Queue Length

1
Queue Length
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Before anything else

• Read the manual carefully. It is your homework
• What is covered in the following slides is just
  general

3
General

• Customer service analysis (restaurants)
• Toll booth
• Parking garage
• Intersections
• Poisson distribution

4
Data Collection

• Choose your best junk food restaurant
• Choose the busiest time they have
• Study one hour

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Service rate data collection
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Queue length variation
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Data Summary
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Calculations
q arrival rate (veh/h) Q service rate
(veh/h) n total number of vehicles, including
served one
Probability of exactly n vehicles in the system
9
Calculations
q arrival rate (veh/h) Q service rate
(veh/h) n total number of vehicles, including
served one
Average number of n vehicles in the system
10
Calculations
q arrival rate (veh/h) Q service rate
(veh/h) n total number of vehicles, including
served one
Average queue length
11
Calculations
q arrival rate (veh/h) Q service rate
(veh/h) n total number of vehicles, including
served one
Average waiting time in queue after arrival
12
Calculations
q arrival rate (veh/h) Q service rate
(veh/h) n total number of vehicles, including
served one
Average time a vehicle spends in the system
including being served and waiting to be served
13
Calculations
q arrival rate (veh/h) Q service rate
(veh/h) n total number of vehicles, including
served one
Probability of a vehicle spending time, t hours,
or less in the system
14
Calculations
q arrival rate (veh/h) Q service rate
(veh/h) n total number of vehicles, including
served one
Probability of a vehicle spending time, t, or
less in the queue
15
Calculations
q arrival rate (veh/h) Q service rate
(veh/h) n total number of vehicles, including
served one
Probability of more than N vehicles being in the
queue
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Interpret and conclude

• Answer questions in manual
• Prepare your presentation