Consider an M/M/1 queue where customers arrive at rate 1/hour and the rate of service is 2/hour. At the exit each customer will receive 3 2 i dollars, where i is the number of people that the customer leaves behind in the system (i.e., number of people that are in the system upon departure). Find the long-term expected amount of money that a customer receives.

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Explanation:

in solving the question above, we need to first calculate:

∡= 1/hour

∡= 2/hour

Server Utilization(\rho) = 1/2= 0.5

Average Number of people in the system

L= ∡/π-∡

= 1/2-1= 1 person in the system in an hour

Expected money in an hour the customer gets = 32* Number of customers in the system = 32*1= 32

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