Analytical solutions for Q.N. with finite capacity queues
Network model parameters
- M number of nodes
- N number of customers
- µi service rate of node i
- Service time distribution: M, G, PHn , GE
- P=||pij|| routing matrix
- Bi finite capacity of node i
- Queue-length probability distribution ?
- C-T Homogeneous Markov Chain
- S = (S1,S2,..., SM) network state
- State space E, transition rate matrix: Q
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- Steady-state probabilities ö(S)
Other average performance indices can be derived from ö and depend on the blocking type
Exact solution becomes soon numerically untractable
Product-form solution in special cases approximate analysis