Pete's Market is a small local grocery store with only one checkout counter

Business Aug 22, 2020

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.

Expert Solution

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

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