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Mathematics · Operations Research

Queueing Theory for Software Delivery

Reference entry · last updated 20260908

Queueing theory is the mathematical study of work arriving for service, waiting when service is unavailable, and departing after completion. Software review queues are one application.[1]

First principles and definitions

An arrival rate counts work entering a system per unit time. Service capacity measures how much work its servers can complete per unit time. The system boundary determines whether a waiting room, a service stage, or both are counted.

For a stable single-server model, utilization is the arrival rate divided by the service rate. Random arrivals and service times can produce queues even when average utilization is below one.[1]

Little’s law

For a stable system with consistent boundaries and finite long-run averages, Little’s law relates average work in the system, throughput, and time in the system:[1]

L = λ × W, where L is average work in progress, λ is average throughput, and W is average time from entry to departure.

Illustrative example: a review process completing 10 PRs per day with an average of 20 PRs waiting or under review has an average residence time of two days.

Application and limits

A review system can limit incoming work, reduce service time, or increase available capacity. These are model-derived options. Actual review includes interruptions, rework, priorities, and reviewers with different expertise.

Little’s law is an accounting relationship, not proof that changing one quantity alone causes another to change. Sustained overload violates the stable finite-backlog assumption.

See also

• Acceleration Whiplash
• Throughput
• Latency
• Theory of Constraints
• Code Review

References

1. MIT OpenCourseWare, 2.854, Fall 2016. Markov Processes and Queues.