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# Elevator Traffic Simulations

In the article Probability the classical method of arithmetic calculation of traffic handling capacity for an elevator was described. As also mentioned, this method has virtually disappeared from use and has been supplanted by computer simulations.

Before getting into the subject of simulations, it is apparent that the formula set out in Probability can be duplicated in a computer routine. A sample of such a routine using VB is as follows:

Public Floor_Stops(1 To 100)
Sub Macro1()
N = InputBox("Enter the number of floors above main")
P = InputBox("Enter the number of passengers")
'N is number of floors above main
'P is number of passengers
'S is the probable number of stops
Total_S1 = 0
MaxStop = 0
Number_of_Tries = 10000
For Tries = 1 To Number_of_Tries
For I = 1 To N
Floor_Stops(I) = 0
Next I
For P1 = 1 To P
Chosen_Floor = Int((N) * Rnd + 1)
Floor_Stops(Chosen_Floor) = 1
If Chosen_Floor > MaxStop Then
MaxStop = Chosen_Floor
End If
Next P1
For I = 1 To N
If Floor_Stops(I) <> 0 Then
Total_S1 = Total_S1 + 1
End If
Next I
Next Tries
S = Format(Total_S1 / Number_of_Tries, "00.0")
MsgBox ("Probable number of stops is " & S)
End Sub

This routine will give the same results as the formula in Probability and is therefore of only minor interest. However, it is illustrative of the methods used in a typical elevator traffic simulation program. In the following, the steps involved in constructing such a program are listed.

Establish the number of people handled by the system. This is typically an input and would normally be expressed as the number of people placing hall calls within a five minute period.

Establish the traffic pattern. Although this is sometimes described using terms such as “up-peak”, “heavier-up”, “balanced”, “heavier-down”, “down-peak”, it is more precise to set up a matrix of “from-to” calls. This matrix would list the expected number of calls from each floor to every other floor.

Input the elevator system characteristics. These inputs would consist of such things as number of elevators, floors served, speed, capacity, door type, acceleration, dispatching features and so on.

As a basis for the simulation, we create a routine that will mimic the movement of an elevator - closing doors, accelerating, running, decelerating, stopping, opening doors and so on. We have the choice of setting up a separate processor for each elevator so that each mimicked elevator can run independently or we can cycle through the elevators, operating each for a given time slice. The time slice may be, for example, 0.01 seconds although less precision will give reasonable results and take less compute time.

We start the simulation from time zero and increment the time by one time slice. We determine, based on the input handling capacity, if a call should be registered. This determination is randomized but based on the probability established by the input handling capacity. If a call is registered, then we determine the origin and destination, once again randomized but based on the traffic pattern set out in the “from-to” matrix.

We then assign this call to a particular elevator based on the call origin and destination, the elevator position, direction of travel and loading and the dispatching algorithm. We then cycle through the elevators incrementing the “time” of each by one time slice.

This is essentially it. The simulation can be run some number of times so as to evaluate the average results and other data that we might want. The key output is the waiting time but other output parameters such as load factor and system trap time are of interest.

There are, obviously, complications at each step of the program construction and much of the coding is tedious.

A number of "philosophical" considerations arise. For example, what dispatching algorithms should be used? Very little information is divulged by the elevator companies as to their dispatching logic. Some sales literature might mention "channeling", "destination dispatch" or some other term but no precise description is given as to what the system will do to control the assignment of calls to cars, the position of the cars, the triggers to invoke certain dispatching features and such other necessary information. Of necessity, the dispatching algorithm for a simulation program must, therefore, default to certain basic logical precepts that any well mannered elevator dispatching system would have. Among the obvious are such things as load non-stop, high and low call return, coincident calls and such similar items.

The use of the five-minute interval for traffic analysis derives from the original concepts established in the 1930's. At that time office building traffic was much more concentrated than it is today. The majority of people working in offices would arrive in the five minutes immediately before the starting time and leave in the five minutes following the finishing time. It was not uncommon to have up to 20% of the building population using the elevators in those five minute periods. Today traffic is much more dispersed and in any given five minutes it would be unusual to have more than 10% to 12% of the population using the elevators. For an evaluation of the elevator plant it would make more sense to look at a ten minute period but the five minute "standard' has become firmly established. Not that there is much difference; in the final analysis the results are quite similar so this is more of a discussion point for elevator aficionados.

The results of simulations tend to be more relative than absolute. A simulation may show that a given group of elevators will give a 34 second waiting time during the busiest five minutes at noon time. But if measured on site on any given day the actual waiting time may be less or more. This is natural given the normal variations of traffic from day to day. What the simulation will show is how well a given group of elevators will perform compared to another group. This is quite adequate since the intent, on a new construction project, is to compete with neighbouring buildings and it is important to know how the new building design stacks up against the competition. Nor are there any absolute standards for such things as waiting time. Some studies have suggested that people waiting for an elevator become restive after a certain number of seconds but this is very much dependent on the objective conditions. In this respect elevators are like other forms of transportation: how long should we wait for a taxi or a bus or an airplane?