Fundamentals of Transportation/Queueing/Problem1

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TProblem
Problem:

Application of Single-Channel Undersaturated Infinite Queue Theory to Tollbooth Operation. Poisson Arrival, Negative Exponential Service Time

  • Arrival Rate = 500 vph,
  • Service Rate = 700 vph

Determine

  • Percent of Time operator will be free
  • Average queue size in system
  • Average wait time for vehicles that wait

Note: For operator to be free, vehicles must be 0