A vending machine dispenses hot chocolate or coffee. Service time is 40 seconds

Question

A vending machine dispenses hot chocolate or coffee. Service time is 40 seconds per cup and is constant. Customers arrive at a mean rate of 60 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 of customers in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.)
  
Average number _____ customers

Explanation / Answer

Service time = 40 sec per cup

Service rate = u = (60/40)*60 = 90 per hour

Mean = lambda = 60

a. Average number of customers waiting in line:

Lq = (lambda^2) / (2u(u-lambda)

=(60^2) / (2*90(90-60) = 0.667

b. Average time customers spend in the system:

Ws= (Lq/lambda) + (1/u) = (0.667/60) + (1/90) = 0.0222

c. Average number of customers in the system:

Ls = Lq + lambda/u

Ls = 0.667 + (60/90) = 1.33

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