Jesse Atkinson, the only mechanic at the service center of New York Taxicab Company (NYTC), provides automotive services for NYTC taxis. Jesse services taxicabs at an average rate of five per hour, with service times being negatively exponentially distributed. Taxicabs arrive at the NYTC service center independently and randomly following a Poisson distribution throughout the day at a rate of one every 15 minutes. Taxis are serviced on a FCFS basis. NYTC is the city's largest taxi company and the number of NYTC taxis is large enough (to be considered infinite for probability purposes). a) What percentage of time is the mechanic busy? b) What is the average number of taxis waiting in line at the NYTC service center? c) On average, how long will an NYTC taxi spend at the service center, including the times waiting in line and being serviced? d) What is the probability that three or more taxis are at the NYTC service center? e) Suppose now that the arrival of taxis for servicing at NYTC's service center has significantly increased to 11 taxicabs per hour. Two additional mechanics have been hired at the NYTC service center, each having the same service rate of 5 taxis per hour.
Jesse Atkinson, the only mechanic at the service center of New York Taxicab Company (NYTC), provides automotive services for NYTC taxis. Jesse services taxicabs at an average rate of five per hour, with service times being negatively exponentially distributed. Taxicabs arrive at the NYTC service center independently and randomly following a Poisson distribution throughout the day at a rate of one every 15 minutes. Taxis are serviced on a FCFS basis. NYTC is the city's largest taxi company and the number of NYTC taxis is large enough (to be considered infinite for probability purposes). a) What percentage of time is the mechanic busy? b) What is the average number of taxis waiting in line at the NYTC service center? c) On average, how long will an NYTC taxi spend at the service center, including the times waiting in line and being serviced? d) What is the probability that three or more taxis are at the NYTC service center? e) Suppose now that the arrival of taxis for servicing at NYTC's service center has significantly increased to 11 taxicabs per hour. Two additional mechanics have been hired at the NYTC service center, each having the same service rate of 5 taxis per hour.
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
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![Jesse Atkinson, the only mechanic at the service center of New York Taxicab Company (NYTC),
provides automotive services for NYTC taxis. Jesse services taxicabs at an average rate of five per
hour, with service times being negatively exponentially distributed. Taxicabs arrive at the NYTC
service center independently and randomly following a Poisson distribution throughout the day at a
rate of one every 15 minutes. Taxis are serviced on a FCFS basis. NYTC is the city's largest taxi
company and the number of NYTC taxis is large enough (to be considered infinite for probability
purposes).
a) What percentage of time is the mechanic busy?
b) What is the average number of taxis waiting in line at the NYTC service center?
c) On average, how long will an NYTC taxi spend at the service center, including the times
waiting in line and being serviced?
d) What is the probability that three or more taxis are at the NYTC service center?
e) Suppose now that the arrival of taxis for servicing at NYTC's service center has significantly
increased to 11 taxicabs per hour. Two additional mechanics have been hired at the NYTC
service center, each having the same service rate of 5 taxis per hour.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F736bd424-1943-4961-9b79-cf6dda15af99%2Fd8a7db90-740a-41a3-b54a-42d5d2ca23f9%2F9pmxde8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Jesse Atkinson, the only mechanic at the service center of New York Taxicab Company (NYTC),
provides automotive services for NYTC taxis. Jesse services taxicabs at an average rate of five per
hour, with service times being negatively exponentially distributed. Taxicabs arrive at the NYTC
service center independently and randomly following a Poisson distribution throughout the day at a
rate of one every 15 minutes. Taxis are serviced on a FCFS basis. NYTC is the city's largest taxi
company and the number of NYTC taxis is large enough (to be considered infinite for probability
purposes).
a) What percentage of time is the mechanic busy?
b) What is the average number of taxis waiting in line at the NYTC service center?
c) On average, how long will an NYTC taxi spend at the service center, including the times
waiting in line and being serviced?
d) What is the probability that three or more taxis are at the NYTC service center?
e) Suppose now that the arrival of taxis for servicing at NYTC's service center has significantly
increased to 11 taxicabs per hour. Two additional mechanics have been hired at the NYTC
service center, each having the same service rate of 5 taxis per hour.
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