## queueing flow and queue length [closed]

Hello everybody,

I do not know if someone can help me. I have an exercise to do but I am stuck:

a) Explain the meaning of each of deterministic arrivals and stochastic arrivals.
(10 Marks)

b) Consider the motorway section shown in Figure 2. Location A has a capacity of 6000 vehicles/h , and the traffic demand d0 on the mainline is 4800 vehicles/h . Inflow d1 from an entrance (on-ramp) connecting to a sports stadium is initially zero.

Figure 2: Motorway section with an entry ramp

Suppose that a sporting event at the stadium finishes at time 0 when d1 increases from zero to 1700 vehicles/h and this demand surge lasts for 45 minutes, after then d1 drops back to zero. You may assume that the traffic queue takes up no physical space:

i) Sketch the cumulative inflow and cumulative outflow at location A from time 0 to the time when the queue due to the demand surge clears.
(10 Marks)

ii) Determine the maximum queue length during the period. (10 Marks)

iii) Determine the maximum delay. (20 Marks)

iv) Determine the time when the queue clears. (10 Marks)

v) Determine the total system delay. (25 Marks)

vi) Suggest and comment on a strategy to manage the congestion on the motorway.