An Optimised System for Queuing at the Post Office (Feat. Wolves)

Introduction

Time runs at a different speed in the Post Office… almost every time I go in, I get stuck behind someone who is posting about 8 parcels at once, all to different locations, whilst telling a lengthy anecdote about the recipient of each package.

Meanwhile, I have one quick parcel to send and will be finished in a minute or two. Surely it would be better if I could hop in front, quickly post my parcel and then be on my way, right?

Well really, this is an optimisation problem – the likes of which are encountered everywhere from the Google search algorithm, to the supply chains of supermarkets.

In this post I will be exploring the following:

  • Is there a better way to serve customers at the Post Office?
  • If so, why don’t we use it?

And most importantly….

  • Why would Wolves queue differently at the Post Office?

A Simple Scenario

Let’s imagine three people walking into the Post Office who need to post parcels. Dave has six parcels to post, Lisa has 2 parcels to post, and Steve only has 1 parcel to post – as demonstrated in this drawing which took significantly longer to make than it should have…

Let’s assume every parcel takes 2 minutes for the Post Office employee to process, what is the optimal way to serve these customers? Let’s look at some options.

The Traditional Queue

The most obvious way to serve these customers is in the order they come into the Post Office – this is the traditional queue. Let’s look at how this plays out.

The total time spent by all customers in the post office is 46 minutes, which makes for an average of 15 minutes.

Fastest First

In this system, the person who it is quickest to serve is served first and the slowest person is served last. Therefore, Steve is served first as he only has the one parcel, next is Lisa with two parcels, and Dave is left to last because he’s going to take ages. You had this coming, Dave.

The total time spent by all customers in the post office is 26 minutes, which makes for an average of 9 minutes.

Comparison So Far

From what we’ve seen so far, the fastest first method achieves an average time in the post office of 9 minutes, whilst the traditional queue results in an average time of 15 minutes.

Whilst the maximum amount of time spent by any one customer is the same for both the fastest first queue and the traditional queue, in the fastest first queue, it is the person who takes the longest at the desk who has to wait the longest. This seems fairer than the traditional queue where, in this case, it is the person who takes the shortest amount of time at the desk who has to wait the longest. However, this may not always be the case, depending on the order in which the customers arrive.

So Why Do We Use a Traditional Queue?

Traditional queues are clearly slower, and are not optimal for saving time. However, they are optimal in a difference sense – information.

It took me a while to get my head around this, but if you think about it, queuing is made up of three processes:

  1. Gathering relevant information to allow sorting of customers
  2. Sorting the customers into a queue, based on the gathered information
  3. Serving those customers

Now if you’re ordering based on the fastest first method, in step 1 you have to find out how long it will take to serve each customer. Then, in step 2 you will order them in a queue from fastest to slowest, and then in step 3 you’ll serve them.

In order to do this, the post office worker would have to come out and speak with each customer, then rearrange the queue to reflect how long they will take to serve. He would then go back behind the desk and start processing the parcels for these customers. This takes a significant amount of organisation and data gathering. It would be even more chaotic if the customers had to order themselves!

So really, the traditional queue is optimal in terms of information….

To order yourself in a traditional queue, the only thing you need to know is how long the other people have been stood there, which you can determine just by looking at the queue – people literally line up in the exact order they arrive, giving you all the information you need with one glance. You don’t have to speak with anyone, order yourself amongst them or assess how long you will take compared to everyone else in the queue.

Following our three step guide above, the traditional queue basically eliminates steps 1 and 2 as you don’t need to gather information (except that which you can see already) and you don’t need to compare. You literally just join the queue – it’s really quite magical.

Not to mention that in British post offices no one ever wants to interact with anyone else, so waiting almost twice as long in the post office (on average) is totally worth it, if it means you don’t have to talk to anyone.

So essentially, our queuing system is optimised to minimise social interaction.  I’m not sure if that’s liberating or a bit depressing…

But What About The Wolves?

Wolves are very interesting (algorithmically speaking) because they already have a hierarchy established within their pack. Therefore, when they successfully hunt down some food and form a queue to eat the food, they already know which wolf should eat first, second, third etc.

This essentially means that step 1 and 2 of the above 3-point plan are pre-established before the queuing begins, so they do not need to go through those steps. Instead, they can form an optimal queue straight away, without additional data gathering and without sorting – go wolves!

Instead of optimising for time, the way wolves queue optimises for value – the most important wolves (the alpha male and female) get to pick the food first, when there is lots of meat on it. As they are the breeding pair, it is most important that they eat well above all other wolves, and their queueing method ensures this.

Furthermore, as it is the alpha male and female who rule the pack, this value-first queuing method means that they always eat the best and therefore are the strongest. This means that the alpha male and female have intentionally selected and imposed a queuing algorithm upon the rest of the pack which keeps them the strongest.

Conclusions

From this I can only conclude that:

  • Humans are anti sociable, and have optimised for minimum interaction with other humans.
  • Alpha wolves intelligently select queuing algorithms which promote their self interests.

… so next time you’re stuck in a queue, you can take comfort in the fact that, yes, it may take longer than it needs to, but at least you don’t have to talk to anyone!

Happy queuing,

Robin

 

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