Queue Length

Before anything else

Read the manual carefully. It is your homework

What is covered in the following slides is just general

General

Customer service analysis (restaurants)

Toll booth Parking garage Intersections Poisson distribution

Data Collection

Choose your best junk food restaurant

Choose the busiest time they have Study one hour

Service rate data collection

Queue length variation

Data Summary

Calculations

Q

q

Q

qn

n

1)Pr(

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

Calculations

qQ

qnE

)(

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

Calculations

)()(

2

qQQ

qmE

q= arrival rate (veh/h)

Q= service rate (veh/h)

n= total number of vehicles, including served one

Average queue length

Calculations

)()(

3

qQQ

qwE

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

Calculations

qQvE

1)(

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

Calculations

qtQ

q

etv

1

1)Pr(

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

Calculations

qtQ

q

eQ

qtw

1

1)Pr(

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

Calculations

1

)Pr(

N

Q

qNn

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

Interpret and conclude

Answer questions in manual Prepare your presentation