Customers in a small retail store arrive at the single cashier on average every 6 minutes. The average service time for the cashier is 5 minutes. Arrivals tend to follow a Poisson distribution, and service times follow an exponential distribution. We need to analyze this waiting-line system. (g) Should the retail store consider creating a second cashier lane? (h) A cash machine manufacturer has offered an advanced system that will reduce service time to 2 minutes per customer. The cost of the new machine would be the same as opening a second cashier lane, so the owner has decided to buy the new system only if it reduces wait times over the two-cash option. Evaluate the two options (advanced cash or a two-cash system) and suggest which option you would choose.

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter12: Queueing Models
Section12.5: Analytic Steady-state Queueing Models
Problem 9P
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Customers in a small retail store arrive at the single cashier on average every 6 minutes. The average service time for the cashier is 5 minutes.
Arrivals tend to follow a Poisson distribution, and service times follow an
exponential distribution. We need to analyze this waiting-line system.

(g) Should the retail store consider creating a second cashier lane?
(h) A cash machine manufacturer has offered an advanced system that will
reduce service time to 2 minutes per customer. The cost of the new
machine would be the same as opening a second cashier lane, so the
owner has decided to buy the new system only if it reduces wait times
over the two-cash option. Evaluate the two options (advanced cash or a
two-cash system) and suggest which option you would choose.

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