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14 Oct

At a ticket counter, customers arrive with an arrival rate of 1 customer

per time unit, but they do not queue up if the queue has already reached a length 3. (The

length of the queue in ludes the customer that is being served.) The cashier feels motivated

by many customers, and her processing rate is equal to the length of the queue, e.g., 2 if

the length of the queue is two customers per time unit.

Build a continuous time Markov chain that models the system (9 marks), and compute the

average length of the queue (9 marks)

At a ticket counter, customers arrive with an arrival rate of 1 customer

per time unit, but they do not queue up if the queue has already reached a length 3. (The

length of the queue in ludes the customer that is being served.) The cashier feels motivated

by many customers, and her processing rate is equal to the length of the queue, e.g., 2 if

the length of the queue is two customers per time unit.

Build a continuous time Markov chain that models the system (9 marks), and compute the

average length of the queue (9 marks)