Students arrive at the Administrative Services Office at an average of one every
ID: 439259 • Letter: S
Question
Students arrive at the Administrative Services Office at an average of one every 6 minutes, and their requests take on average 2 minutes to be processed. The service counter is staffed by only one clerk, Judy Gumshoes, who works eight hours per day. Assume Poisson arrivals and exponential service times. (a)What percentage of time is Judy idle? (Round your answer to 2 decimal places. Omit the "%" sign in your response.) (b)How much time, on average, does a student spend waiting in line? (Round your answer to the nearest whole number.) (c)How long is the (waiting) line on average? (Round your answer to 2 decimal places.) (d)What is the probability that an arriving student (just before entering the Administrative Services Office) will find at least one other student waiting in line? (Round your answer to 3 decimal places.)Explanation / Answer
help: M/M/1 System ? = 4 customers/hour ? = 6 customers/hour What percentage of time is Judy idle? 1-?/? = 33.33% How much time, on average, does a student spend waiting in line? Wq = ? / ?(?-?) = 1/3 hours or 20 minutes M/M/1 System ? = 4 customers/hour ? = 6 customers/hour How long is the (waiting line) on average? Lq = ?Wq = 4/3 customers What is the probability that an arriving student (just before entering the Administrative Services Office) will find at least one other student waiting in line? =1-P0-P1 = 1 – (1-?/?) - ?/?(1-?/?) = 4/9, or 0.44