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.
Answer: The likelihood of 0, 1, 2, and 3 customers is 0.21, 0.32, 0.24, and 0.12, respectively, for a total of 0.88 for the three or fewer customers with three servers. If the number of servers increases to four, then the likelihoods of 0, 1, 2, and 3 are .22, .33, .25, and .12, respectively, for a total of .93.
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