A.The concession stand at the baseball park gets (on average) 20 customers per inning.The cashier can process 30 customers per inning (on average).The concession manager does not understand how they can have any line at all when they are able to process the customers much faster than they arrive.Can you help explain to the manager the characteristics of their waiting line system?(Ws, Wq, Ls, Lq, utilization and Po)(You believe this to be a M/M/1 system)

B.Customers come in to a cell phone repair shop via a Poisson arrival rate of 3 per hour.The repairman at the shop can fix a phone every 12 minutes, according to a negative exponential distribution.

a)how many customers, on average, are in the shop?

b) how many customers are typically in the queue?

c) how long does a customer typically spend in the shop?

d) how long does a customer typically need to wait in line before they are served?

e) what is the probability that the shop is empty?

C.A clerk at the local coffee shop takes about 4 minutes to process each order.Her customers typically arrive at a rate of 12 every hour.Her shop is small, and only has room to hold three customers waiting in line.She wants to wait on her customers in 10 minutes or less.Use Table D.5 and Little's Law to answer these questions.

a)Does she have enough room in her shop for the typical waiting line?

b)Is she meeting her service objective?

c)If she adds another clerk to serve coffee, how does this impact the waiting time of the customers, and her customer service objectives?

D.The local pharmacy gets very busy on weekends, with 40 customers arriving every hour.There are typically 8 customers at the pharmacy (either being served or waiting) on average on the weekends.The pharmacy manager does not know if the arrivals follow a Poisson distribution or not.How long does the typical customer spend in the pharmacy on weekend?

E.

A new shopping mall is considering setting up an information desk manned by one employee. Based upon information obtained from similar information desks, it is believed that people will arrive at the desk at a rate of 15 per hour. It takes an average of 3 minutes to answer a question. It is assumed that the arrivals follow a Poisson distribution and answer times are exponentially distributed.

(a)Find the probability that the employee is idle.

(b)Find the proportion of the time that the employee is busy.

(c)Find the average number of people receiving and waiting to receive some information.

(d)Find the average number of people waiting in line to get some information.

(e)Find the average time a person seeking information spends in the system.

(f)Find the expected time a person spends just waiting in line to have a question answered (time in the queue).

F.

Assume that the information desk employee in Problem E earns $12 per hour. The cost of waiting time, in terms of customer unhappiness with the mall, is $15 per hour of time spentwaitingin line. Find the total expected costs over an 8-hour day.

G.

Four students arrive per minute at a coffee machine that dispenses exactly five cups per minute at aconstantrate. Describe the system parameters (name the model, then calculate parameters such as Lq, Wq, Ls, Ws).