You have started a new business with your friends while you are still a student. You have special clientele.. they like snakes as pets…Hence you start a tea/snake shop (you will serve tea and snakes for entertaining your clients). You decide to hire one server in the beginning. You expect about 15 customers per hour (mean value with Poission distributed arrivals) arriving in the morning hours. The server will take about 4 minutes to serve a customer (mean time). For this situation (Situation A) Find: a. Arrival and service rates b. Find system utilization c. Percentage of time server is idle
You have started a new business with your friends while you are still a student. You have special clientele.. they like snakes as pets…Hence you start a tea/snake shop (you will serve tea and snakes for entertaining your clients). You decide to hire one server in the beginning. You expect about 15 customers per hour (mean value with Poission distributed arrivals) arriving in the morning hours. The server will take about 4 minutes to serve a customer (mean time).
For this situation (Situation A) Find:
a. Arrival and service rates
b. Find system utilization
c. Percentage of time server is idle
d. What is wrong with the picture?
e. What can you do to help the situation?
f. Once you correct the situation (adopt one of the possible solutions), find probability of 5 customers in the system.
g. Find the expected number of customers waiting to be served.
h. What is the service and weight times (system wait time)?
i. Solve the above problem assuming M/M/1 queue discipline.
You are now become more seasoned and want to change your business model (Situation B). You decide to plan things better this time. You don’t want to get into any problem this time..you decide to serve Tea/Snacks (new type of customers you target like to eat a lot).
You want to know the following:
a. You decided to hire 3 servers, with each being of same type as in Situation A. What is the utilization?
b. What is the expected number of customers waiting? And what is the expected wait time?
c. What is the probability that an arriving customer has to wait for service?
d. You decided that your shop needs a check -based on utilization rates..what is the optimal number of servers you should have?
e. Compute wait times based on the new model.
f. You know that cost of customer waiting is 100 per customer/ hour and service cost 120 per customer per hour. Identify the right of servers to be hired.
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