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.

Question

Kingston Hurley

Business

4 January, 19:06

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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Answers (1)

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Edith · Answer 1

Check the explanation

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