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Gabriele

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**Queueing networks...please some experts help me!**

Hello to everyone.

I have a question concerning Queuing Theory and in particular Queueing Networks. For my Ph.D thesis I need to evaluate the steady state behavior of queueing networks featuring finite buffers between nodes and "blocking after service" policy. For simplicity, I'm in the particular case in which the arrival rate and the service rate of each node can be considered "deterministic" (i.e. each node is a D/D/1 queue with finite buffer of K positions).

Now, some queueing nodes can be bottlenecks. A bottleneck in this case means that its service time is greater than its inter-arrival time yields to an utilization factor of the node higher than 1. In this case, due to the bottleneck presence, upstream nodes will be blocked and their effective service times are higher than their corresponding theoretical (ideal) ones.

I need to known where I can find some analytical threatment of such kind of networks. Especially I need to found proper expressions in order to calculate the effective service time of each node of the network, mainly in the case of merge queueing nodes (nodes with multiple in-coming connections with other nodes) and splitting stations (nodes with multiple out-going arcs and a routing probability among them).

Do you know something about this?

Thanks

Gabriele