Open, Closed, and Mixed Networks of Queues with Different Classes of Customers

@article{Baskett1975OpenCA,
  title={Open, Closed, and Mixed Networks of Queues with Different Classes of Customers},
  author={Forest Baskett and K. Mani Chandy and Richard R. Muntz and Fernando G. Palacios},
  journal={J. ACM},
  year={1975},
  volume={22},
  pages={248-260}
}
We derive the joint equilibrium distribution of queue sizes in a network of queues containing N service centers and R classes of customers. The equilibrium state probabilities have the general form: P(S) - Cd(S) $f_1$($x_1$)$f_2$($x_2$)...$f_N$($x_N$) where S is the state of the system, $x_i$ is the configuration of customers at the ith service center, d(S) is a function of the state of the model, $f_i$ is a function that depends on the type of the ith service center, and C is a normalizing… 

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