Sales transactions in the self-checkout lane at a mid-sized supermarket can be modelled as
a Poisson process with a rate of 4.5 transactions per minute, and the time required for a customer to
complete the checkout can be modelled as a random variable uniformly distributed between 0 and 1
minute, independently of everything else.
(a) What is the minimum number of self-checkout machines required to handle sales at this rate?
(b) Customers are encouraged to form themselves into separate queues, one for each self-checkout
machine. Customers are assumed to join whichever queue is shortest at the time they arrive. Use
the queueing-simulation web page to perform a simulation of the process under these assumptions,
for a situation where there are 3 self-checkout machines operating. Use the last 3 digits of
your student ID number as the random seed. Hand in a suitable summary of the simulation
output, relevant to the remaining parts of this question.
(c) Explain why your simulation results are (or are not) consistent with Little’s Law.
(d) Construct a 95% confidence interval for the mean time spent by a customer to complete a purchase,
including both time spent waiting and being served.
(e) An analyst from corporate HQ suggests that it might more efficient if customers were instead
organized into a single queue, with multiple servers. Modify your simulation from part (b) to
represent this proposal, and so make a point estimate of how much time it would save for the average.

Answer rating: 100% (QA)

a The minimum number of selfcheckout machines required to handle sales at a rate of 45 transactions per minute can be calculated using the equation mi... View the full answer