# when customers arrive at gilley’s ice cream shop, they take a number and wait to be called to purchase ice cream from one of the three counter serves….

when customers arrive at gilley’s ice cream shop, they take a number and wait to be called to purchase ice cream from one of the three counter serves. on summer days between 3-10pm, customers arrive at the rate 36 per hour – poisson distributed. it takes an average 4 minutes to serve a customer – exponential distributed. gilley’s want to make sure that customers, on average, wait no longer than 10 minutes. what is the proper queueing model for this problem?

a. m/m/1 queue

b. m/m/s queue

c. m/m/1/c (finite capacity/finite queue)

d. m/m/1/fp (finite population queue)

2. what percentage of time gilley’s has no customer in the shop?

a. 11.1%

b. 5%

c. 5.6%

d. 3.5%

3. what is the average number of customers waiting for the ice cream?

a. 0.889 customers

b. 4.933 customers

c. 2.589 customers

d. 1 customers

4. on average, how long does it take for a customer from the moment he/she arrives until he/she gets hie/her ice cream?

a. 11.59 minutes

b. 5.43 minutes

c. 5.78 minutes

d. 8.32 minutes

5. what percentage of customers who must wait for a counter server to become available?

a. 42.87%

b. 44.44%

c. 64.72%

d. 75.89%

6. what is the maximum number of customers waiting in the room for the probability of 95%

a. 3 customers

b. 5

c. 11

d 18

InputsTime UnitArrival Rate ( lambda )Service rate ( mu)Number of serversIntermediate calculationsAverage time between arrivalsAverage service time per serverCombined service rate ( s*mu)…