Lutfi Al-Sharif

The use of Monte Carlo simulation in evaluating the elevator round trip time under up-peak traffic conditions and conventional group control:

The design of vertical transportation systems still relies on the evaluation of the round trip of the elevators during the up-peak (incoming) traffic conditions in a building. The evaluation of the round trip time for anything other than the most straightforward case becomes very complicated and requires the use of advanced special condition formulae. These formulae become even more complicated when a combination of the special conditions exist within the building being designed. The most four prominent examples of these special conditions are the case of multiple entrances to the building (rather than a single entrance), the case where the top speed is not attained within one floor jump (or even two or three floor jumps), unequal floor heights and unequal floor population. Moreover, no analytical formulae exist for some combinations of these special conditions. The use of the Monte Carlo simulation is presented in this paper as a simple and practical means to calculate the round trip time for an elevator during the up-peak (incoming) traffic conditions, under a combination of any or all of the special conditions such as multiple entrances, top speed not attained within one or more floor journeys, unequal floor heights and unequal floor populations. Analytical methods are used to show that the Monte Carlo simulation produces the same results for real-life cases of multiple entrances and where the top speed is not attained in a one floor jump. The same can be applied to the other two special conditions or any combination of the four special conditions. The structure and architecture of the Monte Carlo simulation tool used is discussed in detail. The practical details that are used to ensure the speed of the tool in producing an answer are also discussed. The method developed here only applies to up-peak traffic conditions under a conventional group control system. Practical Application: Evaluating the elevator round trip time under up-peak traffic conditions is possible using analytical methods by applying well-established formulae. The round trip time is necessary to decide on the number of elevators required for a building. Where special conditions exist in the building, the use of the analytical method becomes very complicated, and is not possible under the combinations of all special conditions. The only alternatives available are discrete time-slice simulation packages. This piece of work provides the designer with a basis to use the Monte Carlo simulation as a software tool to calculate the round trip time, regardless of the special cases that exist in the building. It also offers a reference to allow the benchmarking and verification of calculation and simulation packages in research environments.

Derivation of a universal elevator round trip time formula under incoming traffic

The design of vertical transportation systems still heavily relies on the calculation of the round trip time (τ). The round trip time (τ) 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.

Automated optimal design methodology of elevator systems using rules and graphical methods (the HARint plane)

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.

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

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.

The effect of the building population and the number of floors on the vertical transportation design of low and medium rise buildings

The design of vertical transportation systems for buildings involves the selection of the number, speed and capacity of the lifts required. It also involves the selection of the most appropriate configuration in terms of zoning, group control algorithm and the use or otherwise of double deckers. Interval is the classical performance criterion for vertical transportation design, while modern passenger centric performance criteria are now based on passenger waiting time and travelling time. Both types of performance parameters are used in this work. This work identifies the two most influential demand factors that affect the design output for vertical transportation systems in low and medium rise buildings. These are the total building population and the number of floors served above the main terminal. These are then used to develop general guidelines to find the most optimum configuration for every pair of such parameters. This is then transformed into the form of a 2D chart that can visually aid the designer into using the best configuration for a building. Practical applications: The importance of this article arises from the fact that it justifies the widely held view that single deck lifts in one group are limited to 20 floors and that the direct travel from ground approach is limited to around 60 floors (after which sky lobbies are needed). It shows that the two most important parameters that affect the design of a vertical transportation system are the total building population and the number of floors above the lobby. The two dimensional chart included within the article as Figure 3 allows the system designer to immediately assess the most suitable vertical transportation zoning arrangement for the building, the preferred number of zones and the preference for using single decker or double decker lifts.

Establishing the upper performance limit of destination elevator group control using idealised optimal benchmarks

The concept of an idealised optimal benchmark (IOB) is used in many engineering disciplines. An example of an IOB from the area of thermodynamics is the formula for evaluating the maximum possible efficiency of a heat engine. This paper explores the concept of an IOB in the area of elevator traffic analysis. It shows that the classical method of elevator traffic design by calculating the value of the round trip time is an example of an IOB; it also lists the assumptions that lie behind the formulae to illustrate this. It then extends the concept of an IOB to calculating the maximum performance of an elevator system when destination group control is applied under incoming traffic conditions. Formulae are derived for finding the minimum values of the expected number of stops (S) and the highest reversal floor (H) under destination group control during incoming traffic conditions. The assumption is that the L elevators in the group are sequenced (or rotated) to the L virtual sectors in the building, in order to equalise the handling capacities of the L sectors in the group. A numerical example is presented to illustrate the calculation of the maximum possible handling capacity and comparing it to the handling capacity that is achieved under conventional incoming traffic group control. Three numerical algorithms are also used to find the practical minimum values of H and S, the results of which are compared to the IOB using the equations derived above. Practical application: The concept and the accompanying formulae presented in this paper allow the elevator traffic designer to assess the improvement in the handling capacity of the elevator traffic system when he/she changes the group controller from a conventional group controller to a destination group controller. This improvement could be as much as 200%.

The HARint Space: A methodology for compliant elevator traffic designs

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.

Traffic analysis of a simplified two-dimensional elevator system:

The idea of multicar operation within one hoistway is not new. Two-car systems are currently available on the market, whereby the two cars travel with restricted independence because one car must always remain above the other. With recent advances in linear machines, systems with more than two cars in one hoistway will soon become possible. In this paper, the authors go one step forward by assuming that multiple cars can move in a two-dimensional plane either attached to the facade of the building or across a vertical slice within the building. The analysis has been restricted at this stage to incoming traffic only. It is assumed that elevator cars can move upwards, downwards as well as sideways. In this way, passengers can exit at a stop very close to their destinations. The foreseeable technology is discussed, and two configurations (denoted as setups A and B) are proposed. The traffic analysis equations for such a system are also derived. A simulation is then carried out for the two setups based on one-car operation. The simulation shows that the proposed two-dimensional elevator system can reduce the total traveling time of a passenger as compared with the conventional one-dimensional setup. The system is described as special because the number of hoistways is restricted (up to a maximum of 2). Practical application : This paper provides a practical way of evaluating the round trip time for two different two-dimensional elevator applications. It also then compares three different sizes of buildings and shows that the use of two-dimensional elevator arrangements is only feasible for building with more than 30 floors high by 30 rooms wide.

The current practice of lift traffic design using calculation and simulation

Lift traffic design can employ calculation or simulation methods. Calculation can be split into main categories: analytical equation-based methods and numerical methods. Simulation can be split into discrete event simulation and time-slice simulation. These methods vary in the level of computational complexity, as well as their ability to arrive at a value for the required performance parameters with acceptable accuracy and under the general case. Moreover, the repeatability of the results is an important consideration, as well as the simplicity and calculation time of the method used. This technical note provides a general overview of each of the four methods. It also discusses the suitable areas of application of each of the methods, showing the strengths and weaknesses of each of the four methods. This technical note concludes by outlining the current hybrid method used by designers in lift traffic design, whereby one of the calculation methods is used to find a starting arrangement and then the design is fine tuned using one of the simulation methods (e.g. changing speed, capacity of the lifts as well as the group control algorithm) in order to achieve the required average passenger waiting time and average passenger transit time. Practical application: This technical note provides a blueprint to lift traffic designers for the lift traffic design process. It emphasises the fact that calculation and simulation are not mutually exclusive methodologies, and shows how they complement each other, where the former provides a starting design and the latter allows the designer to fine tune the lift traffic design.

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

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%.