# Fundamentals of Transportation/Queueing/Additional Problems

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## Additional Questions

1. What is a queue?
2. Give examples of queueing in real life.
3. What important variables affect queue length.
4. How do you compute total delay from a Newell Curve? What is vehicle delay? How many vehicles are there in the system at a given time.
5. What are some difficulties with calculating queueing times?
6. Define over and under-saturated?
7. Characterize a queue.
8. Define arrival and service rates.
9. If arrival rates > departure rates, what does that imply.
10. Name three types of statistical distributions that describe the behavior of queues and explain them.
11. Can queueing in succession of a length of road mediate arrival demand which reduces delay?
12. Define congestion.
13. Explain the bus bunching idea in relation to queue.
14. How can you determine if a channel is saturated?
15. What is a loop detector?
1. How do loop detectors communicate with stop lights?
2. How do large vehicles affect queue detectors?
16. When does departure rate depend upon arrival rate?
17. What are examples of service methods?
18. What is the effect of controls systems in series?
19. What is the difference between over and undersaturated queues? Give an example of an oversaturated queue.
20. What is the difference between uncapacitated and capacitated queues?
21. What does the variable ρ mean? What is meant when λ > μ, λ < μ
22. Why is there random congestion if the hourly flow is less than hourly capacity (ρ < 1)?
23. How can constraints be included in predicting how many vehicles are expected in a queue? (i.e. capacity of queue)
24. What happens if the average number of cars exceeds ramp capacity?
25. Do equations change for uncapacitated to capacitated queues?
26. How do you calculate the expected number of units in the system?
27. Explain why E(n) ≠ E(m) in words. Why is the average number of units in the system not the same as the mean queue length?
28. Is the expected number of units in the system an average number of units?
29. When μ and λ are random, what kind of queue is it?
30. What does Poisson refer to?
31. What happens to travel time as arrivals approach capacity?
32. Are most systems under or oversaturated in general?
33. What is the average service time?
34. Graph average travel time vs. rho. How does this relate to the volume delay function in Route Choice.
35. How accurate are these formulas for probability of waiting time and queue length?

## Additional Problems

1. What is probability you will wait 15 minutes or more if on average 15 cars/min arrive and 14 cars/min are serviced
2. What is the average waiting time if there is a 600 vph arrival rate, and a 500 vph service rate.
3. If there is an arrival rate of 100 vehicles per hour, what is the service time?
4. How would you solve for an average time waiting in queue if the arrival rate is 400 vph and service rate is 450 vph?
5. If the arrival rate is 250 vph and the service rate is 600 vph, what is the time for vehicles waiting to get on the system?
6. With the arrival rate of 250 vph and service rate of 275 vph, ho wmuch free time is there on a ramp and how long is the average wait time.
7. Calculate the average number of vehicles (wait) in the system with x arrivals and y departures.