The computer lab at State University has a help desk to assist students working on computer spreadsheet assignments. The students patiently form a single line in front of the desk to wait for help. Students are served based on a first-come, first-served priority rule. On average, 15 students per hour arrive at the help desk. Student arrivals are best described using a Poisson distribution. The help desk server can help an average of 20 students per hour, with the service rate being described by an exponential distribution. Calculate the following operating characteristics of the service system. (a) The average utilization of the help desk server (b) The average number of students in the system (c) The average number of students waiting in line (d) The average time a student spends in the system (e) The average time a student spends waiting in line

The computer lab at State University has a help desk to assist students working on computer spreadsheet assignments. The students patiently form a single line in front of the desk to wait for help. Students are served based on a first-come, first-served priority rule. On average, 15 students per hour arrive at the help desk. Student arrivals are best described using a Poisson distribution. The help desk server can help an average of 20 students per hour, with the service rate being described by an exponential distribution. Calculate the following operating characteristics of the service system. (a) The average utilization of the help desk server (b) The average number of students in the system (c) The average number of students waiting in line (d) The average time a student spends in the system (e) The average time a student spends waiting in line

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section12.5: Analytic Steady-state Queueing Models

Problem 18P

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The computer laboratory at a State University has a help desk to assist students working on computer spreadsheet assignments. The students patiently form a single line in front of the desk to wait for help. Students are served based on a first-come, first-served priority rule. On the average, 15 students per hour arrive at the help desk. Student arrivals are best described using a Poisson distribution. The help desk server can help an average of 20 students per hour, with the service rate being described by a constant distribution. Calculate the following characteristics of the system: The average utilization of the help desk server. The average number of students waiting in line. The average number of students waiting in the system. The average time a student spends in the system
The Clip Joint is a hairstyling salon at University Mall. Four stylists are always available toserve customers on a first-come, first-served basis. Customers arrive at an average rate of fiveper hour, and the stylists spend an average of 35 minutes on each customer Determine the average number of customers in the salon, the average time a customer must wait, and the average number waiting to be served.
The computer lab at State University has a help desk to assist students working on computer spreadsheet assignments. The students patiently form a single line in front of the desk to wait for help. Students are served based on a first-come, first-served priority rule. Students arrive at the help desk at the rate of 4 every 10 minutes. The average service time is 2 minutes. The Poisson distribution is appropriate for the arrival rate and service times are exponentially distributed. a) What is the average time a student is in the lab? b) What is the average number of students in the lab? c) What is the average number of students waiting to receive service? d) What is the average time a student is in the queue? e) What is the probability that there are no students at the computer lab?