A retail shop experiences stable demand all afternoon on Saturdays. During this period the shop has 3 open cash registers located in a unique check-out area, each requiring an average of 4 minutes to serve a customer.
This activity time is subject to unpredictable variability however, and specifically has a coefficient of variation of 0.8.
On average a customer arrives to the check-out area every two 2 minutes, but this inter-arrival time is also subject to unpredictable variability with a coefficient of variation equal to 1.
1. What is the average customer waiting time if customers stand in line for any of the 3 cash registers in a single queue operating on a first-in-first-out basis (i.e., a single pooled queue)?
2. What would be the average customer waiting time if there were 3 separate queues for each one of the cash registers, each seeing a new customer arrival every 6 minutes on average, with a coefficient of variation equal to 1 (i.e. separate dedicated waiting lines)?
3. In the case of separate dedicated waiting lines, what is the average number of customers waiting in each queue?