARint plane, which is a tool to visualise the optimality of an elevator design. This paper extends the concept of the HARint plane to the HARint Space where the complete set of user requirements is used to implement a compliant elevator traffic design. In the HARint Space, the full set of user requirements are considered: the passenger arrival rate (AR%), the target interval (inttar), the target average travelling time (ATT) and the target average waiting time (AWT). The HARint Space provides an automated methodology in the form of a set of well-defined steps that allow the designer to convert these four user requirements into a compliant elevator traffic design. As with the HARint plane method, the target interval is used in combination with the expected arrival rate (AR%) and the building population, U, in order to find an initial assessment of the number of passengers expected to board the elevator. The target average travelling time is then used to select a suitable elevator speed. This is then used to calculate the round trip time and then select the optimum number of elevators. An iteration is then carried out to find the actual number of passengers, and hence the elevator capacity. A check is then carried out to ensure that the target average waiting time has been met, and if not, then a modification of the design is required (usually by increasing the speed or increasing the number of elevators). While the HARint plane provides the optimum number of elevator cars to achieve the two user requirements, the HARint Space provides the optimum rated speed as well as the optimum number of elevators to meet the four user requirements of arrival rate, target interval, target average waiting time and target average travelling time. An obvious consequence of the introduction of the average travelling time as a user requirement is that the speed becomes an outcome of the HARint Space. The method also triggers a zoning recommendation in cases where the average travelling time cannot be met by varying the speed within reasonable limits.Practical application: The work in this paper presents a methodical procedure allowing the designer to select the number, speed and capacity of a group of elevators in a building in order to meet four user requirements: Arrival rate, target interval, target passenger waiting time and target passenger travelling time. Following this procedure ensures an optimal design. It also provides the user with a graphical method for visualising the optimality of the design.

The conventional design methodology for elevator traffic analysis has been applied to the case of up-peak traffic (or incoming traffic conditions). The only user requirements are usually the expected arrival rate (AR%) expressed as a percentage of the building population requesting service in the peak 5 min and the target interval. The interval as classically used will be referred to as the physical interval in this paper as it is only relevant for the case of a single entrance and incoming traffic conditions. This paper presents an integrated methodology for the design of elevator traffic systems for the general case of mixed traffic conditions. It presents a fully integrated framework that covers the steps from user requirements to the selection of the number of required elevators. The user requirements describing the traffic conditions can be specified by the user, expressed as the AR%, the mix of incoming traffic, outgoing traffic, and interfloor traffic. This paper derives equations that can be used to combine the mix of traffic, the floor arrival percentages, and the floor population percentages into an origin-destination matrix. The origin-destination matrix is then adjusted and normalized in order to account for rational passenger behavior (i.e., a passenger will not travel to the same floor that he or she is at). A method is presented for the random generation of passenger origin-destination pairs using the origin-destination matrix (which is necessary when using the Monte Carlo Simulation (MCS) method to calculate the round trip time). A novel equation for evaluating the round trip time under the assumption of equal floor heights and top speed attained in one floor journey is derived and used. The equation is derived using a stepwise derivation and verification process. The verification is carried out against the MCS method for finding the value of the round trip time. The concept of a virtual interval (as opposed to the conventionally used physical interval usually used in elevator traffic system design) is introduced in order to allow the selection of the number of elevators Downloaded from to be carried out. The virtual interval is the average value of the time between the consecutive reversals of the elevators in the group. Practical application The methodology presented in this paper allows the elevator traffic system designer to convert the user requirements specification (in the form of an arrival rate and the percentage floor strengths) into an origin-destination matrix. The origin-destination matrix is a more suitable tool for calculating the expected value of the round trip time and consequently carrying out an elevator traffic design. Thus, this methodology represents a vital step in the design process.