Question: 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 the system

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 the system can store a maximum of 3 packets (including the one in service), and arrivals occur before departures in each time slot. 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?

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