IS IT QUICKER TO TAKE THE STAIRS?
How to reduce waiting times for lifts
You might think that the biggest concern of a lift engineer is making sure that the lift doesn’t break down. As it happens, though, designing a capsule that can dangle safely several hundred feet up is actually the easy part. The basic mechanics of a lift have hardly changed in fifty years, and, despite their reputation, modern lifts hardly ever go wrong.
Instead, the biggest issue with lift design is the time people spend waiting. The challenge has been devising ways of making sure that the lift picks up passengers and takes them where they want to go with the minimum of delay and frustration.
The problems that lift designers face are not dissimilar to those in other industries where waiting is an issue, such as supermarkets or traffic management. However, there is something partic ularly frustrating about waiting for a lift. With traffic and shops the problem is usually visible, and whether or not they are to blame there is at least somebody to shout at. This human element is missing in lifts. Behind those doors, a capsule is drifting up and down with an electronic mind of its own. For this reason, lift customers are particularly sensitive to the time they waste hanging around.
The quality of service is largely measured by the time interval between a customer calling a lift and the lift departing. Strictly speaking, there are two separate factors to consider. One is the average time that it takes a lift to arrive, and the other is the maximum time. Both have to be acceptable for the service quality to be satisfactory.
A lift with service times like this might be acceptable…
Whereas this lift service, with a lower average, might be unacceptable because of the occasional very long wait…
The first example has a high average but a small spread (or standard-deviation), while the second has a low average but a large spread.
How long should customers wait? Rule of thumb
In the experience of the lift company Otis, in a busy office environment lift users start to become impatient after about 15 seconds. Between 25 and 30 seconds some callers will begin to regard the service as poor, and even the most patient users share this view after 35 seconds.
The easy solution – build more lifts
The obvious way to keep the waiting time down is simply to provide lots of lifts. The more lifts there are, the greater the chance that there will be a lift on a nearby floor when a customer calls. However, having more lifts only helps if the lift cabins are distributed at different levels of the building. If all of the cabins are waiting on the ground floor, it doesn’t matter how many lifts there are, as the following simple example demonstrates.
Suppose it takes five seconds for a lift to get to a customer, and customers are spread evenly throughout all the floors of a nine-storey building.
If all of the lifts are on the ground floor, the nearest lift will take zero seconds to reach a customer on the ground floor and forty seconds if they are on the top floor – an average of twenty seconds. This is the same if there is one lift or a hundred lifts.
However, with just three lifts spread at Floors 1,4 and 7, the diagram below shows that the average time it takes for a lift to reach a customer can be cut from twenty seconds to just over three seconds – a sixfold improvement in waiting time for a threefold increase in lift numbers.
With nine lifts, of course, there can be a lift waiting on every floor reducing the wait time to zero.
Clearly, then, it is good for lifts to spread themselves through the building. There will be a tendency for this to happen naturally because of the random requests of customers, but lift designers prefer not to leave it to chance. To ensure that lifts don’t cluster together, they are usually programmed to have a zoning system. Typically, each lift is allocated a particular range of floors that are its home territory, or zone. When not in use, a lift will return to its zone in much the same way as a dog returns to its basket. There it will remain with ears pricked, waiting for a call.
This brute-force approach of putting in lots of lifts and zoning them has two drawbacks. One is that lifts are expensive. The other is that lift shafts take up space. You can probably imagine circumstances where a company wants to house a thousand people in a building and to give them a rapid service by providing plenty of lifts – and then discovers that this can only be achieved if all of the office floor space is occupied by lift shafts! The shortage of space forces the lift designer to think more cannily, with the aim of achieving the best quality of service with as few lifts as possible. One solution adopted in some very tall buildings is to use double-decker lifts. In a double-decker lift, you can board either on Level 0 or Level 1. The Level 0 lift serves all the evennumbered floors, while the Level 1 lift goes to the oddnumbered floors. Because the two lifts are attached to each other, you only need one lift shaft, though there will be some inefficiency because, when the lift stops at Floor 40, those in the ‘odd’ cabin above have to stop at Floor 41 even if nobody wants that floor.
How many floors per lift? Another rule of thumb
For an effective lift system in a typical office building, there should be about one lift for every four floors of building, though the ratio may be more like one per three floors in very tall or densely packed buildings. More lifts will be needed, too, if there are excessive peaks of traffic at certain times of day Usually these peaks are at the start and end of working shifts.
Make the lifts go faster
If you can’t have more lifts, another way of improving the service is to make the lifts go faster. This can mean literally increasing the speed at which the capsule travels. In some very tall buildings, lifts accelerate to a top speed of around 10 metres per second, or about 22 m.p.h. There is, however, an upper limit to how quickly they can reach this speed. Most customers don’t take too kindly to big g-forces or sensations of weightlessness. (If they’d wanted that, they would have signed up for the space shuttle.) The rate at which a lift accelerates is therefore normally limited to about one metre per second every second, which means it takes at least ten seconds to reach a top speed of ten metres per second. There’s a standard formula for working out distance travelled, which says:
So in the ten seconds it takes to accelerate to full speed, the lift will travel 1⁄2 x 1 x 102 = 50 metres.
Fifty metres represents about fifteen floors of the building. The lift will need another fifteen floors to slow down, which means that the building needs thirty floors just to enable the lift to reach top speed for a few moments. And that’s assuming that the lift gets a clear run. In a busy building, a lift is likely to make lots of short trips, which means it will rarely have a chance to accelerate to high speed. Added to this, the time saved in speeding up the lift will be small compared with the time spent opening and closing the doors to let passengers in and out. In other words, making the lifts go faster has little impact on the overall waiting time.
The lift designer, therefore, has to find more subtle ways of speeding up the passenger delivery. One such way is the use of the express lift. In much the same way as train services combine intercity expresses with local commuter trains, lift systems in tall buildings have a combination of ‘short-stop’ and iongdistance’ lifts. Express lifts can reduce the average journey times of customers quite significantly, and the faster that customers can be delivered to their destinations, the less time other customers will have to wait before they are served.
Again, a simple example using our nine-storey building helps to illustrate this. Suppose it is morning rush hour, so all the demand for lifts is at the ground floor, and lifts are then delivering people evenly among all of the other floors, before returning to the ground floor to collect their next batch. There are two lifts, and each of them calls at all floors. As in the first example, it takes five seconds to travel between floors, and added to this we’ll say that it takes ten seconds to unload passengers at a floor, making fifteen seconds per floor on the way up. The down journey takes five seconds per floor, or forty seconds total. The total round trip for the lift is therefore 160 seconds.
Now consider an alternative. Here, the first lift travels only to Floors 1, 2, 3 and 4. The second lift is now a fast service to Floor 5, and then calls at floors from 6 to 8.
The cycle time for the first lift is 4 x 15 + 20 = 80 seconds. The second lift takes 5 x 5 + 10 + 3 x 15 + 40 = 120 seconds. In other words, both lifts now have shorter cycles than before.
Most tall buildings take advantage of this saving, with some or all of the lifts travelling to only a limited range of floors. In buildings of over fifty floors, there are usually additional lift lobbies, known as ‘sky lobbies’, too. Some of the lifts serve purely as expresses between the lobbies, at which point passengers switch to ‘short-haul’ lifts that serve their destination.
Anticipating the flow of traffic
Unfortunately, it’s not enough just to provide extra-fast lifts. For the most efficient lift systems, the designers need to be able to predict the likely flow of people through the building so that the lifts can move to anticipate them. The pattern of human traffic will vary enormously depending on the function of the building and the time of day. In a standard hotel, for example, there will be a heavy flow of people between bedroom floors and the restaurant at breakfast time, and later there will be a steady flow from bedroom floors to reception.
The pattern within offices can be very different. Office blocks where different companies occupy different floors resemble hotels in that most journeys are to and from the ground floor. But, if a company occupies more than one floor, interfloor traffic is much heavier. The heaviest and most complex lift use is in buildings that are occupied by a single large employer – a hospital, for example, or a company headquarters – since the flow of people between floors could be just as heavy as the flow to and from the ground floor.
In the design of large buildings, it’s common for the architects to make use of complex mathematical models to simulate how the traffic will behave at critical times of the day. The models will invariably include bits of probability theory to help them estimate how long a lift will take to deliver its load of passengers.
For example, suppose you enter a lift in the lobby of a building with ten floors above the ground, and five other passengers join you. How many times is the lift going to stop? If you are unlucky, you are heading for the top floor and every passenger decides to press a different button from yours. This means a tedious journey of six stops. Of course you might might be extremely lucky, too. Everyone might choose the same floor as you, making this a rapid journey of just one stop. The average is somewhere in between, and as it happens there is a formula that enables you to calculate this.
If N people get into a lift at the lobby and the number of floors above them in the building is F, then the lift can be expected to stop:
What does this mean? If there are ten floors and six people in the lift, the formula says that you can expect the lift to stop:
In other words, for six people in a ten-floor building, there will typically be almost as many stops as there are people in the lift. But, as the number of people increases, the number of stops that you should expect on average doesn’t increase so quickly. If ten people get into the same lift, the figures work out at:
Four more people have got on, but the lift is only expected to stop one or two more times.
Incidentally, this formula of N people in a building of F floors is the same one that is used in a number of other analogous mathematical problems. For example, exactly the same formula predicts the number of different birthdays there will be in a group of N people. In this case F is always 365, the total number of birthdays available (ignoring leap years).
This ‘F and N’ formula is based on a number of assumptions, in particular that each floor or birthday is equally likely to be chosen. Since this is unlikely to be precisely true in the real world, the formula is only an approximation, albeit quite a reliable one.
Why lifts sometimes go the wrong way
Many lifts operate using a relatively simple logic, and In these lifts it is occasionally possible to board, request a floor and then discover yourself travelling in the wrong direction. This is particularly the case in a type of lift known as the ‘downcollective’, which is often to be found in small hotels. These lifts usually have a single button outside, and they assume by default that the person calling them wants to travel downwards (as is usually the case in a hotel). If you are on floor five, say, and you call a lift as it is on its way from floor eight to a caller in the lobby, it will stop and pick you up ‘en route’, before continuing downwards. If you happen to request a higher floor, it will hold your request until it has completed its downward journey This can lead to the sort of farcical moment loved by comedians, where the scantily clad Romeo hoping to pay a visit to a lover upstairs boards an empty lift and finds himself embarrassingly carried down to the reception to be met by the contingent from the pensioners’ Christmas party. Short of pressing the emergency stop button there is nothing he can do about it.
Lift logic
The logic used to drive lifts has become increasingly sophis -ticated, not only to reduce the waiting time but also to prevent some of that peculiar lift behaviour where the machine seems to have a mind of its own.
This behaviour can include, for example, lifts that appear to go in the opposite direction to the one that the customer requested (see the box above). Just as frustrating is the lift that seems to ignore the customer and just goes sailing by. In the early types of lift, this problem was caused because the lift was not capable of dealing with more than one instruction at a time. Until it had delivered its load, it ignored any other calls.
In more modern lifts, the most likely reason why a lift seems to ignore a caller is that the customer has asked to go down, and the passing lift is currently on an up journey. It could, however, be the case that the lift is full. Most modern lifts have weight sensors, and a fully loaded lift will not stop to pick up any more passengers, just as a full bus will zoom past a crowded bus stop. The main difference between lifts and buses, of course, is that passengers can at least see that the bus is full. Lifts don’t usually have an indicator to convey this information.
However, even the highly sophisticated logic of the most upto-date lifts can cause different types of behaviour that might appear illogical to the observer.
For example, imagine you are three floors down in the basement of a building with two lifts. The indicator tells you that there are lifts sitting on higher floors, one on the ground floor and one on the third floor. You call the lift, and notice that the one that comes to collect you is the one from the third floor – despite being twice as far away. Why didn’t the ground-floor lift come to you? The answer is that ‘intelligent’ lifts are often programmed to have a slight bias towards sticking to the ground floor, where most of the passengers get on. The intelligent lift may calculate that it’s worth sending a more remote lift to collect you if it means that it can keep a lift waiting at the ground floor, where a flurry of passengers could arrive at any moment. You are being sacrificed (modestly) for the greater good.
Here is another possible sacrifice. An intelligent lift is seeking to keep down both the average and the maximum waiting time. A customer on Floor 6 calls a lift, but is dismayed when it bypasses them to collect somebody at Floor 9. The reason might be that the modern intelligent lift is aware that the Floor 9 person has already been waiting for a minute and is therefore top priority. With this urgent case on Floor 9, the lift reckons that you on Floor 6 can wait a few more seconds.
In other words, even the most complex logical system will at times fail to live up to the sometimes irrational and impulsive urges of us humans, and the faster the lift service becomes, the more we seem to demand from it. If it hasn’t surfaced already, it won’t be long before a ‘lift rage’ story hits the headlines.