11 Why do we have queues?

Just about everyone has experience of being in some sort of queue. If you phone your bank, telecoms provider or similar service you will almost certainly be phoning a call centre where you can often expect to wait before someone picks up the phone. Similarly if you visit a supermarket you can expect to wait before you pay. In a barbers shop you wait your turn. If you go to a theme park many of the rides can have queues that are an hour long on busy days.

So why is it that all of these different types of service make you wait? Are they all just incompetent at managing capacity? Is it they are greedy and won’t pay enough staff on duty to meet demand?

Download the following excel file and open it so you can see the content (open the file in a new tab or window by holding down Ctrl [or Cmd on a Mac] when you click on the link).

Basic capacity model [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)]

Now watch the following screencast that shows you how to use the spreadsheet in the following exercise.

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Transcript: Screencast 2: Instructions

[MUSIC PLAYING]

 

PAUL WALLEY

In this screencast, I'm going to provide some instructions on how to use the capacity and demand simulation spreadsheet that we have provided for you. This is a screenshot of what you'll see when you open up the file. The spreadsheet allows you to change five different variables within the spreadsheet so that you can experiment to understand queue behavior.

The first change you can make is to adjust the amount of demand that comes in by setting the minimum and maximum demand levels. The two cells you can change are both highlighted in yellow. You can also adjust the capacity again, minimum and maximum values in those yellow boxes. The final variable you can change is the size of the queue at the start of the simulation. The cells that are colored in pale blue are outcomes of the simulation.

OK, so I've opened the spreadsheet and you can see here that I've got the five cells colored in yellow while I can now change the numbers. If I want to adjust the demand, I can change these in cells B3 and C3. So if I want to increase demand by 10, I just add another 10 to the figure in those cells. And you can see the behavior of the queue has adjusted the demand and capacity ratio in cell L4.

I now know that I've got zero unused capacity, but I can make adjustments to the capacity. I can increase this in both cells to 50. You may have seen that it came up with an error at one point, where I had got the minimum greater than the maximum. The spreadsheet will warn you about things like that. All of the other data has readjusted as we have made that change, including both charts.

You can also change the size of the queue at the start as long as it's a positive number. So if I wanted to have a simulation where I had 200 people in a queue at the start and then wanted to see how long it would take to drain down the queue with revised capacity levels, I could put that into the simulation. So the course sets you an exercise, and that is all you need to be able to complete the work.

Once you've opened up the spreadsheet, we ask you to do three separate exercises. The first is to set the capacity much below average demand so that you can see what happens to the size of the queue and make a note of this, perhaps even taking a screen copy of the graphs. Once you've done that, set the capacity equal to the average demand but with a little bit of either demand or capacity variation or both, and see if the behavior changes. Once again, make a note of that.

The final exercise is to incrementally increase capacity until you think you have enough capacity to prevent any problems with queuing. However, you can use the exercise to understand the trade offs between queue length and wasted capacity. Once you've completed the exercise, you should have a much better understanding of the relationship between capacity, demand, and queuing.

[MUSIC PLAYING]

 

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Screencast 2: Instructions

Using the average demand of 40 (ranging between 20 and 60) as has been set in the spreadsheet, compete the following tasks:

Task 1 Set your capacity much below average capacity. What happens to the size of the queue? Make a note of this. Repeat this a few times to see if the answer is always the same.

Task 2 Set your capacity at the average demand. Has the queue behaviour changed? Again make a note. Again, repeat this a few times to see if the answer is always the same.

Task 3 Now incrementally increase capacity until you think you have enough. How much capacity makes your queue disappear to almost zero?

Does the existence of a queue provide a clear indication there is not enough capacity to meet demand?

Once you have completed all the tasks watch the following screencast that provides feedback about the findings that you should have got from the exercise. Check that you did get the same kinds of results.

Download this video clip.Video player: Screencast 3: Feedback

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Transcript: Screencast 3: Feedback

[MUSIC PLAYING]

 

PAUL WALLEY

I just want to show you the results that you should have got when you did your simulation exercise using the spreadsheet that we have provided. In the first part of the simulation, we suggested to you that you should set demand greater than capacity or reduce the capacity so that there was insufficient capacity to meet the demand over time. What you see from the spreadsheet is that the number of people in the queue steadily increases over time. This is just the kind of classic situation where a work backlog is continually building.

In practice, it isn't common to see queues build up steadily in this way. For physical queues such as at a supermarket or bank, the queue often self-limits as customers renege, leave the queue, or balk. They don't join a long queue instead of waiting for a long time. This simulation doesn't replicate that behavior. In a situation where demand and capacity are about the same but you have some variation in either demand or capacity or both, you tend to find is that the queue fluctuates over time.

In this example, I had set the demand and capacity as approximately equal but with variation. We see that a fairly substantial queue builds up quite quickly and towards the end of the simulation, the queue seems to continually grow, which is obviously a concern. Despite this, just note that 2% of the time, we had unused capacity when the queue had fallen to zero. So we're in a situation where queues are long, services poor, but we still waste some capacity. This is not a great place to be.

In the final situation, we set capacity quite considerably in excess of demand. In this case, we can see that the number of people in the queue was actually relatively small on average. In fact, on average, it was less than one person at a time, but the queue did peak at nine people. Here, we are in a very different situation, where we had 38% more capacity than demand and that created a lot of wasted capacity over time.

So here's the trade off. You can have some excess capacity to make sure that the queue is moderately small, but it means that you do waste some of your resource. This can be very difficult to reconcile when senior managers are looking at staff productivity and staff costs, but you need to maintain the availability of the service.

[MUSIC PLAYING]

 

End transcript: Screencast 3: Feedback

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Screencast 3: Feedback

The exercise shows that queues can form even when capacity is greater than demand. The following screencast explains the theory underpinning this idea.

Download this video clip.Video player: Screencast 4: What causes a queue?

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Transcript: Screencast 4: What causes a queue?

[MUSIC PLAYING]

 

PAUL WALLEY

In this screencast, I would like to address what causes a queue in services. There is a good body of knowledge about how and why queues form. You have the opportunity to simulate this with a spreadsheet exercise, and now we look at the theory behind queues.

In pretty much all services, you'll find that as you experience the service, you will be involved in queuing. Most of us will have waited a long time to check baggage in at an airport, been hanging on the telephone waiting in the queue to speak to a call handler, or in a line at the post office.

So the question is, can queues be avoided, or are there some underlying reasons why queues form naturally? Just imagine a situation where you are checking in to go and visit somebody in an office, maybe at a reception. On average, it might take three minutes to sign in to that reception and receive your visitor's pass.

In this situation, on average, one visitor arrives every three minutes. So here we have a situation where capacity and demand are supposedly matched. So will there be a queue at reception? In the narrative, I used a very dangerous word, average.

In the situation I described, demand will fluctuate over time caused by natural, random variation. And sometimes the capacity can vary, because some people will take longer to check in than others. So we have both demand and capacity variation.

In these kinds of situations, if demand and capacity don't perfectly match, even at very low levels of utilization, a queue may form some of the time. While we have plenty of capacity and relatively little demand, we won't get much of a queue, but queues can exist.

The problem occurs when resource utilization levels get above, say, 60% or 70% in these circumstances. At this point, our expected to queue length really does increase. And mathematically, if you have 100% utilization, with demand and capacity variation, you are likely to get an infinite queue unless there is some other controlling mechanism. This is a really strange mathematical phenomenon.

The underlying mechanism for queue development are the short-term mismatches in capacity and demand. In the diagram, demand is going to fluctuate randomly, and so might capacity. Where both demand and capacity are fluctuating over time, it is highly likely that most of the time capacity and demand will not be the same.

So sometimes demand is in excess of capacity, and that is where queues build up. At other times, where capacity is in excess of demand, and any queues we have will start to reduce So it is these mismatches that create these queues, and the queue length will not be stable. You would have seen that if you did the simulation exercise.

Our design of the queue actually influences queue length and waiting time. Think about these two different queue designs. Queue type A is a typical situation that you'd get at an airport baggage check in, for example, where the queue is entirely combined into one, and people go to the next available server.

Queue type B is where you have to pick a server and join a queue. And you can't move from that queue no matter how long it takes. So the demand is split into two or more separate queues. What we find in practice is that queue type B creates a longer wait. This is for a number of reasons. One of the main reasons is that by splitting the demand into more than one pool, we actually get more variation in demand.

This is where we get some surprising results. So if we split demand into priorities, so urgent, not so urgent, lesser, and so on, we artificially increase the demand variation and create even more waits. So prioritization can actually cause delays.

There are other mechanisms in queue type B. Some servers might be less busy running out of work, therefore wasting some spare capacity. In a lot of situations, pooling the demand into one creates shorter waits. So there are some key points here.

Queues form in two different types of situation. We will get a work backlog where demand exceeds capacity, but in practice most of the queues that we see where the capacity exceeds demand, but we have variation. Take time to understand these two different types of queue, and have a think about waits and delays might be minimized, through either controlling the variation in demand or capacity, and also perhaps planning capacity better.

End transcript: Screencast 4: What causes a queue?

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Screencast 4: What causes a queue?

Waits and delays example: Ambulance service responsiveness

Ambulance services are a good example of where demand must be understood so that planning can take place to ensure enough ambulances are available to meet all emergency demand. In the UK ambulance services are tasked with responding to life-threatening, urgent demand (“Category 1”) with an average response time of seven minutes and 90% within 15 minutes or less. The services have to plan the right number of ambulances and crew each day, anticipating any seasonal fluctuations in demand and taking into account random variation in demand that makes some days unexpectedly busy. As we can see from the previous section, there would need to be some spare capacity in the system if queues are not to develop.

When calls come in they are triaged so that urgent cases are put ahead of those less serious. When ambulances attend calls they will try to deal with the patient without a time-consuming journey to hospital either by treating and discharging those less seriously hurt in situ or by seeking alternative forms of transport to hospital for “walking wounded”. Some services even organise taxis for patients where an ambulance is not strictly necessary.

At busy times for emergency care one of the biggest problems is that ambulances often have to queue to drop patients off at A&E. This means the ambulances become unavailable for new patients and response times increase.

Figure 11 Ambulance queue outside an emergency department

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The figure is a photograph of ambulances queueing outside an accident and emergency department. It illustrates the waits and delays experienced by both paramedics and patients when trying to enter an emergency department that has a work backlog and arrivals queue.

Figure 11 Ambulance queue outside an emergency department

We can see from queue theory that a small reduction in demand might make a big difference to waits and delays. The next section looks at an approach that tries to reduce demand entering a service by eliminating unnecessary demand.