The average cost to the user is more or less the same for private and public transport, even though the balance between costs of time and other costs is very different. Public transport is cheaper but takes longer.
Figure 2 compares perceived rather than actual costs.
For car users, little of the non-time cost is perceived at the time of travel. Parking costs if any are perceived. Perhaps half the cost of the fuel is perceived (and even that may be an over-estimate) and nothing else. The major annual charges are usually perceived as sunk costs not connected with usage, and depreciation may not be perceived at all.
However for public transport users, the major element of cost is perceived as being higher than it actually is. Time passes slowly when you are waiting for a train or bus. It is usual in behavioural modelling to double access (walk) time, more than double waiting time and add about ten minutes on for each interchange in arriving at the "perceived" travel time for a journey. If walk and wait time are doubled and interchange is ignored (thus underestimating), the perceived difference between the modes becomes as shown in Figure 2.

Figure 2: Perceived user costs for average peak trip by public and private transport in Sydney 1991
The perceived cost difference is at least three to one, even though the actual costs are roughly the same. It's not that bad, it just seems to be.
Therefore to improve public transport use, it is particularly necessary to adress the things which cause this disadvantage - the access times (implying greater coverage by road-based services) ; the wait times (implying reliability, higher frequencies and perhaps smaller vehicles) ; the need for interchange ; and the relation of road pricing to road use. These are more important than increasing bus or train speeds.
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