Founded by Agner Krarup Erlang (The Theory of Probabilities and Telephone Conversations, 1909), with David G. Kendall's notation (1953), Leonard Kleinrock's Queueing Systems (1975), and the textbook of Frederick S. Hillier and Gerald J. Lieberman (Introduction to Operations Research, 1967).
Models waiting lines from arrival rates, service rates, and server counts to predict waits, queue lengths, and utilization, showing how waits explode as utilization nears full.
When to reach for it
When planning capacity for a call center, clinic, production line, or help desk where demand arrives unevenly.
How it runs
- Estimate the arrival rate and the service rate.
- Choose the model that fits the number of servers.
- Compute utilization: arrivals divided by total service capacity.
- Apply the model's formulas for wait time and queue length.
- Set staffing for a utilization with acceptable waits.
Where it sits in SOLVE eX
Go to the source
- The Theory of Probabilities and Telephone Conversations, 1909
- Stochastic Processes Occurring in the Theory of Queues and their Analysis by the Method of the Imbedded Markov Chain, Annals of Mathematical Statistics 24(3), 1953
- Queueing Systems, Volume 1, 1975
- Introduction to Operations Research, queueing chapters, 1967