Consider an open queueing network of the central server type. Customers arrive at the centralserver according to a Poisson process with rate $0\mathrm{.}1.$ The central server behaves stochastically like an M$/$M$/2$queue in which each of the servers operates at rate $2\mathrm{.}0.$ After receiving service at the central server, customerseither leave the network $($with probability $0\mathrm{.}2)$ or else proceed to one of three other nodes with probabilities $0\mathrm{.}3,0\mathrm{.}3,$ and $0\mathrm{.}2$ respectively. Service at each of the three service centers is exponentially distributed at rate $0\mathrm{.}5,1\mathrm{.}0,$and $2\mathrm{.}0$ respectively. After receiving service at one of these three nodes, customers return to the central server.Compute the probability that the central server is idle and the mean number of customers in the network.