Throughput
Topic of Birth–death chains and queues, part of Stochastic processes
Throughput
| Type | Topic |
| Taught in | Birth–death chains and queues |
| Part | Stochastic processes |
The long-run rate at which customers are accepted, and in equilibrium also served. For a queue that refuses arrivals when full it is \lambda(1-\pi_K), below the offered rate \lambda. Little’s law must use this rate, not the offered one.
In Birth–death chains and queues
An M/M/c/K system stops at state K. An arrival that finds K customers present is blocked and does not enter. The state space is finite and irreducible for \lambda>0 and \mu>0, so a stationary distribution exists for every positive load, including \lambda\ge c\mu. The chain cannot drift to infinity because the state cannot pass K. The cost is lost arrivals. Throughput, the long-run rate of accepted arrivals, is \lambda(1-\pi_K), not the offered rate \lambda.
Used in
See also
Little’s law · Birth–death balance · M/M/1 queue · M/M/∞ queue · Multi-server and finite-capacity queues · Machine-repair model · Three capacity rules · Blocking, throughput, and Little’s law