(2) Metro Quick Lube is a lube-bay service facility located next to a busy highway in...

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(2) Metro Quick Lube is a lube-bay service facility located next to a busy highway in an urban area. The facility has only one vehicle in service and four vehicles lined up for service. There is no space for cars to line up on the busy adjacent highway, so, if the waiting line is full (four cars), prospective customers must drive on. The Bay is open 8 hours a day. The mean time between arrivals for customers seeking lubrication service is three minutes. The mean time required to perform the lube operation is 2.5 minutes, distributed exponentially. Find below the operating characteristics of the shop. COMPUTER OUTPUT (Times are in minutes RESULTS-COMPUTER OUTPUT (Times = Minutes) METRO QUICK LUBE QUEUE 1: M/ M /C/K QUEUE STATISTICS Number of identical servers. Mean arrival rate.... Mean service rate per server Waiting room capacity. 0.5000 0.4000 4 Mean server utilization (%)....... Expected number of customers in queue.... Expected number of customers in system Probability that a customer must wait.... Probability of service denial... 91.1181 2.2205 3.1317 0.9112 .... 0.2711 ... METRO QUICK LUBE QUEUE 1: M/ M/C/K PROBABILITY DISTRIBUTION OF NUMBER IN SYSTEM Number Prob 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 tet t ttt- t--+----t---+ 0 0.0888|****+ 1 0.1110|******- 2 0.1388|*** 3 0.1735|* 4 0.2168|*********** 5 0.2711|** +----t-t ******* ***** (a) What percentage of the time is the server idle? ANSWER (b) Suppose the bay is open 8 hours a day, what is the average number of arrivals in a day? ANSWER (c) What is the probability of being denied service because the system is full? (d) What is the percentage of customers who are denied service because the system is full (busy)? ANSWER (e) How many customers will be denied service in a day because the system is full (busy)? ANSWER Oự profit generated by one customer is $20, how much money is lost because the system is (busy) full? ANSWER (2) Metro Quick Lube is a lube-bay service facility located next to a busy highway in an urban area. The facility has only one vehicle in service and four vehicles lined up for service. There is no space for cars to line up on the busy adjacent highway, so, if the waiting line is full (four cars), prospective customers must drive on. The Bay is open 8 hours a day. The mean time between arrivals for customers seeking lubrication service is three minutes. The mean time required to perform the lube operation is 2.5 minutes, distributed exponentially. Find below the operating characteristics of the shop. COMPUTER OUTPUT (Times are in minutes RESULTS-COMPUTER OUTPUT (Times = Minutes) METRO QUICK LUBE QUEUE 1: M/ M /C/K QUEUE STATISTICS Number of identical servers. Mean arrival rate.... Mean service rate per server Waiting room capacity. 0.5000 0.4000 4 Mean server utilization (%)....... Expected number of customers in queue.... Expected number of customers in system Probability that a customer must wait.... Probability of service denial... 91.1181 2.2205 3.1317 0.9112 .... 0.2711 ... METRO QUICK LUBE QUEUE 1: M/ M/C/K PROBABILITY DISTRIBUTION OF NUMBER IN SYSTEM Number Prob 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 tet t ttt- t--+----t---+ 0 0.0888|****+ 1 0.1110|******- 2 0.1388|*** 3 0.1735|* 4 0.2168|*********** 5 0.2711|** +----t-t ******* ***** (a) What percentage of the time is the server idle? ANSWER (b) Suppose the bay is open 8 hours a day, what is the average number of arrivals in a day? ANSWER (c) What is the probability of being denied service because the system is full? (d) What is the percentage of customers who are denied service because the system is full (busy)? ANSWER (e) How many customers will be denied service in a day because the system is full (busy)? ANSWER Oự profit generated by one customer is $20, how much money is lost because the system is (busy) full? ANSWER

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