Bobby, another enterprising barber, is thinking about advertising in the local newspaper because he is idle 45 percent of the time. Currently, customers arrive, on average, every 40 minutes. What does the arrival rate need to be for Bobby to be busy 85 percent of the time?

Give and explain briefly that in what kinds of situations is queuing analysis is most appropriate.

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 anexponential 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 willreduce service time to 2 minutes per customer. The cost of the newmachine would be the same as opening a second cashier lane, so theowner has decided to buy the new system only if it reduces wait timesover the two-cash option. Evaluate the two options (advanced cash or atwo-cash system) and suggest which option you would choose.

Mom and Pop own and operate the Fuzzy Belly Deli. On average, customers arrive at the deli every 6 minutes. Pop fulfills their orders one at a time. It takes him an average of 3 minutes to fulfill each order. Customers then proceed to the cash register, where Mom receives their payment. Mom loves to chat and is somewhat slow in operating the cash register, taking an average of 4 minutes to receive payment from each customer. Assume that customer interarrival times, as well as order fulfillment and payment times are exponentially distributed. What is the throughput of the deli's operation? What is the capacity of the deli's operation? On average, how long does a customer spend at the deli from the time she arrives until her order is fulfilled by Pop?