Attendees at the National Management Science Society (NMSS) Conference register by first standing in line to pay their fees. They then proceed to a designated line based on the first letter of their last name to collect their conference materials.

At the conference, it is planned to have three different parallel lines for the collection of materials: one each for people whose last names begin with A-H, I-Q, and R-Z respectively.

During each minute of the morning registration period it is anticipated that attendees will arrive to pay their fees according to the following distribution:

The time to pay one's fees is either one minute or two minutes depending upon whether one uses a check or credit card. The probability of a one-minute time is .60.

After paying his fees, an attendee then goes to the correct line for the conference materials. At this year's conference 35% of the attendees have last names beginning with A-H, 36% with last names beginning with I-Q, and 29% with last names beginning with R-Z. The time required to pick up conference materials is fixed at 2 minutes.

a. Simulate the waiting line for the first 10 minutes of the morning registration that begins at 8:00 AM. Use the following random numbers to generate:

Number of arrivals in any given minute: 71, 95, 83, 44, 34, 49, 88, 56, 05, 39
Registration fee service time: 51, 79, 09, 67, 15, 58, 04, 78, 30, 56
First letter of the last name: 15, 08, 19, 45, 76, 42, 38, 47, 82, 37

b. What is the average size of the waiting line to pay fees (not including the person being served), and the average customer waiting time to pay fees based on this simulation?

Question

Attendees at the National Management Science Society (NMSS) Conference register by first standing in line to pay their fees. They then proceed to a designated line based on the first letter of their last name to collect their conference materials.
​
At the conference, it is planned to have three different parallel lines for the collection of materials: one each for people whose last names begin with A-H, I-Q, and R-Z respectively.
​
During each minute of the morning registration period it is anticipated that attendees will arrive to pay their fees according to the following distribution:
​  ​
​The time to pay one's fees is either one minute or two minutes depending upon whether one uses a check or credit card. The probability of a one-minute time is .60.
​
After paying his fees, an attendee then goes to the correct line for the conference materials. At this year's conference 35% of the attendees have last names beginning with A-H, 36% with last names beginning with I-Q, and 29% with last names beginning with R-Z. The time required to pick up conference materials is fixed at 2 minutes.
​ 
a. Simulate the waiting line for the first 10 minutes of the morning registration that begins at 8:00 AM. Use the following random numbers to generate:
​
Number of arrivals in any given minute: 71, 95, 83, 44, 34, 49, 88, 56, 05, 39
Registration fee service time: 51, 79, 09, 67, 15, 58, 04, 78, 30, 56
First letter of the last name: 15, 08, 19, 45, 76, 42, 38, 47, 82, 37
​
b. What is the average size of the waiting line to pay fees (not including the person being served), and the average customer waiting time to pay fees based on this simulation?

Quizplus · Accepted Answer

The Answer of Attendees at the National Management Science Society (NMSS) Conference register by first standing in line to pay their fees. They then proceed to a designated line based on the first letter of their last name to collect their conference materials.
​
At the conference, it is planned to have three different parallel lines for the collection of materials: one each for people whose last names begin with A-H, I-Q, and R-Z respectively.
​
During each minute of the morning registration period it is anticipated that attendees will arrive to pay their fees according to the following distribution:
​  ​
​The time to pay one's fees is either one minute or two minutes depending upon whether one uses a check or credit card. The probability of a one-minute time is .60.
​
After paying his fees, an attendee then goes to the correct line for the conference materials. At this year's conference 35% of the attendees have last names beginning with A-H, 36% with last names beginning with I-Q, and 29% with last names beginning with R-Z. The time required to pick up conference materials is fixed at 2 minutes.
​ 
a. Simulate the waiting line for the first 10 minutes of the morning registration that begins at 8:00 AM. Use the following random numbers to generate:
​
Number of arrivals in any given minute: 71, 95, 83, 44, 34, 49, 88, 56, 05, 39
Registration fee service time: 51, 79, 09, 67, 15, 58, 04, 78, 30, 56
First letter of the last name: 15, 08, 19, 45, 76, 42, 38, 47, 82, 37
​
b. What is the average size of the waiting line to pay fees (not including the person being served), and the average customer waiting time to pay fees based on this simulation?

Attendees at the National Management Science Society (NMSS) Conference Register