Jackson's theorem (queueing theory)
From Wikipedia, the free encyclopedia
Jackson's theorem is the first significant development in the theory of networks of queues. It assumes an open queueing network of single-server queues with the following characteristics:
- M = # of queues in the system, not counting queue 0 which represents the outside world
- μi = service rate at queue i
- λi = total rate at which jobs arrive at queue i
utilization of the service at queue 
- ni(t) =# of jobs in queue i at time t
= the system state at time t
- Arrivals from the outside world are Poisson. All queues have exponential service time distributions.
[edit] Product form of Jackson's network
![P(k_1,k_2,\dots,k_M)=\prod_{i=1}^{M}
\left[\left(\frac{\lambda_i}{\mu_i}\right)^{k_i}\left(1-\frac{\lambda_i}{\mu_i}\right)\right]
= \prod_{i=1}^{M}[(1-\rho_i)\rho_i^{k_i}]](../../../../math/4/5/4/454ecd45f0b40ed22348573eb770ff26.png)
(where 
)
[edit] See also
[edit] External links
- Sinclair, B. (2005, June 9). Jackson's Theorem. Connexions
