In past presidential elections in the United States, very long wait times have been witnessed at precincts (voting stations) in states that ultimately decided the election (Florida in 2000 and Ohio in 2004). In Chicago as well, some voters complained about the long lines in some precincts. Suppose most complaints came from a fictitious precinct A. In 2012, the average number of voters arriving at Precinct A was 35 per hour and the arrivals of voters was random with inter-arrival times that had a coefficient of variation of 1 (CVa=1). Chicago had deployed 1 voting machine in Precinct A. Suppose that each voter spent on average 100 seconds in the voting booth (this is the time needed to cast her/his vote using a voting machine), with a standard deviation of 120 seconds. (a) How long on average did a voter have to wait in line at precinct A in 2012 before entering in a booth to cast her/his vote? (b) Given the long wait times for Precinct A, the city of Chicago is thinking of alternative solutions to improve voting conditions. One of the proposed solutions is to deploy an additional voting machine in precinct A. Assume that the voter turnout is expected to have similar characteristics in 2012 as in the previous election. Under the proposal, how long on average would a voter have to wait in line in precinct A in 2012 before casting her/his vote? (c) Under the proposal above at precinct A, what would be the ratio of the average number of people voting (at a booth) over the average number of people in the line (waiting)?
In past presidential elections in the United States, very long wait times have been witnessed at precincts (voting stations) in states that ultimately decided the election (Florida in 2000 and Ohio in 2004). In Chicago as well, some voters complained about the long lines in some precincts. Suppose most complaints came from a fictitious precinct A. In 2012, the average number of voters arriving at Precinct A was 35 per hour and the arrivals of voters was random with inter-arrival times that had a coefficient of variation of 1 (CVa=1). Chicago had deployed 1 voting machine in Precinct A. Suppose that each voter spent on average 100 seconds in the voting booth (this is the time needed to cast her/his vote using a voting machine), with a standard deviation of 120 seconds.
(a) How long on average did a voter have to wait in line at precinct A in 2012 before entering in a booth to cast her/his vote?
(b) Given the long wait times for Precinct A, the city of Chicago is thinking of alternative solutions to improve voting conditions. One of the proposed solutions is to deploy an additional voting machine in precinct A. Assume that the voter turnout is expected to have similar characteristics in 2012 as in the previous election. Under the proposal, how long on average would a voter have to wait in line in precinct A in 2012 before casting her/his vote?
(c) Under the proposal above at precinct A, what would be the ratio of the average number of people voting (at a booth) over the average number of people in the line (waiting)?
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