Using Idealised Optimal Benchmarks in Elevator ...

Lift Report 2016; 42(5): 45-59

Using Idealised Optimal Benchmarks in Elevator Group Control to Establish Upper Performance Limits Lutfi Al-Sharif Professor Mechatronics Engineering Department The University of Jordan, Amman 11942, Jordan Abstract 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 chapter 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. Keywords: Elevator, lift, round trip time, interval, up peak traffic, destination group control, probable number of stops, highest reversal floor, Monte Carlo Simulation, simulation, calculation, optimisation, idealised optimal benchmark. Nomenclature a the rated acceleration in m/s2 AR% the arrival rate of passengers as a percentage of the building population in the busiest five minutes d f the height of a floor in m epoch is the time taken for an elevator to complete a complete set of round trips for all the L sectors HC% the elevator group handling capacity as a percentage of the building population in the busiest five minutes HC% max the elevator group handling capacity as a percentage of the building population in the busiest five minutes under destination group control © Copyright held by the author 2016: Prof. Lutfi R. Al-Sharif

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H des is the minimum value of the average highest reversal floor in a round trip under destination group control int act the actual achieved interval in seconds int tar the target interval in seconds j the rated jerk in m/s3 λ the arrival rate in passengers per second λS the arrival rate in passengers per second for each sector L the number of elevators in the group N the total number of floors above the main entrance N eff the effective number of floors under full sectoring group control P the number of passengers served in one round trip P des the number of passengers boarding the car in one round trip under destination group control at a constant handling capacity S is the expected number of stops in a round trip S des is the minimum value of the average number of stops in a round trip under destination group control τ min the minimum value of the round trip time under destination group control in s

τ Si the round trip time for the ith sector in s τ the round trip time in s t ao the door advance opening time in s (where the door starts opening before the car comes to a complete standstill) t dc the door closing time in s t do the door opening time in s t pi the passenger boarding time in s t po the passenger alighting time in s t sd the motor start delay in s U is the total building population U(i) the building population on the ith floor expressed as a percentage of the total building population U Si is the population of the ith sector v the rated speed in m/s 1. INTRODUCTION The classical elevator traffic design process relies on the calculation of the optimum average value of the elevator round trip time under idealised conditions. This design process has thus far been limited to evaluating the round trip time under conventional elevator group control and incoming traffic conditions. In effect, the calculations assume that each elevator is operating on its own with very little interaction with the other elevators in the group during incoming traffic conditions. Some work has been carried out in order to extend the calculations to account for the effect of group control by Barney ([1], [2]). This chapter attempts to extend this process to the case where destination group control is applied under incoming traffic conditions. This extension also assumes idealised optimum conditions and uses calculation to find the optimum average value of the new round trip time. The concept of an Idealised Optimal Benchmark (IOB) as a design tool is introduced in section two, discussing the similarity to another field of engineering. A review of the classical method of design using calculation is reviewed in section three, emphasising the fact that the round trip time [3] (as already used in classical design), is an example of an IOB. A description of up-peak sectoring as a tool to © Copyright held by the author 2016: Prof. Lutfi R. Al-Sharif

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enhance the handling capacity of an elevator system is provided in section four, which is an essential preamble to section five. Section five is the core of this chapter, and details the application of the IOB concept to the elevator traffic design process where destination group control is applied under incoming traffic conditions. A numerical example is introduced in section six, showing how the method can be used to calculate the maximum possible handling capacity of an elevator system in a building when destination elevator group control is applied. Section seven compares the results of the derived equations with equations derived in previous pieces of work ([4], [5]). Section eight deals with the general criticism of this idealised optimal benchmark. Conclusions are drawn in section nine. 2. IDEALISED OPTIMAL BENCHMARKS (IOB) Although the term has not been previously used in the elevator context, Idealised Optimal Benchmarks (IOB) are widely used in the elevator traffic analysis and design field. Definition An Idealised Optimal Benchmark is the optimal (minimum or maximum) possible value of a critical design variable that attains its value under idealised conditions. It is then subsequently used as a benchmark to assess the efficiency of an elevator traffic design. Thus the value of the IOB is attained under idealised conditions and not under practical operating conditions. This is understood and accepted, as it allows an objective outcome that is not dependent on the randomness of the elevator movements or the randomness of the passenger decisions. By definition they are average values. In addition, they are optimum values that can only be attained under the most favourable conditions. They are used as benchmarks allowing designers to understand how far their designs deviate from optimum performance. A good example of an IOB from engineering is in the area of thermodynamics. It is well established that the maximum possible efficiency of a heat engine under ideal conditions is restricted by the ratio of the hot system absolute temperature (T 1 ) and the cold system absolute temperature (T 2 ) [6]. It is a useful benchmark to establish the maximum possible efficiency that a heat engine can achieve. In practice, the actual efficiency of the heat engine will be lower than this efficiency. The best and most widely used example of an IOB in the area of elevator traffic analysis and design is the round trip time, that will be denoted here as τ . The round trip time is the time taken by each elevator to do a complete round trip in the building, picking up passenger, delivering them to their destinations and then returning to pick up more passengers. It is used as the basis for elevator traffic design as a tool to arrive at the required number of elevators in a group. This chapter develops the concept of the Idealised Optimal Benchmark (IOB) to measure two performance parameters (namely the round trip time and the handling capacity) achieved in an elevator system when destination elevator group control is applied in place of conventional group control under incoming traffic conditions. IOBs are used because they provide measures for upper performance limits for elevator traffic analysis and design that are objective and implementation independent. 3. CLASSICAL ELEVATOR TRAFFIC DESIGN PROCESS

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This section provides a brief overview of the classical elevator traffic design process, based on the simplest case. The aim of the section is not to present the classical elevator traffic design process and related equations, as this is well documented elsewhere [3]. The aim is to show how the use of the round trip time and the interval relies on idealised conditions and is thus a good example of an Idealised Optimal Benchmark (IOB). As the equations are introduced, the idealised condition assumptions on which they are based will be clearly stated. Assuming equal floor populations and independent passenger decisions, the equation for deriving S is shown below [3]. P   1    S = N ⋅ 1 − 1 −    N   

……….(1)

Assuming equal floor populations and independent passenger decisions, H can be derived as shown in equation (2) below [3]: N −1

 i  H = N − ∑  i =1  N 

P

……….(2)

Substituting the values of S, H and P into the round trip time equation provides the average value of the round trip time as shown below [3]. Equation (3) assumes that the top speed is attained in one floor journey, equal floor heights, incoming traffic only and a single entrance.

τ = 2H ⋅

d   + (S + 1) ⋅  t f − f + tdo + tdc  + P ⋅ (t pi + t po ) v v  

df

……….(3)

It is important to emphasise that the round trip time is a random variable, the value of which depends on the destination choices of the P passengers. In fact, a probability density function (pdf) for the round trip time can be produced, and a standard deviation extracted from it. Moreover, S and H are also random variables dependent on the passenger destination choices. The formulae for the standard deviation of S and H have been derived in [7]. Using the obtained value of the round trip time, the required number of elevators is obtained by dividing the value of the round trip time by the target interval [3]. A ceiling operator is used in recognition of the fact that a whole number of elevators must be selected.

 τ  L=   inttar 

……….(4)

Due to the rounding up effect above, there will be some extra capacity in the design, and thus the actual interval will be smaller than the target interval [3]. The value of the actual interval is shown below in equation (5).

int act =

τ L

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……….(5) Page 4 of 25

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Equation (5) is based on the following two assumptions: 1. The round trip time is a constant (not a random variable). 2. The elevator movements around the building are evenly spaced out in order to equalise the interval (no bunching exists, [8]). Finally the handling capacity is calculated using equation (6) below [3], and is obviously inversely proportional to the value of the round trip time.

HC % =

300 ⋅ P ⋅ L ⋅ 100% τ ⋅U

……….(6)

The handling capacity HC% presented in equation (6) is the relative handling capacity and has units of percentage of the building population in five minutes. It will simply be referred to in this chapter as the handling capacity. It could refer to the whole building or to a specific sector. The absolute handling capacity, HC, has units of passengers per five minutes, and will be referred to in this chapter as the absolute handling capacity. It could refer to the whole building or to a specific sector. It is evaluated using equation (6a) shown below.

HC =

300 ⋅ P ⋅ L

τ

……….(6a)

In presenting the equations above, at least nine idealised conditions have been assumed. Specifically the following assumptions are worth noting: 1. Although the round trip time is a random variable, continuously varying in every round trip, the average value is used for the design. It is the randomness of the passenger destination decisions that causes the randomness in the values of H and S that in turn causes the randomness in the value of round trip time. 2. The round trip time can be evaluated for non-integer values of the number of passengers, in recognition of the fact that the number of passengers used is an average value over a large number of round trips. In reality, the number of passengers boarding the car is obviously an integer in each round trip. 3. It is assumed that bunching does not take place and the elevator round trips are equally spaced [8]. This is critical to the validity of the concept of finding the value of the interval by dividing the round trip time by the number of elevators (equation (5)). 4. UP-PEAK SECTORING AND DESTINANTION GROUP CONTROL This section introduces the concepts of up-peak sectoring and destination group control. 4.1 Up-peak Sectoring © Copyright held by the author 2016: Prof. Lutfi R. Al-Sharif

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Up-peak sectoring is an elevator group control algorithm that emerged in the 90’s. It provides a boost to the handling capacity of the elevator system when subjected to heavy incoming traffic during the morning peak and is usually applied where the building has a single entrance [9]. It has many variations, but a common theme is that the building is subdivided into a number of sectors during the morning peak. Passengers press the landing call in the lobby as in the conventional control system. The sector that an elevator will serve is displayed to allow passengers to board it. The allocation of the elevator to a sector could be static (same allocation every round trip) or dynamic (changes every round trip), and the composition of the sector could be static or dynamic, whereby the floors comprising the sector are usually contiguous. At the end of the sectoring period, the elevator control system reverts to an un-sectored conventional group control. The main advantage of applying up-peak sectoring is that it provides a boost to the handling capacity of the system at the expense of increasing waiting time. This is especially useful in cases where the population of the building has increased beyond the original design population, or where the elevator system has been originally under-designed. When the building is sectored, the number of sectors can vary from two (as a minimum) to L as a maximum (i.e., the number of elevators). Where the number of sectors is equal to two sectors, this can be thought of as minimal sectoring; where the number of sectors is equal to L, this can be thought of as full sectoring. Minimal sectoring provides the smallest increase in handling capacity, whereas full sectoring provides the largest increase in handling capacity. Where the sectoring is static, each elevator serves the same sector in every round trip. In such a case and where the sectors comprise contiguous floors, this results in unequal round trip times for the different sectors. As the elevator car capacities and rated speed are usually equal, the handling capacities for the different sectors/elevators become unequal. Unequal handling capacities for the different sectors are unacceptable as they will result in the under-service of some sectors and wasteful over-service of others. In order to address this problem and equalise the handling capacity of the different sectors, elevator traffic designers attempt to reduce the variance by altering the size of the sectors. This is usually achieved by increasing the number of served floors (and hence the served population) of the lower sectors and decreasing the number of served floors (and hence the served population) of the upper sectors. In this chapter an alternative approach to equalising the handling capacity of the sectors is presented that is based on three elements: 1. Splitting the building into sectors of equal size populations (and hence equal size floors assuming that the floor populations are equal). The size of each sector is equal to the division of the number of floors above the main terminal (N) by the number of elevators (L) assuming that the number of sectors (S) is equal to the number of elevators. 2. Sequencing the elevators between the sectors in an epoch. 3. Alternating the size of the sectors between successive epochs to deal with non-integer values resulting from dividing N by L.

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This alternative approach is necessary in order to allow the derivation of the two new equations for H des and S des that are necessary for finding the idealised optimal benchmark. As presented in [5], it is worth nothing that equalising the round trip time between sectors/elevators per se does not necessarily achieve the objective of equalising the handling capacity of the sectors/elevators. 4.2 Destination Elevator Group Control Destination elevator group control refers to an elevator group control system in which passengers select their destination at the landing upon arrival and are allocated an elevator car to board ([4], [10], [11]). Once the allocation has been made it cannot be altered. It allows the passenger to move towards his/her allocated elevator and await its arrival. Where operating under incoming traffic conditions, destination elevator group control is in effect an advanced form of full up-peak sectoring. The additional advantage is that all the passenger destinations are available, and thus a more efficient allocation is possible. Consequently, the composition of the sectors can be dynamically altered to suit the registered destinations in every round trip. There are different methods of applying destination control systems (an example of which can be found in [11]). For the sake of clarity, a detailed description is presented in this sub-section to explain the specific application of destination group control algorithm in this chapter. Although destination group control can be applied under general traffic conditions, only the incoming traffic conditions are considered in this chapter. Moreover, destination group control algorithm will be applied as a form of dynamic sectoring dynamic allocation. Dynamic sectoring refers to the fact that the size and constitution of the sectors is dynamic and could change from one round trip to the next. Dynamic allocation refers to the fact that elevator assignment to the sectors is not fixed and that each elevator can be assigned to a different sector in each round trip. Dynamic sectoring is sometimes referred to as dynamic zoning, and comprehensive analysis can be found in references [12] and [13]. A discussion on the application of destination control and the precautions that need to be applied is contained in [14]. A simulated analysis of the performance of destination control systems under lunch hour traffic is contained in [5]. It concludes that the elevator traffic system can be designed based on the boost in handling capacity obtained from the application of destination group control under up-peak conditions, but the assumed passenger arrival rate must be increased by 20% to 30% in order to ensure that the system can cope with lunch hour traffic [5]. 4.3 Destination Group Control: Dynamic Sectoring Dynamic Allocation One of the main advantages of destination elevator group control systems over conventional up peak sectoring elevator group control systems is the feature of dynamic sectoring dynamic allocation. By exploiting this feature the real power of destination group control can be realised. Dynamic sectoring is the feature by which the size of the sectors changes continuously (e.g., every elevator round trips or every L elevator round trips). The advantage of this feature is that it can allow the control system to deal with noninteger values of the sector size (i.e., non-integer values of N/L) by alternating the size of the sectors between different consecutive elevator round trips. The preferred © Copyright held by the author 2016: Prof. Lutfi R. Al-Sharif

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arrangement under conventional up-peak sectoring elevator group control systems has been to keep the sector sizes fixed for the convenience of passengers, but this is no longer a requirement under destination group control. Dynamic allocation refers to the feature by which the elevators are allocated to different sectors in different round trips. The preferred arrangement under conventional up-peak sectoring has always been to keep the allocation between the sector and the corresponding elevator fixed, to avoid confusion to the passengers. But this is no longer a requirement under destination elevator group control systems, whereby any elevator can be allocated to any sector. This allows the feature of sequencing that is discussed in more detail in sub-sections 5.2 and 5.3, which illustrate how the use of sequencing can be used to equalise the relative handling capacity of the different sectors. 5. IDEALISED OPTIMAL BENCHMARKS APPLIED TO DESTINATION ELEVATOR GROUP CONTROL In this section, the equations for the IOB under destination group control algorithm are derived. These equations are based on the earlier assumptions introduced in sub-section 4.2. 5.1 Assumptions for the IOB In finding the IOB of the handling capacity of the elevator group under destination elevator group control, the following assumptions will be made. The full sectoring of the building under destination group control is represented graphically in Figure 1. 1. There are as many soft sectors in the building as there are elevators in the group. 2. The allocation of the elevators to the sectors is dynamic; thus the elevator can be assigned to any of the sectors in each round trip. 3. As a general rule, the sectors comprise contiguous floors and are nonoverlapping. In some cases, minor breaches to this rule are allowed if they lead to a reduction in the number of stops. 4. The nominal delineation of the sectors is such that each sector contains the same population as the other sectors. 5. The destination elevator group controller has full advance knowledge of the destination of all the passengers prior to them registering their destinations. 6. The destination elevator group controller can make the ideal allocation of passengers to the elevators in order to maximise the overall handling capacity of the elevator group within the building. 7. The elevators are sequenced in rotation to the different sectors, in order to equalise the handling capacity (HC%) of the different sectors. 8. The sizes of the sectors can be dynamically changed between consecutive epochs in order to cope with the randomness of the passenger arrivals and in

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order to cope with the non-integer values of the sector sizes resulting from the division of N by L.

Figure 1: General overview showing the arrangement and size of the L sectors.

Although the assumption of equal floor populations has been made when deriving the new equation for the highest reversal floor later, it is not necessary for the validity of the concepts presented in this chapter. 5.2 Sequencing of the Elevator Cars in the Group Rather than simply equalising the round trip time of the elevators serving the different sectors ([12], [13]), it is preferable to equalise the handling capacity of the different elevators [5]. This section suggests a simple method that leads to the equalisation of the handling capacity of the elevators serving the sectors. As discussed earlier, dynamic allocation of the elevators to the sectors is a powerful feature of destination group control systems. Figure 2 shows a suggested sequencing of the elevators to the different sectors. As there are as many sectors as there are elevators, the elevators can be rotated or sequenced to the different sectors. It is done by alternating the elevators to the different sectors in rotation such that each elevator serves all the sectors in succession. This allows the size of all the sectors to be kept equal, and the number of the passengers boarding each car also equal. The physical round trip times of the sectors are not equal under this arrangement but the effective round trip times are equal for the sectors and thus the handling capacities of the sectors are equal. The terms physical and effective are introduced in section 5.3.

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Figure 2: Elevator sequencing to the different sectors (using 4 elevators as an example).

5.3 Numerical Example Showing How Sequencing Equalises Handling Capacity In order to illustrate how sequencing can be used to equalise the handling capacity for the sectors a numerical example is presented in this sub-section. A building is sub-divided into four sectors and has four elevators in the group, where each elevator will fill up with 10 passengers in each round trip. The round trip time for the elevators serving each of the sectors is 40 seconds, 60 seconds, 100 seconds and 120 seconds for sectors S1, S2, S3 and S4 respectively. It will be assumed that the populations of all sectors are equal, with 300 persons in each sector. For simplicity, it will be assumed that the number of floors in each sector is an integer number, although an approach for dealing with non-integer values of N/L will be presented in a later sub-section. If each elevator is permanently allocated to a specific sector, then the handling capacities of the four sectors will be unequal. Using equation (6) it can shown that the handling capacity of each of the sectors is 25.0%, 16.7%, 10.0% and 8.3% for sectors S1, S2, S3 and S4 respectively. However, if sequencing is used (i.e., dynamic allocation) where each elevator serves a different sector in each round trip, the effective round trip time for each of the sectors is equalised. This is explained in detail as follows. Figure 2 shows a timeline of the four elevators serving the four sectors in sequence. Elevator 1 starts by serving sector S1, then immediately sector S2 and so on. The same is shown for the other three elevators, serving the four sectors in the same order (i.e., S1, then S2, then S3 then S4) but with a shift in time. This shift in time is critical and is equal to the average of the four round trips. Figure 2 showed each elevator on one timeline. The timelines in Figure 3 have been completely rearranged in order to show each sector on one timeline. Both Figure 2 and Figure 3 contain exactly the same data. Examining Figure 3 shows the gaps in service for sectors S1 and S2 where the gaps have been shown as hatched rectangles. On the other hand, the elevator service for sector S3 and S4 shows overlapping round trips between different elevators serving the sectors where the overlaps have been shown as dotted rectangles. This overlap is acceptable as there is a time-shift between the overlapping elevators serving the same zone, so that they © Copyright held by the author 2016: Prof. Lutfi R. Al-Sharif

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are in different phases (e.g., one elevator is boarding passengers at the main terminal for sector S4, while the other elevator has already nearly arrived at sector S4). It is interesting to note that each gap shown for the lower sectors (S1 and S2) occurs at the same time as an overlap for the two upper sectors (S3 and S4) as can be clearly seen in Figure 3.

Figure 3: A diagram showing how each of the sectors is served by each of the elevators.

Focussing on sector S1, a timeline diagram is shown Figure 4. Despite the fact that the round trip time to serve sector S1 is 40 seconds (this has been denoted as the physical round trip time), it is only served by an elevator every 80 seconds, which is the effective round trip time. The handling capacity in reality is a function of the effective round trip time, not the physical round trip time. For sector S1, it takes 80 seconds to deliver 10 passengers (not 40 seconds). The gaps in the service (shown as hatched rectangles) ensure that the effective round trip time is 80 seconds and not 40 seconds. These gaps are used in boosting the handling capacity of the upper sectors.

Figure 4: Timeline showing that the effective round trip for sector S1 is 80 seconds, despite the fact that the physical round trip is 40 seconds.

Focussing on sector S4, a timeline diagram is shown Figure 5. Despite the fact that the round trip time to serve sector S4 is 120 seconds (this has been denoted as the physical round trip time), it is actually served by an elevator every 80 seconds, which © Copyright held by the author 2016: Prof. Lutfi R. Al-Sharif

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is the effective round trip time. The handling capacity in reality is a function of the effective round trip time, not the physical round trip time. For sector S4, it takes 80 seconds to deliver 10 passengers (not 120 seconds). The overlaps in the service ensure that the effective round trip time is 80 seconds and not 120 seconds. These overlaps have been provided at the expense of the lower sectors (where gaps in service arise).

Figure 5: Timeline showing that the effective round trip for sector S4 is 80 seconds, despite the fact that the physical round trip is 120 seconds.

The total time that each elevator spends serving all the L sectors will be referred to as an epoch which is the sum of the L round trip times. The effective value of the round trip time is the average of the L round trip times to the L sectors. L

τ eff

epoch = = L

∑τ i =1

Si

……….(7)

L

The effective round trip time is now equal between all the sectors and is equal to the epoch divided by the number of elevators, as shown below in equation (7). Effectively, the round trip time as shown in equation (7) is the interval for each sector. The effective round trip time for this example is 80 seconds. Substituting the effective round trip time in the handling capacity equation (6) gives a handling capacity for each of the sectors of 12.5% (which is also the handling capacity for the whole building). Sequencing effectively uses the spare capacity that the lower sectors have and uses it to boost the handling capacity of the upper sectors. The effective round trip time of the lower sectors is increased by having gaps between the round trips of elevators serving these sectors (Figure 4). The effective round trip time of the upper sectors is reduced by having overlapping between the round trips of elevators serving these sectors (Figure 5). 5.4 Dealing with Non-Integer Values of Sector Sizes The methodology presented in sections 5.2 and 5.3 has assumed equal sector sizes. In cases of equal floor populations, the size of the sectors is set to N/L. This is not necessarily an integer value. In order to deal with this problem, the feature of dynamic sectoring can be used. The sizes of the sectors can be alternated between consecutive elevator round trips (or sets of elevator round tips). For example, with a building with 10 floors above the main entrance and 4 elevators in the group, the size of the sectors is 2.5 floors. As this a non-integer, it is © Copyright held by the author 2016: Prof. Lutfi R. Al-Sharif

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necessary to change the size of the sectors between alternating round trips or epochs, as shown in Table 1. In the long term, the effective size of each sector will converge to 2.5 floors. Table 1: Suggested alternation of the size of the sectors in consecutive sectors.

Sector # S1 S2 S3 S4

Epoch 1 1-3 4-5 6-8 9 - 10

Epoch 2 1-2 3-5 6-7 8 - 10

Epoch 3 1-3 4-5 6-8 9 - 10

Epoch 4 1-2 3-5 6-7 8 - 10

Dynamic sectoring is necessary anyway for the destination elevator group controller to deal with the random nature of the passenger arrivals at the main terminal. Due to the random nature of the arrivals, it might be necessary to enlarge certain sectors in some epochs and reduce them in other epochs. So the dynamic sectoring featuring is necessary anyway, regardless of the non-integer problem of the size of the sector. 5.5 Methods for Finding the IOB under Destination Group Control There are three methods to assess the IOB for the improvement in the performance of the elevator system under destination group control that are outlined below. These methods are not intended as real time elevator group control algorithms and cannot be implemented inside a real time controller. They are presented here as tools used to evaluate the values of H and S that can be achieved on average by the use of destination group control for a specific building. Four methods are discussed below. The first two are analytical. The last two are numerical. 1. Generic analytical equation-based method: This group of methods only depend on the values of N, L and P for finding the value of H and S and assume equal floor populations. They involve finding a set of equations to calculate the minimum value of the round trip time, which corresponds to the maximum value of the handling capacity. It is assumed that the round trip time attains its minimum value when H and S attain their minimum values. These equations are derived in detail in the next sub-section (11) and (18) and form the basis for the IOB suggested in this chapter. Suggested equations for H and S have also been presented in [4] and [5] and these will be compared to equations (11) and (18) presented in this chapter in section 7. 2. Building specific analytical methods: An alternative approach to finding the IOB for a building operated under destination group control is presented in [5] and is more building specific. The approach is based on splitting the building into L contiguous-floor sectors that have the least variance in handling capacity (HC%). The round trip times are then evaluated for each of the L sectors, and the overall handling capacity of the building is evaluated. It is referred to as optimised contiguous zones analysis in [5]. 3. Listing and solving all possible scenarios (exhaustive enumeration): Another possibility is to assume equal size contiguous-floor sectors, enumerate all the possible scenarios and solve each of them analytically. The steps that need to be followed are: © Copyright held by the author 2016: Prof. Lutfi R. Al-Sharif

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i.

Split the building into equal size sectors.

ii.

List a new possible scenario: Each scenario comprises a selection of destinations for each of the L∙P passengers. There are NL∙P possible scenarios for any building. In order for the assessment to be complete all the possible scenarios have to be listed.

iii.

For each of the possible scenarios generated in i above, list all the possible solutions of allocating the L∙P passengers to the L elevators and pick the solution that provides the smallest value of the round trip time and hence the largest handling capacity. Allocating the L∙P passengers in this case is not meant to be a real time algorithm, but a way to assess the benefit of destination in reducing the values of H and S. The number of unique possible solutions can be shown to be equal (L ⋅ P ) ! . to (L!) ⋅ (P !)L

iv.

Steps ii and iii have to be repeated until all the possible scenarios are completed. Once done, the average value of the best solution for all the scenarios is calculated, which is representative of the IOB. The average values of H and S are calculated for all the scenarios and used to find the IOB.

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 the 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. For these reasons, the methods suggested in 4 below are more practical. 4. Monte Carlo Simulation for the generation of scenarios and numerical or rule based solution: A more practical solution is to take a sample of the possible scenarios using Monte Carlo simulation, and then to solve each scenario using optimisation techniques, heuristics or rules of thumb. Monte Carlo simulation is simply used as a tool to pick a representative sample of the large group of possible scenarios (i.e., L∙P passenger arrivals and their destinations). Under each scenario, passengers are generated each with a randomly generated destination (based on the floor populations). These passengers, each with his/her specified destination, are allocated to the elevators, and the resulting round trip time is calculated. The resulting round trip time is compared to the conventional control round trip time, to reveal the boost in the handling capacity. The optimisation techniques, heuristics or rules of thumb aim to arrive at a solution that minimises the expected number of stops, S, the highest reversal floor, H, or both by simply allocating the passengers to the sectors in a way that minimises the average value of H for the L sectors, or the value of S for the L sectors. It is also possible to solve the scenarios using other optimisation techniques (e.g. genetic algorithms, dynamic programming, single © Copyright held by the author 2016: Prof. Lutfi R. Al-Sharif

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step and multi-step random searches). These 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 use of genetic algorithms has been presented in [15] and shown to provide a solution at speeds that are suitable for implementation in real time controllers. The use of genetic algorithm could be also used to assess the IOB performance, by replacing the allocation step of passengers to sectors in order to minimise H, S, the round trip time or maximise the handling capacity of the sectors. This is a possible piece of future research to further improve the IOB found using numerical (as opposed to analytical) methods. 5.6 Derivation of the Equations for the Analytical Method The aim of finding the IOB under the operation of destination elevator group control will be to find the new handling capacity of the elevator group control assuming that the number of elevators and the number of passengers transported in a round trip remain fixed. In other words, finding the handling capacity IOB will answer the question: By how much can the handling capacity be increased following the introduction of destination elevator group control under incoming traffic conditions, using the same number of elevators running at the same rated speed and holding the same number of passengers in each round trip? Thus the derivation of the equation will aim to find the new value of the handling capacity of the elevator group control with destination control assuming that the cars will be boarded by the same number of passengers, P, in every round trip. In order to maximise the handling capacity, it will be necessary to minimise the round trip time (equation (6)). The derivation of the minimum value of the round trip will be inspired by the round trip time equation (3). It contains three terms: one depends on the highest reversal floor, H; the second term depends on the expected number of stops, S; and the third and last term depends on the number of passengers, P. But as shown in the earlier discussion in this sub-section, the value of P will not change. Thus, it is necessary to minimise the values of H and S. in order to minimise the value of the round trip time and thus maximise the value of the handling capacity. Once destination elevator group control is applied the building will effectively be split in L sectors, all having equal populations (see Figure 1) as shown in equation (8) below. U S 1 = U S 2 = ....... = U SL

……….(8)

Obviously, the sum of the population of all the L sectors is equal to the total building population. L

U = ∑ U Si

……….(9)

i =1

© Copyright held by the author 2016: Prof. Lutfi R. Al-Sharif

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The fact that all the sectors have equal populations has important consequences. It provides equal weights to all the sectors, as they all pertain to the same number of passengers in the building. For each elevator, the number of floors in a round trip will be reduced to N eff , as shown in equation (10) below. N eff =

N L

……….(10)

Thus the minimum value of the expected number of stops can be evaluated by substituting the effective value of the number of floors (N eff ) into the original equation of the expected number of stops (1), whereby the number of passengers (P) remains unchanged. S des = N eff

P     1   ⋅ 1 − 1 −   N   eff    

……….(11)

Deriving the minimum value of the highest reversal floor is more involved, as the effective highest reversal floor for each sector is unique. Referring to Figure 6 below, it can be seen that the effective highest reversal floor for any sector is the sum of two parameters: the local highest reversal floor for the sector (H local ) and the shift in the position of the sector (H shift ) [16]. H eff = H shift + H local

……….(12)

th

Figure 6: General overview for the derivation of H eff for the i sector. © Copyright held by the author 2016: Prof. Lutfi R. Al-Sharif

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In a similar way to that used in the derivation of S des , the effective number of floors is equal to N/L, as shown in equation (10). Substituting the value of N eff in the conventional formula for the highest reversal floor (equation (2)) provides a formula for the local highest reversal floor for the sector. N

H local

−1

N L  j⋅L = − ∑  L j =1  N 

P

……….(13)

A formula is then developed for the shift for each sector. H shift =

(i − 1) ⋅ N

……….(14)

L

So the effective highest reversal floor for the ith sector is the sum of the two quantities: N

H eff

L (i ) = (i − 1) ⋅ N + N −

L

−1

 j⋅L   ∑ j =1  N 

L

P

……….(15)

Simplifying gives:

H eff (i ) =

N −1 L

i⋅N  j⋅L − ∑  L j =1  N 

P

……….(16)

The effective highest reversal floor is the average of all the effective highest reversal floors over all the sectors (remembering that the populations of all the sectors are equal, and thus have equal weight): L

H des =

∑ H (i ) i =1

eff

L

N −1  P  i⋅N L  j⋅L  1 = ⋅∑ − ∑   L i =1  L j =1  N     L

N

−1

P

−1

P

N L i L  j⋅L = ⋅∑ − ∑  L i =1 L j =1  N  N

N L +1 L  j ⋅ L  = ⋅ − ∑  L 2 j =1  N 

……….(17)

Rearranging gives the final important results for the highest reversal floor for the whole building under destination elevator group control.

© Copyright held by the author 2016: Prof. Lutfi R. Al-Sharif

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H des =

N −1 L

N L +1  j⋅L ⋅ − ∑  2 L j =1  N 

P

……….(18)

It is worth noting that by substituting L=1 in equation (18) above the expression reverts back to the classical equation for H shown in the original equation (2). In deriving the values of S des and H des above, it has been assumed that the destination elevator group controller has full knowledge of the destination of all the passengers before they are registered and is also able to perfectly allocate the passengers to the elevators in such a way that achieves such minimum values. Such an assumption, although not achievable in practice, is compatible with the concept of the idealised conditions assumed to prevail in finding an IOB. The values of S min and H min are then substituted in equation (3) to find the value of the round trip time, τ des . The value of the round trip time, τ des , is then used in order to find the maximum value of the handling capacity under destination group control using equation (6), denoted as HC% max . On the other hand it is possible to find the number of passengers boarding the elevator under destination elevator group control if the elevator system is subjected to the original arrival rate (AR%). Under such conditions, the number of passengers boarding the elevator will be smaller than the original value of P. In order to find the value of the lower P, it is necessary to find the effective arrival rate for each of the sectors in passengers per second, which is one Lth of the original value of the arrival rate in passengers per second.

λS =

λ L

=

AR% ⋅ U 300 ⋅ L

……….(19)

Thus the number of passenger boarding each elevator can be found as follows: Pdes = λS ⋅ τ des

……….(20)

Expanding gives the important equation:

Pdes =

AR% ⋅ U ⋅ τ des 300 ⋅ L

……….(21)

In equation (21) above, the number of passenger, P des , is a function of the round trip time, τ des , and the round trip time, τ des , is a function of the number of passengers, P des . So equation (21) cannot be solved algebraically and can only be solved iteratively using numerical methods. In the numerical method, a starting value of P des is selected. This is used to evaluate the value of the round trip time using equation (3). The resulting value of τ des is then used to find a new value of P des using equation (21). These two steps are repeated until the values converge. The iterations are stopped when the difference in the value of τ des is smaller than a certain preset threshold. 6. NUMERICAL EXAMPLE © Copyright held by the author 2016: Prof. Lutfi R. Al-Sharif

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A numerical example is presented in this section to illustrate the use of the IOB method in establishing an upper limit on the elevator system performance under destination elevator group control. A building has the following parameters. N number of floors above the ground floor (the main entrance) 10 floors v rated speed, 1.6 m/s a rated acceleration, 1 m/s2 j rated jerk, 1 m/s3 U building population, 1000 persons (equal floor populations) d f floor height, 4.5 m (equal floor heights) t do door opening time, 2 s t dc door closing time, 3 s t pi passenger boarding time, 1.2 s t po passenger alighting time, 1.2 s AR% percentage arrival rate in the busiest five minutes, 12.42% int tar target interval, 30 s The first step is to carry out a traffic design for the building under conventional control, using a method such as that presented in [17]. This results in the following parameters: P=12 passengers in the car in each round trip round trip time ( τ ) = 144.92 s L= 5 elevators int act = 28.984 s HC%= 12.42% Thus under conventional group control and incoming traffic conditions, the building will require five elevators and will achieve the required arrival rate of 12.42% at an actual interval of 28.984 s. The IOB will now be used to answer the following question: What handling capacity can be achieved if the system is run under destination group control and incoming traffic conditions using five elevators and carrying 12 passengers in each elevator car? In order to answer the question, the building will be split into five sectors (equal to the number of elevators) representing a destination control system that uses equal passenger size sectors and alternates the elevators to these sectors. As the floor populations are equal in this example, the number of floors in each sector is the same. Each elevator will be sequenced (alternated) to each of the five sectors, each time carrying 12 passengers. In order to calculate the average value of the round trip time under destination control, it is necessary to calculate the values of the number of stops (S des ) and the highest reversal floor (H des ), using equations (15) and (23) respectively, under destination elevator group control, resulting in value of 1.9995 stops per round trip for S des and 5.99975 floors for H des .

© Copyright held by the author 2016: Prof. Lutfi R. Al-Sharif

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Then the value of the round trip time can be evaluated using equation (3) and the two values above and a value of 12 for the number of passengers, P, resulting in a value of 85.35 seconds. Equation (6) can then be used to find the maximum value of the handling capacity at a constant value of P, resulting in a value of HC% max = 21.07%. Thus the use of destination group control will increase the handling capacity from 12.42% to 21.09% with the same number of passengers boarding the elevator in each round trip (P=12), a factor of around 1.7 or a boost of 70%. In practice, the controller will not achieve such a value. Using Monte Carlo simulation to generate random scenarios and heuristics to find the minimum possible values of S, H and a hybrid of S and H achieves the values shown in Table 2 below. The algorithm for minimising the value of S finds the minimum possible value of S, assuming full advance knowledge of the passenger destinations. The algorithm for minimising the value of H finds the minimum possible value of H, assuming full advance knowledge of the passenger destinations. The algorithm for simultaneous minimising H and S tries to achieve a simultaneous minimisation of the two parameters (H and S) that results in a minimum value for the round trip time. Table 2: The values of H and S from the equation and three different algorithms for the example (all round trip time values in seconds).

Parameter

Minimising S

Minimising H

Minimising of H and S simultaneously (hybrid)

S H

2.2438 7.4088 95.1274

2.6736 6.3246 92.2952

2.4256 6.4582 91.1619

τ

IOB Equations (15), (23) 1.9995 5.99975 85.35

Examining Table 2 it is worth noting the following: 1. The equation method gives the best values for both H and S. But in practice these two ideal values cannot be simultaneously achieved. 2. The first algorithm for minimising S gives a low value for S, but at the expense of the value of H. The second algorithm for minimising H provides a low value of H at the expense of S. 3. The third algorithm (hybrid) balances the two in order to minimise the value of the round trip time. In effect the third algorithm minimises the value of H, then sacrifices some of that in order to reduce S and thus minimise the value of the round trip time. The IOB method can also be used to answer the following question: What would the number of passengers boarding the car in each round trip be if the system is run under destination group control and incoming traffic conditions using five elevators when subjected to same arrival rate (AR%) for the which the system was designed (i.e., AR%=12.42%)? Under such conditions the number of passengers boarding each car will drop below the original value of 12 passengers, until steady state conditions are achieved. The © Copyright held by the author 2016: Prof. Lutfi R. Al-Sharif

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balance conditions are achieved in accordance with equation (21) that has to be solved iteratively used numerical methods. This provides the following results: S min =1.937089 stops per round trip H min =5.968544 floors P= 4.99 passengers Using these three values, the new value of the round trip time can be calculated:

τ min =60.27222 s As expected, the handling capacity is 12.42%. Thus by applying destination elevator group control under the same number of elevators and the same design arrival rate, the number of passengers boarding the car drops from 12 passengers down to 5 passengers, or a reduction by a factor of 2.4. This is equivalent to a reduction in car loading by around 59%. So to summarise, using the IOB method has shown that for this building the application of destination elevator group control can potentially either increase the handling capacity by a factor of 1.7 at the same car loading, or reduce the car loading by a 59% at the same handling capacity. 7. COMPARISON WITH PREVIOUS WORK Reference [4] develops equations for the probable number of stops, S, and the highest reversal floor, H, as shown in equations (22) and (23) below respectively: Sd =

2⋅ N L

L⋅P   1   ⋅ 1 − 1 −   2 ⋅ N    

N −1

 i  H = N − ∑  i =1  N 

……….(22)

Sd

……….(23)

Reference [5] uses the same equation (23) for H as that used in reference [15] but amends the equation for S d as shown below: Sd =

N L

L⋅P   1  ⋅ 1 − 1 −     N   

……….(24)

Equation (24) gives approximately the same results as equation (11), although it is based on different assumptions in its derivation. This is shown below:

© Copyright held by the author 2016: Prof. Lutfi R. Al-Sharif

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L⋅P L P  N       1 1   ⋅ 1 − 1 −   = ⋅ 1 −  1 −      N   L   N          P N    L L(L − 1)    ....   = ⋅ 1 −  1 − + 2⋅ N2 L    N   

N Sd = L

≈

N L

……….(25)

P   L  ⋅ 1 − 1 −     N   

A numerical example is used in this section to compare the results from [4], [5] and the new equations presented in this chapter. The numerical example is based on the example given in reference [5] for a building that has 19 floors above the main entrance (N), 24 passengers boarding the elevator car (P) and 8 elevators in the group (L). The values of H and S for different algorithms/methods have been listed in Table 3 and in Table 4. The methods have been sorted by ascending values of H in Table 3 and by ascending values of S in Table 4. As expected, the IOB equations outperform all other methods for both H and S, while the conventional control underperforms all other methods for both H and S. Table 3: Results for the values of H and S for the example used in [5] for different methods/assumption sorted by ascending values of H. Method/Algorithm/Assumptions IOB equations (11) for S des , (18) for H des Offline allocation of passengers, minimising H only algorithm (contiguous sectors) assuming perfect knowledge of future passenger destinations Simulated Contiguous Zones, Minimum variance HC% (Sorsa et al [5]) Suggested values from Sorsa et al [5] using equations (24) for S and (23) for H Offline allocation of passengers minimising S only algorithm (non-contiguous sectors) assuming perfect knowledge of future passenger destinations Equations from Schröder [4] equation (22) for S and (23) for H Online real time allocation of passengers, aiming for contiguous sectors Conventional control, equations (1) for S and (2) for H

H 10.688

S 2.375

11.0

3.181

12.6 14.0

2.4 2.375

14.056

2.719

16.1 16.469 18.64

4.72 6.106 13.8

Table 4: Results for the values of H and S for the example used in [5] for different methods/assumption sorted by ascending values of S. Method/Algorithm/Assumptions IOB equations (11) for S des , (18) for H des Suggested values from Sorsa et al [5] using equations (24) for S and (23) for H Simulated Contiguous Zones, Minimum variance HC% (Sorsa et al [5]) Offline allocation of passengers minimising S only algorithm (non-contiguous sectors) assuming perfect knowledge of future passenger destinations Offline allocation of passengers, minimising H only algorithm (contiguous sectors) assuming perfect knowledge of future passenger destinations Equations from Schröder [4] equation (22) for S and (23) for H Online real time allocation of passengers, aiming for contiguous sectors Conventional control, equations (1) for S and (2) for H

© Copyright held by the author 2016: Prof. Lutfi R. Al-Sharif

S 2.375 2.375 2.4

H 10.688 14.0 12.6

2.719

14.056

3.181

11.0

4.72 6.106 13.8

16.1 16.469 18.64

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The following can be noted from the values of H and S in Table 3: 1. The Idealised Optimal Benchmark (IOB) equations (equation (11) for S des and equation (18) for H des ) provide the lowest values for H and S, compared to any other method as they assume ideal conditions and would never be achieved simultaneously in practice. They provide a benchmark against which all other methods can be compared. 2. The value of S des from equation (11) is equivalent to a situation in which the number of passengers is 24 and the number of floors above ground is N/L or 2.375 floors (which is the average size of each sector assuming equal size sectors). Both the optimised contiguous zones results from [5] and the equation for S from [5] provide approximately the same result. Equation (22) for S from [4] overestimates the value of S. 3. The value of H des given by the IOB equation (18) approaches a value equal to half the number of floor above the main entrance as the number of elevators increases. Visually examining Figure 1 and Figure 6 it can be seen that as the number of elevators in the group increases, the number of sectors increases and thus the value of H approaches half the number of floors, N/2. This can also be corroborated by examining equation (18). The second term in equation (18) becomes very small with reasonably large numbers of passengers. With large values of L, the value of H min approach N/2 assuming contiguous sectors. H min ≈

N L +1 N ⋅ ≈ 2 2 L

……….(32)

4. Equation (23) from [4] overestimates the value of H. It is difficult to explain the difference as no justification is given in [4] for its derivation. 5. The simulated results from [5] perform very well compared to the IOB equations (11) for S des and (18) for H des . 8. CRITICISMS OF THE IDEALISED OPTIMAL BENCHMARK The main criticism of the idealised optimal benchmark that has been presented in this chapter and that is based on equations (11) for S des and (18) for H des is that it cannot be implemented in practice and that is does not represent reality. Specifically the following points can be cited: 1. The size of the sectors found using N/L will rarely be an integer. A solution suggested earlier (section 5.4) is that dynamic sectoring can be used to alternate the size of the sectors around the non-integer value resulting from N/L. The average value of the sector size will approach N/L over a large number of epochs. 2. The handling capacity of the sector cannot be equalised if the population of the sectors are equal and the number of floors are equal: A possible solution has been suggested earlier (sections 5.2 and 5.3) whereby dynamic allocation can be used to sequence the elevators to the different sectors in one epoch, © Copyright held by the author 2016: Prof. Lutfi R. Al-Sharif

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thus allowing the handling capacity of the sectors to be equalised. Over a large number of epochs this objective will be attained as an average. However, the issue of implementation should not be the criterion for applying the IOB or not. The round trip time as an IOB has been used for the last 50 years for the design of elevator traffic systems. It accepts non-integer values of P, H and S. It is accepted that these values are averages that are only attained over a large number of round trips. It assumes that P passengers are always ready to board the elevator when the elevator doors open, regardless of the length of the latest round trip. The round trip time as presented in equation (3) is probably a very poor reflection of reality. Nevertheless, it has proved to be a very powerful tool for providing a lower limit for the average value of the round trip time. Providing an upper or lower limit for the variable is exactly the role of the IOB. It is accepted that these values will not be achieved when the system is implemented in practice. 9. CONCLUSIONS An Idealised Optimal Benchmark (IOB) is a tool that can be used to identify the optimal possible performance of a system under idealised condition; it can be used to assess the performance of a specific design and how far it is from optimal performance. The round trip time is in fact a form of an IOB applied in the area of elevator traffic analysis. The concept of an IOB has been extended to the calculation of the round trip time and hence the maximum possible handling capacity of an elevator system when destination group control is applied. Two formulae have been derived for the average of the minimum values of the expected number of stops (S) and the highest reversal floor (H). The formulae assume that the elevators in the group are alternated to the different sectors in the buildings, the number of which is equal to the number of elevators in the group. A numerical example has been solved showing the IOB for the maximum possible handling capacity that the destination group controller can achieve. A figure of around 1.7 is achieved (i.e., a boost of 70% in the handling capacity). An algorithm is also used to find in practice the minimum possible values of S and H for each building, based on hypothetical full advance knowledge of the passenger destinations. This cannot be implemented in a real controller and is only used for comparison of purposes. The results obtained are worse that those obtained by using the equations. The IOB as used in this case for finding the maximum possible performance of the elevator group controller under destination group control is a valuable tool for elevator traffic designers. It allows them to understand how far their designs deviate from the hypothetical optimal possible performance, effectively providing a benchmark. REFERENCES [1] Barney G C. Uppeak revisited. Elevator Technology 4 1992; 4: 39-47. The International Association of Elevator Engineers (Brussels, Belgium), proceedings of Elevcon ’92, Amsterdam, The Netherlands, May 1992. [2] Barney G C. Uppeak, down peak and interfloor performance revisited. Elevator Technology 9 1998; 9: 31-40. The International Association of Elevator Engineers (Brussels, Belgium), proceedings of Elevcon ’98, Zurich, Switzerland.

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[3] [4]

[5]

[6] [7] [8] [9]

[10] [11]

[12] [13]

[14]

[15]

[16]

[17]

Barney G C. Elevator Traffic Handbook: Theory and Practice. Spon Press/Taylor & Francis, London and New York, ISBN 0-415-27476-1, 2003. Schroeder J. Elevatoring calculation, probable stops and reversal floor, “M10” destination halls calls + instant call assignments. Elevator Technology 3 1990; 3: 199-204. Proceedings of Elevcon ’90, The International Association of Elevator Engineers (Brussels, Belgium), Rome, Italy, March 1990. Sorsa J, Hakonen H and Siikonen M L. Elevator selection with destination control system. Elevator Technology 15 2005; volume 15. The International Association of Elevator Engineers (Brussels, Belgium), proceedings of Elevcon 7th to 9th June 2005, Peking, China. Spalding D B and Cole E H. Engineering Thermodynamics. Third edition, Edward Arnold (Publishers) Ltd., London, United Kingdom, 1973, pp 238. Alexandris N A. Statistical Models in Lift Systems. Ph.D. Thesis, University of Manchester Institute of Science & Technology (UMIST), 1977. Al-Sharif L. Bunching in lifts: Why does bunching in lifts increase waiting time? Elevator World (Mobile, AL, USA) 1996; 44(11): 75–77. Powell B. Important issues in up peak traffic handling. Elevator Technology 4 1992; 4: 207-218. The International Association of Elevator Engineers (Brussels, Belgium), Proceedings of Elevcon ’92, May 1992, Amsterdam, The Netherlands. Lauener J. Traffic performance of elevators with destination control. Elevator World (Mobile, AL, USA) 2007; 55(9): 86-94. Smith R and Peters R. ETD algorithm with destination dispatch and booster options. Elevator Technology 12 2002; 12: 247-257. The International Association of Elevator Engineers (Brussels, Belgium), proceedings of Elevcon 2002, Milan, Italy, June 2002. So A T P and Yu J K L. Intelligent supervisory control for lifts: dynamic zoning. Building Services Engineering Research & Technology 2001; 22(1): 14-33. 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. Peters R. Understanding the benefits and limitations of destination dispatch. Elevator Technology 16 2006; 16: 258-269. The International Association of Elevator Engineers (Brussels, Belgium), the proceedings of Elevcon 2006, June 2006, Helsinki, Finland. Siikonen M L. On traffic planning methodology. Elevator Technology 10 2000; 10:267-274. The International Association of Elevator Engineers (Brussels, Belgium), the proceedings of Elevcon May 2000, Berlin/Germany. Malak M, Tuffaha D and Hussein M. Modeling and Simulation of dynamic sectoring in Elevator Traffic Analysis and Control. Final year graduation project, Supervisor: Dr. Lutfi Al-Sharif, Mechatronics Engineering Department, The University of Jordan, December 2012. Al-Sharif L, Abu Alqumsan A M and Abdel Aal O F. Automated optimal design methodology of elevator systems using rules and graphical methods (the HARint plane). Building Services Engineering Research and Technology 2013; 34(3): 275-293. August 2013. doi: 10.1177/0143624412441615.

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