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A four-lane freeway (two lanes in each direction) has the arrival flow rate of λ(t)=40-0.15t (with...

A four-lane freeway (two lanes in each direction) has the arrival flow rate of λ(t)=40-0.15t (with t in minutes and λ(t) in vehicles per minute). At 7 am, an accident occurred in the northbound and blocked both lanes. Twenty minutes later, one lane was opened. At 7:40 am the accident was cleared and both lanes were opened. The capacity of the highway is 2,200 vehicles per hour per lane if not impacted by an accident. (Assuming D/D/1 queuing).

  1. When did the queue caused by this accident completely dissipate?
  2. What is the total number of vehicles affected by this accident?
  3. What is the queue length at 7:30 am?

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