Queue Analysis at Toll and Parking Exit Plazas: A Comparison between Multi-server Queuing Models and Traffic Simulation

Multi-server queuing analysis can be used to estimate average wait times and queue lengths at toll and parking exit plazas given arrival rates, number of servers, and service rates. These queuing models approximate the performance of queuing systems with multiple queues. While the queuing equations are useful where there are multiple servers, they do not fully reflect the operation of a toll plaza where vehicles can stack in multiple queues and can change lanes. To gain an understanding of how such a system will operate, a traffic simulation model that reflects the specified vehicle arrival and service rates, and allows for multiple channel arrivals was applied to several parking exit plaza concepts. This paper compares the results obtained from both methods and describes how these estimations compared with queue and waiting time data collected at exit plazas in actual operation. The analysis here described was based on the application of the analytical queuing model in conjunction with traffic simulation in parking exit plazas at four different airports: the Ronald Regan Washington National Airport, the Dulles International Airport, the Salt Lake City International Airport, and the Atlanta Hartsfield International Airport. The measures of effectiveness used to evaluate the models’ performance were average and maximum queuing delay, and average and maximum queuing length. Additionally, the output values, including the throughput volume estimated by the simulation model were compared to collected field values. The paper shows that simulation provides a more comprehensive understanding of the toll plaza operation allowing for a more in-depth analysis of its performance. While the simple queuing models could be used as an initial, in some cases more conservative estimation in early stages of planning, simulation should be used for advance planning, design, operation and management of toll and exit plaza facilities.