EVENT INDUSTRY

Waiting sucks. I can t think of a single human being that enjoys a good long wait. Waiting is the womb of all bad things: irritability, customer complaints, bad PR, sometimes even riots. Happily, the world is full of good-guy scientists using teh mathz to make sure your attendees are queuing for the shortest possible times. There s a whole field of study about it, and it s called Queueing Theory . The tools are there. Just reach out and take them.

Queuing theory applications

The applications for queuing theory are numerous, and extend well beyond the ticket-purchasing sphere. To quote from queuing theory researcher Myron Hlynka, Queueing theory is useful in telecommunications, traffic control, determining the sequence of computer operations, predicting computer performance, health services (eg. control of hospital bed assignments), airport traffic, airline ticket sales, the mining industry, layout of manufacturing systems. It is even useful in determining when to remove a goalie in a hockey game.

But in terms of straight-up ticket windows or event registration lines, the goal of well-applied queueing theory is to determine how you can acheive the shortest possible wait time for attendees at the lowest possible resource cost to you or your event. In other words: How many ticket windows need to be open at the same time to keep wait times to an acceptable minimum?

It s a Numbers Thing

Look, queuing theory is, at its root, a mathematician s field of study. It s all about algorithms defining how many customers are arriving, how quickly they re arriving, how long it takes them to get served and leave. It factors in how regularly people are arriving, delays at each step of the process, and what kind of delays those are. Nobody over here at Decibel is a mathematician, and we imagine most event producers aren t either, and we can t teach you how to do algebra here, but we can tell you the right words to use when describing issues with lines, and different ways to think about your line setups.

But if you re a numbers persona and you re looking to take a deep dive into the calculus that drives these computations, you ll want this: Basic Queuing Theory, by Dr. Janos Sztrik.

The Basic Equation: Little s Law

I may have lied a little: we are going to talk about math, but just for a short and painless second. Queuing theory is based on an equation called Little s Law, which helps us sort out the average number of customers waiting in any line. In smart-numbers-people speak, that looks like this:

N = T

N = The number of people waiting.
(Lambda) = The average rate at which people arrive
T = The average service time

In other words, there will be more people waiting in the line if people are arriving quickly and the service time is slow. There will be less people waiting if people are arriving slowly and service time is fast. Duh, right?

When T is less than , the queue is working.

Factors in line speed: Service Systems

Let s say that you ve got four ticket windows open. How are the lines organized? Is there one long line, and when someone reaches the front of it, they are directed to the first open window, who provides them total service? If so, this is called Parallel Queues :

Or does each ticket window have its own distinct line? If so, that s called Single Queues :

Or, do customers get serviced at several different windows, each window handling one part of the process, assembly-line style? For example, you pay at window 1, take a picture at window 2, and receive your registration badge at window 3? This is called Service Facilities in Series :

Service Disciplines

But how, exactly, do people get served once they do reach the front of the line? The order in which people are served can influence the speed at which the line moves. Here are some of the most commonly discussed service disciplines that apply to events:

• First-Come-First-Served (FCFS): This system, under which customers are served in the order of their arrival, is probably the easiest to understand. A checkout line at the grocery store, for example.
• Last-Come-First-Served (LCFS): You can think of this system like an elevator; the last people to get in are the first people to get out.
• Shortest Processing Time first (SPT): You might think of this as the 10 Items or Less line in a supermarket whichever customer is perceived to have the easiest task to process would go to the front of the queue
• Loudest-Voice-First-Served (LVFS): Get rid of the guy making the most trouble first.
• Service in Random Order (SIRO): Someone gets chosen out of the crowd at random. (Sounds like mayhem to us)
• And more besides

Kendall s Notation

So how do we talk about all this? Math guys use a form of shorthand called Kendall s Notation to talk about what kind of line they re dealing with. The notation format five, like this: A/B/C/D/E.

• Position A: represents how people are arriving. Is their arrival in the line random (random numbers of people come at random times, sometimes one person, sometimes groups)? Or is it controlled or timed (one person always arrives every two minutes)? If so, we write D in this spot. Is it totally undefined? Write G.
• Position B: represents service time distribution. In other words, how long does it take to serve a customer once they reach the front of the line? Is this undetermined (could take five minutes, ten minutes, or an hour)? If so, we write M in this spot. Is it fixed (it always takes exactly 3 minutes to process someone through the line)? If so, we write D in this spot. Is it totally undefined? Write G.
• Position C: Number of service windows that are open at one time.
• Position D: How many waiting spots are available. If there s only room in the line 120 people (including people being served at the window), then this number is 120.
• Position E: Which service discipline is being followed (First Come First Serve, maybe?)

The guys over at Stack Exchange help us out with a few examples:

M/G/1

DASD performance is modeled most accurately as an M/G/1 queue. M means that customers, or requests for disk access, behave according to a Poisson process. This is referred to as a stochastic, or Markov process, thus the use of M . The rate at which the disk drive is able to meet these requests for service is unknown. Since job service times can have an arbitrary distribution, this is designated by G for general . Finally, if there is only one disk-drive, c = 1.

M/M/c

Let s consider another example, where customers arrive randomly, with exponentially distributed service times. There are multiple servers. This would be described as an M/M/c queue.

This is the typical situation at Walmart, during the night shift (with few cashiers on duty), or at a bank with tellers, or when making a phone call for customer support. Customers arrive randomly (M). The time required to check out their groceries or answer their question is also random (M) e.g. when grocery queues don t have a 10 items or less configuration for some checkers. Meanwhile, there are a fixed number of cashiers or telephone support staff on duty, we ll say five. This would be an M/M/5 queue.

Interesting, huh

So what does that mean for you? It means there *are* ways to keep wait times down, and to predict how event registrations are best arranged. It means that it s not a bad idea to hire an expert to look into your lines and double-check that your arrival, registration and intake processes are optimized if you re dealing with large-scale events.