a. What are the arrival rate of 911 calls and the service rates for each precinct?

b. Does the arrival rate of calls for each precinct appear to follow a Poisson distribution?

c. Does the service rate for each precinct appear to follow an exponential distribution?

d. Using an M/M/s queue, on average, how many minutes must a 911 caller in each precinct wait before a police officer begins responding?

e. Suppose Craig wants to redistribute officers among precincts so as to reduce the maximum amount of time callers in any one precinct have to wait for a police response. What should he do and what effect would this have?

f. How many additional police officers would Newport have to hire for the average response time in each precinct to be less than two minutes?

“I hope this goes better than last time,” thought Craig Rooney as he thought about having to walk into the city council’s chambers next week. Craig is the assistant chief of police in Newport, VA, and, each September he has to provide the city council with a report on the effectiveness of the city’s police force. This report immediately precedes the council’s discussion of the police department’s budget. So Craig often feels like a tightrope artist trying to find the right balance in his presentation to both convince the council that the department is being run well and also persuade them to increase the department’s budget for new officers.

The city of Newport has a total of 19 police officers assigned to five precincts. Currently, precinct A has three officers assigned to it while the others each have four officers. One of the town council’s primary concerns each year is the amount of time it takes for an officer to begin responding when a 911 emergency call is received. Unfortunately, the city’s information system does not track this data exactly, but it does keep track of the number of calls received in each precinct each hour and the amount of time that elapses between when officers first begin responding to call and the time they report being available again to respond to other calls (this is also known as the service time for each call).

A student intern from a local university worked for Craig last summer and collected data shown in the file named CallData.xls found on your data disk. One of the sheets in this workbook (named calls per hour) shows the number of 911 calls received during 500 randomly chosen hours of operation in each precinct. Another sheet (named service times) shows the services time required for each of these calls.

The student intern also set up a worksheet (based on the formulas in Figure) to calculate operating characteristics of an M/M/s queue for each of the Newport’s five precincts. Unfortunately, the student intern had to return to school before finishing this project. But Craig believes that with a little work he can use the data collected to figure out appropriate arrival and service rates for each precinct and complete the analysis. More importantly, he feels sure the queuing model will allow him to quickly answer many of the questions he expects the city council toask.

Transcribed Image Text:

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