Fundamentals of Transportation/Queueing/Problem1

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

• Solution