Car Parks - Analysis and Optimisation

(updated  31st August 2007)

Keywords: simulating people, simulating crowds, simulating crowd dynamics

The following example is a case study in car park analysis.

Step 1. We begin with a CAD plan of the car park.

Step 2. We convert this (via Myriad) to a free space map.

Step 3. We run a Spatial Analysis and generate a utilisation map.

The red areas are utilised 100% the black areas utilised < 20%. This is a least effort/direct path to the exit analysis. The purpose of creating this map is to determine the optimal design criteria and assess how far this specific design/layout may be from the optimal.

Step 4. Utilisation analysis.

We assess the >80% interaction spaces (Red - probability of a delay/interaction/collision is greater than 1) the areas between 50% and 80% interaction (yellow). Between 20% and 50% interaction (turquoise) and those below 20% (blue).

From our model we can determine the probability that each square metre of space will encounter more than one car in at any given moment (taking the superposition of all possible utilisation factors - ingress/egress and general circulation solutions).

The final row in the table above gives us an indication of the space that is not being used in an optimal manner. This analysis is relevant to risk associated with delay (frustration) of using this car park.

There are a number of metrics we can determine from this analysis. For example.

Distance to exit by row (the horizontal axis is left to right from the plan and the distance from each simulation run is plotted against the distance scale - we have tested  3,000 simulation runs for random start location against the probability of delay encountered during ingress/circulation and egress).

From the graph above we can ascertain that there are two slope (on from distances to the left of the exit, the other from the right. The slope determines our overall efficiency (high slopes have disproportional utilisation of space). The optimal design would not be biased - clearly the right hand side is much easier to navigate, the left hand side has much higher average travel distances. When parking a car the driver would encounter a longer route, more probability of interactions and a higher level of frustration. To optimise this design we need to change the location of the exit to make both left and right unbiased in the utilisation factor.

We can also test the car park layout on the vertical distances (from each point to the exit).

We can see from the above analysis that the slope on this graph indicates that we could improve the layout. In effect the flatter the slope the more evenly the car parking will be, the less frustrating and the less probability of two cars trying to occupy the same space. The principles here are Least effort and minimum interactions. Clearly the ideal design would be fair for all.

Combining the above into a single analysis for all space (the first graph shows the system left to right, the second from front to back the graph below is the overall efficiency of the design).

We can determine other values for efficiency from the following relationships. This process uses a Matrix map of the horizontal, vertical and test distances- (1,2 and 3 below) and provides a picture of the area to utilisation from our tests.

We can also examine the ease of use for the pedestrian to car routes.

Step 5. Pedestrian routing analysis.

This map above is the pedestrian least effort routes (path from car to store entrance).

We now superimpose this against the car utilisation map to produce a pedestrian/traffic interaction map of this area. Again >80% utilisation on this map indicates a greater than 1:1 probability of a person and a car trying to occupy the same space at the same time.

This map tells us ALL combinations of pedestrian and traffic interactions. Some areas are used less (hence have fewer pedestrians/cars) others have more utilisation hence have much more pedestrian/traffic interactions. By this process we can determine the best location for lanes/trolley parking bays/traffic calming measures and safe walkways.

Step 6. Testing routes

We can test a route for probability of interaction by drawing a line from any point to any other point in the design. To the left below we have a route to the store entrance using the least effort path (shortest distance). The the right we have a route to the store taking the maximum walkway path. Other routes that can be tested include minimum interaction routes (the safest route) which is an output from the system (it draws the safest routes for you).

Analysis of the above. Route 1 (below left) and Route 2 (below right). Reading from left to right (travel distance) the peaks are the exposure to conflict (people and car in the same place at the same time) as a probability distribution analysis. We are testing relative risk along both routes using probability of conflict as our metric.

These two graphs indicate the interactions on a 0-100% probability scale. What is interesting is that the route taking the pedestrian along the walk way will encounter a very high probability of a person/car interaction in a very small distance. This is the "risk" element in the design. By taking a wide cross section of these graphs we can build up a risk of interaction map (between people and cars). The last stage of this analysis is that map.

Step 7.  Overall interaction map of the Car Park design/Risk Map.

The map above is the topographical map (read it like a ordinance survey map - the closer the lines are together - the higher the rate of change from low probability of interaction to high probability of interaction). These areas have the highest risk factors as they are sudden changes in the utilisation of space. We obtain numerical results from the above by applying the isophotic map which truncates all space below a threshold. We call this a risk map which indicates the highest risk of a person and a car being in the same place at the same time. Again >80% utilisation on the risk map is a greater than 1:1 probability of accident in that space.

We can read the values (and slide the scales up and down - see below) to determine that 67.88 m2 of this area has a greater than 1:1 probability of interaction between pedestrian and car. This does not indicate that there will be an accident - but it does indicate where and what proportion of this space has a high risk associated with pedestrian and traffic.

To make this clearer to understand we can contour the surface and then rotate it around an axis.

Highlighting the problems areas in a visual manner. We can perform this type of analysis on car parks, stations, shopping malls, towns, transport terminals, traffic calming, congestion charging schemes and many, many other pedestrian and traffic designs.

Analysis of existing car parks

Every Christmas we get stuck in this car park (DeepDale in Preston) for over two hours at the end of the day rush. The study below shows the main reasons why this design is far from optimal.

First we grab the relevant area and, using the isophotic mapping process, highlight the road network. The analysis will consist of a congestion (network) analysis and a spatial utilisation analysis. Together these two processes represent the overall picture of how the car park fails during evening rush hour.

Interaction contour map                                  Exit analysis map

We perform a spatial analysis and find that 20.8% of the area of this car park has travel distances greater than 300 metres (blue areas above). The analysis graphs are shown below.

The regression analysis tells us the confidence limits for our test. We have 87.6% statistical confidence that our slope and intercept are correct for this design. Given that we are using a satellite image for our car park analysis this is a reasonable goodness of fit for a rough cut efficiency analysis.

By applying a route analysis along the network from a variety of test points we construct the graph below.

The graph above gives a clear indication of how progress is increasingly fraught with delays/interactions as a car travels from a parking space to the single exit. An ideal car park would have an inverted slope (less interactions over distance during exit). For normal and emergency evacuation analysis the slope on this graph is a key metric for the egress efficiency. This car park would fail that metric. We can also see from the configuration of the feed roads that every car on the feed roads will inhibit the egress for ALL cars on the main route out. A simple network analysis of this car park demonstrates several flaws in the efficiency.