Consider the single-server queue with geometrically distributed inter-arrival times and service times, with parameters and respectively, as discussed in class. Now assume that

Consider the single-server queue with geometrically distributed inter-arrival times and service times, with parameters λ and µ respectively, as discussed in class. Now assume that the system can store a maximum of 3 packets (including the one in service).

• Draw the state transition diagram of the queueing system.

• Write down the balance equations of each state.

• Solve the steady-state probabilities.

• What is the probability that a new arrival will be rejected because the queue is full?

What is the average number of packets in the system?

• What is the average packet delay in the system?