How to Make Things Faster

Chapter 44. Traffic Intensity

The queueing theory plots I’ve shown illustrate the hyperbolic relationship between traffic intensity (ρ) and response time (R). Traffic intensity is a measure of how busy a resource is. Mathematically, traffic intensity is ρ = λS/c—a function of three parameters: λ, S, and c.¹

Arrival rate (λ)

Traffic intensity varies directly with arrival rate, which is the pace at which requesters make service requests.

Service time (S)

Traffic intensity varies directly with service time, which is the average response time of a request on an unloaded system. 

Service channel count (c)

Traffic intensity varies inversely with service channel count, which is the number of requests that can be processed in parallel. The service channel count is the c in the “M/M/c” plots I’ve been showing you.

You can manipulate traffic intensity by manipulating any of these three parameters. You reduce traffic intensity either by reducing event counts and event durations or by increasing the number of service channels.

¹ Most textbooks define traffic intensity as ρ = λ/(cμ), where μ = 1/S, but since S = 1/μ, the formula I used here is equivalent, and it affords you and me both the luxury of not having to introduce another symbol μ (the service rate) for you to have to think about.