Question

Dan's Store has installed a self-service checkout counter, and wishes to understand how this has affected customer service. Shoppers arrive on average the rate of one every other minute (Poisson distribution). Each shopper takes an average of 82 seconds to use the checkout, and that time is exponentially distributed.

a.	Calculate how long it takes, on average, for a shopper at the self-service counter, including how long they wait in line and how long it takes them to do their own checkout.   (Do not round intermediate calculations. Round your answer to the nearest whole number.)

Average time

minutes

b.	Calculate the probability that a shopper will be able to use the self-service checkout without waiting. (Round your answer to 2 decimal places.)

Probability

c.	Calculate the average number of shoppers who are waiting to use the self-service checkout.  (Round your answer to 2 decimal places.)

Average number

customers

Answer 1

Answer:

Arrival rate, Lambda =30 per hour

Service rate mu = 60 x 60 /82 = 43.90 per hour

Utilization rho = lambda /mu = 30/43.90 =0.6833

(a) Avg time spent in the system = 1/ mu-lambda = 1/43.90-30 = 0.0719 hours = 4.314 = 4 minutes

(b) Probability of having zero customers in the system = 1-rho = 1-0.6833 =0.3167 = 0.32

(c) Avg queue length = (lambda)2 / mu ( mu-lambda)

               = 900 / 43.90 (43.9-30)

               = 1.4749 = 1.47