Shortest Paths and Minimal Spanning Trees; Queueing Theory

Consider the network defined in 2.1 above, but now ignore orientation and regard the weights as distances between the nodes.

Consider the network defined in 2.1 above, but nowignoreorientation and regard theweights as distances between the nodes.(IFind the shortest paths fromOto all other nodes of the network(iiFind a minimal spanning tree of the network.(b)Queuing theory.2.4. A grocery store has one checkout stand with a full time cashier. Customers arrive atthe stand following the Poisson distribution with a mean rate of 30 per hour. When there isonly one customer at the stand, the average service time spent by the cashier is 1.5 min.Whenever two or more customers are at the stand, another staff joins to help the cashier bybagging. This reduces the average service time to 1 minute per customer. It is assumed thatthe service time is distributed exponentially.(i)]Sketch the rate diagram for this queueing system.(ii)Find the steady state distribution of the number of customers at the checkoutstand