Using a model based upon Poisson arrivals and exponentially distributed service times, some simple values can be derived for this model. The toll booth serves at rate of 500 vph. Plot the expected number of vehicles in the system vs the ratio of arrival to service rate. Interpreting this diagram can provide parameters about the queue. It may be less.
Cumulative departures can never exceed cumulative arrivals.
When a queue is present, there are more complicated situations such as storage areas with limited capacity, servers which turn themselves off and on periodically and servers whose service rate changes with the queue length. However, the 3 items above always apply. Cars arrive at a traffic signal at a rate of 360 vph. The green time is 30 seconds, and the cycle time is 60 seconds. During the green time, vehicles can depart from the queue at a rate of 1200 vph.