The Entrepreneur and The Queueing Theorist - Episode 2

The Analysis

When we left our protagonists at the end of Episode 1, the Advisor had explained to the Entrepreneur the importance of a causal model that would help connect output metrics such as throughput, cycle time, and customer lead time to controllable inputs such as arrival rate, service rate, and utilization and explain how changes in the inputs cause changes in the outputs.

In particular, the Entrepreneur was surprised by the tradeoff between throughput or productivity and customer lead time and the role of randomness introduced by queueing in creating this tradeoff.

We pick up the story here. Read Part I of The Entrepreneur and The Queueing Theorist if you are just joining.

Understanding Queueing

“It’s straightforward to understand queueing if you think of it as orders backing up in front of your services as customers place their orders simultaneously. Your developers can only work on a small number of orders simultaneously, and if new orders come in when they are busy with other orders, the new order will have to queue up and wait.” said the Advisor.

“Very often, there is no queueing if orders are spaced well enough apart in time. At other times, queues build up for a little while and get drawn down as your developers catch up.”

“This is precisely the same thing that happens when you are in line at the supermarket or the security line at the airport. Depending on how long the queueing lasts, the time it takes a customer to fulfill their order will vary quite a bit, even if the actual development cycle time needed for each order is very stable.”

“In particular, if orders consistently arrive at a rate that your process cannot service, we have a situation where queueing happens continuously. When this happens, there is no limit to how long customers might have to wait for their orders. We never want to be in this situation.”

“Queueing introduces randomness into even deterministic processes; thus, we need probabilistic tools to reason about this behavior. Luckily, queueing theorists have been studying this problem for over a century, and we have powerful mathematical tools called queueing models that will allow us to analyze queueing in stochastic processes and reason about its causes.”

The Queueing Model

“We’ll construct a probabilistic model of how your customers interact with your service, which will clearly explain how queueing is causing you to lose money on the one-day guarantee.” the Advisor says.

“This model, like all queueing models, consists of

1. The Arrival Distribution A: A probability distribution that describes how requests arrive at the service over time - the shape of the demand for the service.
2. The Service Distribution S: A probability distribution that describes how long it takes your service to fulfill requests and
3. The Service Concurrency c: The maximum number of requests the service can process simultaneously.

Note that all three components relate to time: how often requests arrive, how long they take to process, and how many the service can process simultaneously.

Queueing models explain how delays?emerge in a system, and these three components are the basic building blocks you need to reason about this.”

“Let’s look at what these components look like for your system,” she says.

Read the rest of the article at The Polaris Flow Dispatch.

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