Jackson network

The concept of Jackson networks, named after James R. Jackson, is the first significant development in the theory of networks of queues, in which each node of the queueing network can be analyzed separately.

Definition

A network of "m" interconnected queues is known as a Jackson network if it meets the following conditions:

# Customers arriving from outside the system arrive as a Poisson process.
# The servers each act as a Poisson process (exponentially distributed service times).
# A customer leaving queue "i" will either move to some new queue "j" with probability $P\_\{ij\}$ or leave the system with probability $1-sum\_\{j=1\}^\{m\}P\_\{ij\}$. Those events are independent and identically distributed.
# The utilization of all of the queues is less than one.

In such a network, Jackson's theorem applies and the distribution of customers in each queue when the system is in equilibrium is exactly the distribution of an M/M/1 queueing model with the same utilization.

ee also

*Jackson's theorem
*BCMP network