An urban area is connected by a ring network comprising N=7 nodes. Node 1 is a gateway to the Internet, while the other six nodes are the access nodes of six different local networks. All the traffic...

An urban area is connected by a ring network comprising N=7 nodes. Node 1 is a gateway to the Internet, while the other six nodes are the access nodes of six different local networks. All the traffic from local networks(upstream traffic) is addressed to the Internet: the corresponding mean bitrate for each local network is Rout = 100 Mbit/s. The traffic coming from the Internet and directed to the local networks (downstream traffic) is uniformly distributed among them. The overall mean bit rate of that traffic is R In =1 G bit/s. Both traffic flows can be modeled as Poisson processes at the packet level. Packet lengths are random variables, with negative exponential distribution, and the mean packet length is L=500 bytes. The links connecting neighboring nodes are bidirectional, with a capacity C in each direction.

(a) Identify a queueing model of the ring network at packet level.

(b) Find the minimum value of C that guarantees that the utilization coefficient in each link is not greater than 0.8.

(c) Find the mean delay from node 1 to each other node with the dimensioning of point (b).