You are planning the new layout for the local branch of the Sixth Ninth Bank. You are considering separate cashier windows for the three different classes of service. Each class of service would be separate with its own cashiers and customers. Oddly enough, each class of service, while different, has exactly the same demand and service times. People for one class of service arrive every 3 minutes and arrival times are exponentially distributed (the standard deviation is equal to the mean). It takes 15 minutes to service each customer, and the standard deviation of the service times is 8 minutes. You assign 7 cashiers to each type of service.
On average, how long will each waiting line be at each of the cashier windows? (Round your intermediate calculations to 4 decimal places and final answer to 3 decimal place.)
On average how long (in minutes) will a customer spend in the bank? Assume they enter, go directly to one line, and leave as soon as service is complete.(Round your intermediate calculations to 4 decimal places and final answer to 3 decimal place.)
You decide to consolidate all the cashiers so they can handle all types of customers without increasing the service times.
| a. | On average, how long will each waiting line be at each of the cashier windows? (Round your intermediate calculations to 4 decimal places and final answer to 3 decimal place.) | b. | On average how long (in minutes) will a customer spend in the bank? Assume they enter, go directly to one line, and leave as soon as service is complete.(Round your intermediate calculations to 4 decimal places and final answer to 3 decimal place.) | You decide to consolidate all the cashiers so they can handle all types of customers without increasing the service times. |
| c. | What will happen to the average amount of time a customer spends in the bank? | | | | | It will stay the same | | It depends on the queue structure | | It will decrease | | No such conclusion can be drawn | | It will increase | | | |
arrival rate every 3 min cumulative arrival rate , a 20 customers/hour arrival rate /cashier 2.8571 customers/hour (=20/7) service time 15 min service rate/ cashier 4 customers/hour no. of cashiers/window 7 cumulative service rate, s 28 customers/hour a) On average, how long will each waiting line be at each of the cashier windows? (Round your intermediate calculations to 4 decimal places and final answer to 3 decimal place.) Avg. no. in the queue = arrival rate ^2 / (service rate* (service rate-arrival rate)) Avg. no. in the queue = 1.786 Hence, each waiting line at each of the cashier windows will be 1.786 customers long b) On average how long (in minutes) will a customer spend in the bank? Assume they enter, go directly to one line, and leave as soon as service is complete.(Round your intermediate calculations to 4 decimal places and final answer to 3 decimal place.) Avg time in the system = 1 / (service rate -arrival rate) = 0.8750 hours 52.500 mins Hence, on avg every customer spends 52.5 minutes in the bank c) You decide to consolidate all the cashiers so they can handle all types of customers without increasing the service times. What will happen to the average amount of time a customer spends in the bank? Avg time in the system = 1 /(s-a) 0.125 hours 7.5 mins Hence, average amount of time a customer spends in the bank decreases when the cashiers are consolidated.
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