Problem 5: 10 points Consider a service station with N- 8 servers. Customer arrivals form a…

Problem 5: 10 points Consider a service station with N- 8 servers. Customer arrivals form a Poisson process with the rate ? = 7 per hour. However, if there is a vacant seat (that is if the number of customers ongoing their services is n S 7, then the new customer begins the service. However, if n 8, the new customer leaves the system Individual service times are independent exponentially distributed with the mean t o20 minutes. 1. Describe the queueing system in terms of the finite state Markov chain with the state space, S- 10,1,8) Indicate the birth rates and death rates for this system. 2. Determine the stationary distribution, Tm = lino P [x(t) = ml, for all mE S.