Question: During the previous presidential elections in the United States, very long wait times have been witnessed at precincts (voting stations) in states that ultimately decided the election (for example, Florida in 2000, Ohio in 2004). In New Jersey, as well, some voters complained about the long lines in some precincts, with most complaints coming from a particular precinct in Hoboken, NJ. The average number of voters arriving at this precinct was 35 per hour and the arrival of voters was random, with CVa=1. The officials had deployed 1 voting machine in this precinct. Service times were random as well, with CVp=1; 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).
(a) Suppose that the disabled citizens are prioritized over the others. If the percentage of the disabled voters in this precinct is 5% of the total number of voters, how long do the citizens who are not prioritized wait before voting on average?
(b) If the average time a voter spends in the voting booth increases to 4 minutes, what would be the utilization rate of a stable queuing system with the minimum number of voting machines?
(c) Still assume that the average time each voter spends is 4 minutes. If each voting machine costs $100/hr to operate, and the cost of waiting is assessed at $2/min, what would be the optimum number of voting machines that should be utilized?