M/M/1, M/M/1/K - compulsory test

Consider a queuing system with a single server, infinite queue, Poisson arrivals and Exponential service times. The arrival intensity is 2 arrivals per time unit, the service intensity is 4 services per time unit. Answer the following questions, considering the system in steady state.

1. Give the offered load and the utilization of the server. Give the queuing model.
2. Give the probability that at a random point of time there is exactly one customer waiting in the queue, and another one under service.
3. Give the average number of customers in the system, the average number of customers in the server, and the average number of customers waiting in the queue.
4. Give the average system time, the average service time and the average waiting time.