The Use of Numerical Methods to Evaluate the ...

The Use of Numerical Methods to Evaluate the Performance of Up Peak Group Control Algorithms Lutfi Al-Sharif, Mohamed Hussein, Moh’d Malak, Daoud Tuffaha Mechatronics Engineering Department The University of Jordan, Amman 11942, Jordan Abstract Incoming traffic group control algorithms are an important aspect of elevator traffic management. In order to allow an objective repeatable comparison of different up peak traffic group control algorithms, it is necessary to have an evaluation mechanism of their effectiveness. The use of equations in evaluating elevator group control algorithms has been very limited. Simulation has traditionally been the tool that is used to assess and compare elevator group control algorithms. However, simulation suffers from a number of disadvantages such as lack of repeatability, reproducibility and transparency. Numerical methods are very effective in providing a mechanism for objectively assessing and comparing elevator group control algorithms. This paper provides an overview of the use of such numerical methods in assessing the efficacy of different group control algorithms. It shows how the method can be used to expose the group controller to different scenarios, and then finding an optimum solution. Keywords: Elevator; lift; round trip time; interval; up peak traffic; group control algorithms; up-peak group control algorithms; Monte Carlo Simulation method; numerical methods; analytical methods. 1. INTRODUCTION Elevator group control is probably the most important mathematical problem to solve in elevator systems. It is a very demanding task as it has, even for the simplest of situations, an excessively large number of possible solutions. The aim of the elevator group control algorithm is to find the solution that optimises a certain parameter of interest. The optimisation could involve one or more of the following: maximising the handling capacity, minimising the average waiting time or the average travelling time. Elevator group control is only applicable to systems having two or more elevators operating in the same group. They have a common set of landing calls. The function of the group controller is to allocate the landing calls as soon as they are registered to one (and only one) of the elevators in the group, in order to minimise one or more of the parameters above. It is usually not possible to de-allocate the landing call from the elevator and re-allocate it to a different elevator in case a better allocation becomes available. Moreover, the decision on the allocation of a new landing call to a specific elevator in the group has to be taken within a very short period of time (usually less than 500 ms). This places a large burden on the elevator group real time controller.

With the proliferation of new elevator group control algorithms, it has become necessary to objectively assess and compare these different group control algorithms. This is critical to the successful design of the vertical transportation system for a building, independently of the specific implementations that the suppliers adopt. Simulation has traditionally been the tool used to do so. However, simulation suffers from a number of drawbacks. This paper suggests the use of numerical methods as an alternative to simulation in assessing the efficacy of up-peak elevator group control algorithms. It outlines the advantages of such methods and the methodology used. The proposed method can be extended to general traffic elevator group control algorithms. Section two provides a general introduction to elevator group control. Section three lists the four methods used generally in engineering and specifically in elevator traffic engineering for solving problems. The large number of possible scenarios to analyse is calculated in section four, illustrating the difficulty with exhaustively enumerated approaches. Section five outlines the elevator group assessment methodology suggested in this paper. Section six draws conclusions from the paper. 2. ELEVATOR GROUP CONTROL ALGORITHMS Group control algorithms can be sub-divided into two main categories in accordance with the type of prevailing traffic as follows: 1. Up-peak Group Control algorithms: These group control algorithms are used in cases where the main component of passenger traffic is entering the building from the main entrance and heading to the occupant floors above. This group of group control algorithms are discussed in more detail below. 2. General traffic group control algorithms: These group control algorithms are applied under any mix of traffic patterns (incoming; outgoing; inter-floor). Although some of the ideas presented in this paper could be applied to these group control algorithms, this will not be discussed in any detail in this paper and it thus beyond its scope. It has usually been accepted that once an up-peak situation has been detected or manually selected there is very little that the group controller can do under the conventional up peak conditions other than two obvious actions. These two actions consist of returning the cars back to the main terminal as soon as they have delivered the passengers to their destinations; and controlling the status of the doors of any cars present at the main terminal in order to fill up one elevator car at a time and allow it to depart and then opening the doors of other waiting cars one at a time. However, this has changed with the introduction of a number of up-peak group control algorithms, such as static sectoring, dynamic sectoring and destination group control. In static sectoring [1], the building is split up during the up-peak period into a number of sectors where each sector contains a number of contiguous floors having equal populations. Every time an elevator arrives at the main terminal, the elevator is assigned to a certain sector, and this is communicated to the waiting passengers at the

main terminal. Dynamic sectoring operates in a similar way but with the difference that the size of the sectors changes continuously ([2], [3], [4], [5], [6]). Destination group control systems allow the passengers to register their destinations prior to boarding the elevator ([7], [8], [9], [10], [11]). The group control system can thus allocate that landing call to the most suitable elevator in the group and inform that passenger waiting in the lobby. As the elevator has more information, it is possible to make a better allocation decision. The three algorithms provide an improvement in handling capacity of the elevator system. This boost attains it largest value under up peak traffic conditions ([45], [46]). The methodology outlined in this paper is suitable for assessing and comparing these three elevator group control algorithms. 3. METHODS OF SOLVING PROBLEMS IN ENGINEERING Problems in engineering systems can be solved by a number of methods, listed below. Possible methods of design and analysis of engineering systems, which are also applicable to the elevator traffic system design process, are listed below: 1. Analytical/equation based methods: Equations are derived for certain conditions and under specified assumptions and simplifications in engineering systems. These equations can then be used to analyse and design engineering systems. A large number of equations have been developed to evaluate the round trip time in elevator traffic systems ([12], [13], [14], [15], [16], [17], [18]), the average travelling time [19] and to assess the handling capacity of the system ([12], [13]). A number of equations have also been developed to assess the effect of elevator group control algorithms ([20], [21]). 2. Graphical methods: These methods rely on the use of a chart or graph to carry out the design or visualise a selected design or course of action but are restricted to problems that can be described using three or fewer dimensions [24]. Examples in engineering include the following: the root-locus method in control system design; the Smith chart in radio frequency engineering. It has also been used in elevator traffic design [22]. 3. Numerical methods: Numerical methods are iterative methods that are used to arrive at a solution using a computer. Numerical methods invariably involve large numbers of tedious arithmetic calculations ([23], [24]). Convergence and accuracy are two critical issues that need considerations when using these methods. They have been used in elevator traffic analysis in general ([25], [26]), in order to evaluate the value of the round trip time ([27], [28], [29], [30]) and the average travelling time [16]. It is impractical to try to apply numerical method manually, due to the excessively large number of iterations necessary for convergence and achieving the required accuracy. It thus customary to use computer software to implement numerical methods. 4. Simulation methods: Simulation is the widely used tool for assessing group control algorithms ([31], [32], [33], [34], [35], [36], [37], [38], [39], [40]). Its main

advantage is that it is very reflective of real life situations. It can easily show the effect of random passenger arrivals (such as under a Poisson passenger arrival model). Simulation is either implemented as time-slice simulation [41] or discrete event simulation [42]. The main drawback it suffers from is that it is time consuming and thus only a limited number of runs can be carried out. It is also rarely repeatable or reproducible. Any tool used to assess the efficacy of an elevator group control algorithms must meet the following four requirements: 1. Repeatable: It is essential that the original designer must be able to get the same result over a number of runs of the same system with the same parameters. 2. Reproducible: It is essential that other designers/users must be able to get the same results as the originator of the group control algorithm. 3. Transparent: It is essential that the user can easily understand how the group control algorithm works and how it has been implemented and what parameters have been assumed, as well as the values used for each parameter. 4. Objective: The tool must be an objective tool that will allow comparisons between different group control algorithms under similar conditions. While it is accepted that simulation is a powerful tool for assessing the effectiveness of elevator group control algorithms, and can deal with the most complicated of conditions and scenarios, it still does suffer from some drawbacks and in most cases does not meet the four conditions above. The numerical methods suggested in this paper address some or all of the four requirements above. It is accepted that they cannot deal with the complexity of scenarios that the simulation methods can deal with. Hence these numerical methods are suggested as complementary to the simulation methods, rather than as a replacement. 4. EXHAUSTIVELY ENUMERATING ALL THE POSSIBLE SCENARIOS It is important to gain an appreciation of the large number of possible scenarios, even under the most simple of conditions in up-peak group control. It is assumed that an elevator group comprises L elevators. Each elevator car is boarded by P passengers from the main entrance in each round trip. Each passenger can select one of N destinations, where there are N floors above the main terminal. For a group algorithm to be effective is has to deal with a large number of possible scenarios. Each scenario comprises a selection of destinations for each of the L∙P passengers. Ideally, it is necessary to assess the performance of the elevator group control algorithm when faced with all of these scenarios. There are obviously a large number of scenarios. There are NL∙P possible scenarios for any building [46]. It is assumed, for example, that an assessment is required of a certain destination elevator group control algorithm. It is necessary in each scenario to allocate

the passenger destinations to the L elevator cars. It can be shown that the number of (L ⋅ P ) ! unique possible solutions [46] is equal to (P !)L . This method is not practical due to the large number of possible scenarios and the large number of possible solutions even for the simplest of buildings. For example for a building with 10 floors above the main entrance, five elevators and 12 passengers boarding each elevator car, the number of possible scenarios is 1x1060 and the number of possible solutions for each scenario is 3.3x1038, giving a total number of solutions to investigate of 3.3x1098. Thus exhaustive enumeration is not a practical method. The next section presents a more realistic methodology. 5. METHODOLOGY FOR ASSESSMENT This section outlines the methodology used for assessing the group control algorithm ([43], [44], [45], [46]). As discussed in the last section, it not practical or realistic to list all of the possible scenarios and to enumerate every possible solution to each scenario. A more practical solution is to take a sample of the possible scenarios using Monte Carlo simulation, and then to solve each scenario using heuristics or rules of thumb. It is also possible to solve the scenarios using other optimisation techniques (e.g. single step and multi-step random searches). These solution methods are not intended in any way to be used in real time elevator group control systems, but they are used for off-line evaluation studies. The following are the steps followed in assessing a group control algorithm using numerical methods: i.

List a new possible scenario: A new scenario is generated using a random scenario generator. This is done by randomly assigning each passenger to a floor with the probabilities linked to the floor populations.

ii.

For each of the possible scenarios generated in i above, find the most suitable solution by using heuristic (rule based) methods or by using random search techniques. The solution will show an allocation of the L∙P passengers to the L elevators. The solution will attempt to optimise a certain parameter (e.g., the smallest value of the round trip time and hence the largest handling capacity).

iii.

Steps i and ii are repeated until a large number of scenarios have been considered (e.g., 10 000 or 100 000).

iv.

Once done, the average value of the best solution for all the scenarios is calculated and is used as a representative assessment of the group control algorithm.

When considering an elevator group control such as destination for example, there are a number of methods in which the L·P passengers can be allocated to the L elevators.

These methods fall mainly into two broad categories: Random searches and rule based algorithms. These are discussed below: a) Fixed step size random search. Using this tool, the software randomly makes a single change in the allocation by swapping the allocation of two passengers to two different elevators. If the optimisation target is reduced, then the swap is retained; otherwise it is rejected. This process is repeated until no more improvement can be achieved after a certain number of steps. b) Rule based allocation. Using this tool, a set of rules guide the user to splitting the sectors in the building such that the target parameter is optimised. 6. CONCLUSIONS Simulation has traditionally been the most widely used tool for assessing elevator group control algorithms. However, it suffers from a number of drawbacks. It is suggested in this paper that numerical methods could be used to complement the results from simulation in assessing the efficacy of elevator group control algorithms. In solving engineering problems, there are a number of possible approaches: analytical (equation based); graphical; numerical; and simulation. Equations are very difficult to derive even for the most simple of situations. Simulation methods can deal with extremely complex scenarios. Any tool that is to be used in assessing an elevator group control algorithm must meet four requirements: repeatability, reproducibility; transparency; objectivity as a comparison tool. Simulation does not meet some or all of these requirements. Numerical methods could address some of these drawbacks. It has been shown that the number of possible scenarios to be assessed is extremely large. It is thus more practical to use Monte Carlo simulation to assess a representative sample of scenarios. The allocation of calls to cars can be solved by using heuristic rules or numerical search techniques. REFERENCES [1] Bruce Powell, “Important issues in up peak traffic handling”, in Elevator Technology 4, International Association of Elevator Engineers, Proceedings of Elevcon ’92, May 1992, Amsterdam, The Netherlands, pp 207-218. [2] W. L. Chan and Albert T. P. So, “Dynamic zoning for intelligent supervisory control”, International Journal of Elevator Engineering, Volume 1, 1996, pp 47-59. [3] W. L. Chan and Albert T. P. So, “Dynamic zoning in elevator traffic control”, in Elevator Technology 6, International Association of Elevator Engineers, Proceedings of Elevcon ’95, March 1995, Hong Kong, pp 133-140. [4] Zhonghua Li, Zongyuan Mao and Jianping Wu, “Research on Dynamic Zoning of Elevator Traffic Based on Artificial Immune Algorithm”, 8th International Conference on Control, Automation, Robotics and Vision”, Kumming, China, 6th9th December 2004. [5] Albert T.P. So, J.K.L. Yu, “Intelligent supervisory control for lifts: dynamic zoning”, Building Services Engineering Research & Technology, Volume 22, Issue 1, 2001, pp. 14-33.

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Biographical Notes Lutfi Al-Sharif received his Ph.D. in lift traffic analysis in 1992 from UMIST (Manchester, U.K.). He worked for 9 years for London Underground, London, United Kingdom in the area of lifts and escalators. In 2002, he formed Al-Sharif VTC Ltd, a vertical transportation consultancy based in London, United Kingdom. He has 40 published papers in the area of vertical transportation systems and is co-inventor of four patents. He is currently Associate Professor in the Department of Mechatronic Engineering at The University of Jordan, Amman, Jordan.

Moh’d Munir Malak graduated from The University of Jordan in January 2013 with a degree in Mechatronics Engineering. His research interests include elevator traffic analysis and control. He is currently working as a coiled-tubing field engineer in Baker Hughes. Mohamed Hussein and Daoud Tuffaha both graduated from The University of Jordan in January 2013 with a degree in Mechatronics Engineering. Their research interests include elevator traffic analysis and control.