Caditz/Newman

Our thoughts about autonomous vehicles and traffic flow

Golden Gate Bridge Vista Point Backups

What M/M/c queuing theory tells us about traffic on the Golden Gate Bridge

 

       

  

 

My wife and I are blessed with one of the most iconic commutes in the world. The Golden Gate Bridge separates home and work. Beautiful sunsets, world-class views, the shining sunlit San Francisco skyline, filled with high-tech promise, piercing a river of thick grey fog. More than ten million people visit the Golden Gate Bridge annually. Summer brings high season and it seems that everyone wants to visit Vista Point with its straight-on city views across the beautiful San Francisco Bay. Vista Point is the first Northbound exit after passing the Golden Gate Bridge’s northern anchorage.

Google maps shows that Vista Point has 122 single car parking spaces. Likewise, we can measure a roadway distance of 1200 feet for the on ramp plus parking lot loop. Assuming each car uses 12 feet of the roadway’s length, Vista Point’s driveway can accommodate a queue of about 100 cars waiting for parking. Any more would back up onto Highway 101, blocking its rightmost lane and causing a bottleneck for Northbound traffic. (Drivers usually ignore the largely unenforced California Vehicle Code Section 22500-22526 which prohibits stopping on a highway off-ramp or a bridge.)

 

  

M/M/c queuing theory allows us to estimate average queue length and wait times for the Vista Point. Let’s assume that, on average, each parking space accommodates μ=2 vehicles per hour (VPH). It is easy to show that the queue becomes unstable, i.e., grows unbounded, when the average vehicle arrival rate, λ, exceeds:

λ =  cμ = 122 spaces ×2 VPH/space  = 244 VPH

A 2013 study commissioned by the Golden Gate Bridge Highway and Transportation District puts the average weekday peak volume at 104 VPH. This figure, uncomfortably close to the critical value, will inevitably be higher during peak season and on weekends. Once the critical arrival rate is exceeded, a traffic queue will back up onto Highway 101, blocking the rightmost lane and creating a bottleneck which can slow northbound traffic to a crawl.

This analysis assumes that the average parking space occupancy time is equal to the length of stay of the visiting passenger group. However, if entry is limited to taxis, ride sharing services and, in the future, connected autonomous vehicles, which, on average spend 4 minutes dropping off or picking up passengers, the critical vehicle arrival rate would increase to

λ =  cμ = 122 spaces ×15 VPH/space  = 1830 VPH

This figure would be even greater if curb space in addition to parking spaces were used for passenger loading.

The Golden Gate Bridge Highway and Transportation District recognizes this situation and, apparently with some effort, has obtained permits from Caltrans to restrict Vista Point traffic to busses and ride sharing vehicles on some of the busiest summer weekends. While the restrictions had some positive effect, many drivers simply diverted to the next Alexander Avenue exit, resulting in similar backup situations while drivers competed for even fewer parking spaces and taking even longer time walking to and from Vista Point.

Once again, it seems that the best solution is to reduce parking space occupancy times by decoupling them from visitor staying times – in other words eliminating low-utilization personal automobiles in favor of mobility as a service.