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Homework answers / question archive / Pete's Market is a small local grocery store with only one checkout counter
Pete's Market is a small local grocery store with only one checkout counter. Assume that shoppers arrive at the checkout lane according to a Poisson probability distribution, with an arrival rate of 15 customers per hour. The checkout service times follow an exponential probability distribution, with a service rate of 20 customers per hour.
a. Compute the operating characteristics for this waiting line.
Given,
Arrival rate= 15
Service rate= 20
So,
Utilization= 15/ 20
= 0.75
Average no. of customer in system= 15/ (20- 15)
= 3
Average time in system= 3/ 15
= 0.2 hour
Average time waiting in queue= 0.2- 1/ 20
= 0.15 hour
Average no. of customer waiting in queue= 0.15* 15
= 2.25
