A vending machine dispenses hot chocolate or coffee. Service time is 30 seconds

Question

A vending machine dispenses hot chocolate or coffee. Service time is 30 seconds per cup and is constant. Customers arrive at a mean rate of 78 per hour, and this rate is Poisson-distributed.

Determine the average number of customers waiting in line. (Round your answer to 2 decimal places.)

Determine the average time customers spend in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Determine the average number in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

A vending machine dispenses hot chocolate or coffee. Service time is 30 seconds per cup and is constant. Customers arrive at a mean rate of 78 per hour, and this rate is Poisson-distributed.

a.

Determine the average number of customers waiting in line. (Round your answer to 2 decimal places.)

  Average number of customer   
b.

Determine the average time customers spend in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

  Average time minutes  
c.

Determine the average number in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

  Average number customers  

Explanation / Answer

R= 78

U = 120

a. I = R^2/ 2 U ( U -R ) = 78^2/ 2(120)(120-78) = 0.6035

b. T = I /R+1/U = 0.6035/78 + 1/120 = 0.0160 hrs

c. I = 0.6035 + 78/120 = 1.2535

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