# Fundamentals of Transportation/Queueing/Additional Problems

## Additional Questions[edit]

- What is a queue?
- Give examples of queueing in real life.
- What important variables affect queue length.
- 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.
- What are some difficulties with calculating queueing times?
- Define over and under-saturated?
- Characterize a queue.
- Define arrival and service rates.
- If arrival rates > departure rates, what does that imply.
- Name three types of statistical distributions that describe the behavior of queues and explain them.
- Can queueing in succession of a length of road mediate arrival demand which reduces delay?
- Define congestion.
- Explain the bus bunching idea in relation to queue.
- How can you determine if a channel is saturated?
- What is a loop detector?
- How do loop detectors communicate with stop lights?
- How do large vehicles affect queue detectors?

- When does departure rate depend upon arrival rate?
- What are examples of service methods?
- What is the effect of controls systems in series?
- What is the difference between over and undersaturated queues? Give an example of an oversaturated queue.
- What is the difference between uncapacitated and capacitated queues?
- What does the variable ρ mean? What is meant when λ > μ, λ < μ
- Why is there random congestion if the hourly flow is less than hourly capacity (ρ < 1)?
- How can constraints be included in predicting how many vehicles are expected in a queue? (i.e. capacity of queue)
- What happens if the average number of cars exceeds ramp capacity?
- Do equations change for uncapacitated to capacitated queues?
- How do you calculate the expected number of units in the system?
- 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?
- Is the expected number of units in the system an average number of units?
- When μ and λ are random, what kind of queue is it?
- What does Poisson refer to?
- What happens to travel time as arrivals approach capacity?
- Are most systems under or oversaturated in general?
- What is the average service time?
- Graph average travel time vs. rho. How does this relate to the volume delay function in Route Choice.
- How accurate are these formulas for probability of waiting time and queue length?

## Additional Problems[edit]

- What is probability you will wait 15 minutes or more if on average 15 cars/min arrive and 14 cars/min are serviced
- What is the average waiting time if there is a 600 vph arrival rate, and a 500 vph service rate.
- If there is an arrival rate of 100 vehicles per hour, what is the service time?
- How would you solve for an average time waiting in queue if the arrival rate is 400 vph and service rate is 450 vph?
- 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?
- 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.
- Calculate the average number of vehicles (wait) in the system with x arrivals and y departures.