An Introduction to Queues

“What’s a ‘cue-you,’ Curmudge?”

“It’s not a ‘cue-you,’ Jaded Julie; it’s pronounced just like the letter ‘Q.’ It comes from the French word for tail, and it means a line of people waiting their turn. So when you walk into McDonald’s, you are at the tail end of the tail.”

“Well that’s something everyone should know. If you can justify this enlightening discussion, now would be an excellent time to do it.”

“Of course, Julie. Today we are going to talk about customer flow management, a part of which is queuing theory; and before you ask me ‘why?’ I’m going to tell you why. An important aspect of the Toyota production system is one-piece flow. They build cars in an essentially continuous process with minimal inventory, work in process, and waste. Wouldn’t our patients be delighted if we could treat them in a similar, efficient process?”

“They definitely would like to be treated efficiently but probably not like a partially-built car. While patients are sitting in a waiting room, it probably wouldn’t make them any happier to think of themselves as ‘work in process.’”

“You’re right as usual, Julie. We certainly must treat our patients with respect, dignity, and compassion. But for today’s discussion, let’s think of patients as people who just want to arrive, receive a service, and depart ASAP.”

“Okay, Curmudge. I’m with you, at least for the moment. But if any of our discussion is going to involve queuing theory, I really need to know what that is.”

“Queuing theory uses mathematical models in analyzing how to match demand (usually variable) with capacity (usually fixed). Unfortunately, there’s a major limitation to elementary queuing theory: it can only be applied when customers arrive in a random manner. It doesn’t apply when service is provided on an appointment basis, which excludes most of the hospital. The ED and walk-in clinics would be examples of where patients arrive randomly.”

“If the use of queuing theory is so limited, why should we even study it?”

“Traditionally, when a patient walks into a clinic or hospital they expect they will have to spend time waiting. If queuing theory might help shorten waiting times, it’s certainly a subject with which we should have an acquaintance.”

“I guess it’s okay to get acquainted, but I don’t want to get too close to any mathematical models. Can you give me a non-mathematical introduction?”

“I’d be delighted, Julie. Linear queuing means that the customer waits physically in a line. (1) The simplest version is Single-Queue-Single-Service-Point, like waiting in line to buy your ticket for a popular movie. Several of these side-by-side make a Multiple-Queue-Multiple-Service-Point system like in a grocery store. This can be made more efficient by adding Segmentation, where certain lines handle only customers with 15 items or less. The most advanced form of linear queuing is Single-Queue-Multiple-Service-Points. A common example is the Post Office, where the line is not held up when one of the clerks is delayed by a customer sending a package to Timbuktu.”

“I must admit that I haven’t given much thought to the type of queue that I’m in. I do know that in the grocery store Erma Bombeck’s Law applies, ‘The other line always moves faster.’” (2)

“There are several variations on these simple systems. One is virtual queuing, where, after registering, a customer is sent to a waiting room rather than a physical line. Because the customer does not know his/her exact position in the queue, the staff is able to exercise some segmentation. An example would be an ED in which more urgent patients are seen first. A variation of this, virtual queuing with buffering, is also used in an ED; the next patient to be seen is taken to an exam room (the buffer) to minimize the service provider’s delay.”

“I know there are more, Curmudge. There always are.”

“Another fairly simple one is the multiple stage system in which the customer is served by more than one facility before leaving. This is termed ‘serial servers.’ I’ve seen this in European fast food restaurants where one decides what he wants, lines up to pay for it, and then lines up again to receive the food in exchange for the receipt. A similar system exists in a hospital where an outpatient must go to the lab and then to radiology.”

“Is there no end to this, Curmudge?”

“There is for us today, Julie, and it’s right now. Let’s go down to the cafeteria and stand in a queue.”

Affinity’s Kaizen Curmudgeon

(1)http://www.q-matic.com White Paper: An Introduction to Customer Flow Management

(2)Maister, David H. Note on the Management of Queues, Harvard Business Review (March 17, 1995): 1-14, Reprint #9-680-053.