Little's law comes up in the beautiful book 'Programming Pearls' by Jon Bentley in 'Back of the Envelope' calculations: - `Little’s Law`: The average number of

Little's law comes up in the beautiful book 'Programming Pearls' by Jon Bentley in 'Back of the Envelope' calculations: - `Little’s Law`: The average number of objects in a queue is the product of the entry rate and the average holding time - Response-time formula for a multi-user system: - Assume n users of average think time z are connected to an arbitrary system with response time r. - Each user cycles between thinking and waiting-for-response, so the total number of jobs in the meta-system (consisting of users and the computer system) is fixed at n. - If you cut the path from the system's output to the users, you see a meta-system with average load n, average response time z + r, and throughput x (measured in jobs per time unit). - Little’s Law says n = x × (z + r), and solving for r gives r = n/x – z.