Exam 13: Queuing Analysis

At Joe's Pool Hall they rent tables by the hour and also rent Balabushka pool cues for purists that can't afford their own. The rental process for these cues is exhaustive and takes an hour and a half for each application. There are three leasing agents that conduct these interviews, and on average, it is one hour between customer arrivals. -What is the likelihood that there are three or fewer customers in the entire system? How does this compare with the likelihood of three or fewer customers in a system with the same arrival and service rates but staffed by four servers?

At Joe's Pool Hall they rent tables by the hour and also rent Balabushka pool cues for purists that can't afford their own. The rental process for these cues is exhaustive and takes an hour and a half for each application. There are three leasing agents that conduct these interviews, and on average, it is one hour between customer arrivals. -On average how many people are waiting in line at any time and what is the average wait?

In a factory, machines breakdown at an average of 6 machines per hour according to a Poisson distribution. The time a repair person takes to repair the machine is not defined by any probability distribution, but has a mean of 8 minutes and a standard deviation of 3 minutes. -On average, how many machines are in the system either being repaired or waiting in line to be repaired?