Blocking probability
Topic of Birth–death chains and queues, part of Stochastic processes
Blocking probability
| Type | Topic |
| Taught in | Birth–death chains and queues |
| Part | Stochastic processes |
In a queue with room for at most K customers, the long-run fraction of arrivals turned away, which under Poisson arrivals is the stationary probability \pi_K that the system is full. It rises with the load \rho, and it is the price a finite queue pays for having a stationary law at every load.
In Birth–death chains and queues
At \rho=1 the weights are constant and \pi_n=1/(K+1). Blocking probability \pi_K increases with \rho. The stationary law exists on both sides of \rho=1 because the room is finite.
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