Assignment Task: In a previous election in Toronto, very long wait times have been witnessed at voting stations. Some voters complained about the long lines in some stations, with most complaints coming from voting station A. In 2014, the average number of voters arriving at Station A was of 35 per hour and the arrivals of voters were random with inter-arrival times that had a coefficient of variation of 1 (CVa=1).
Toronto had deployed 1 voting machine in voting station 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 90 seconds.
Q1. How long on average a voter had to wait in line at voting station A in 2014 before entering in a booth to cast her/his vote?
Q2. What would be the probability that a voter does not have to wait in line in 2014?
Q3. What is the probability that a voter spends more than 1 hour (in waiting plus voting) at voting station A in 2014?
Q4. Given the long wait times for voting station A, the city of Toronto thought of alternative solutions to improve voting conditions in 2018. One of the proposed solutions is as follows.
Q5. Proposal: Deploy an additional voting machine for voting station A. Assume that the voter turnout had similar characteristics in 2018 as in 2014. Under the proposal, how long on average would a voter had to wait in line at voting station A before casting her/his vote in 2018?
Q6. Under the proposal, at voting station A in 2018, 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)?