Please help me understand queuing theory.

| March 31, 2017

Question
Question 1 (16 Points) On the tab labeled “Arrival” you will see the number of calls received for the 500 randomly chosen hours at each of the five precincts. Compute the Arrival Rate for each precinct and enter those values (to 2 decimal places) accordingly in the matrix to the left. On the tab labeled “Service”, you will see the service times (in minutes) for each call logged at each of the five precincts during the sampled period. Note that each precinct logged a different number of calls. For each precinct, compute the Service Rate and enter those values (to 2 decimal places) accordingly in the matrix to the left. As a reminder, both rates should be entered based on the number per hour; be particularly careful in computing the service rates!!

Question 2 (16 Points) For each precinct, you will note I have entered the number of servers currently serving. After completing Question 1, enter the Arrival and Service Rates and # of Servers for each precinct into Q.xls and obtain the queue characteristics. Copy and paste the results from each Q.xls run into the appropriate column in the matrix to the left. Report all values to 2 decimal places.

Question 3 (16 Points) Based on expected wait times in the queue before speaking with an operator, which precinct is currently most efficient? In answering this questions be sure to include the wait time in minutes.

Question 4 (16 Points) Based on expected wait times in the queue before speaking with an operator, which precinct is currently least efficient? In answering this question, be sure to include the wait time in minutes.

Question 5 (16 Points) It is the city’s goal to limit the before speaking to a 911 operator to two minutes or less. In the Number of Added Servers line to the left, state the minimum number of servers that must be added to each precinct to meet the city’s goal of two minutes or less in the queue before speaking with an operator. Discuss how you arrived at each answer.

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