ing single precision calculation). Therefore, the equilibrium model will locally degenerate to a all-or-nothing assignment, where the slightest change (or error) in free flow time may result in a complete shift of volume from one path to another path. Also, the solution is no longer guaranteed to be unique on the level of link flows, since the volume-delay functions are no strictly increasing functions of the volume any more.

c)

Even though the formula of the BPR function is very simple, its evaluation requires the computation of two transcendental functions, i.e. a logarithm and an exponential function to implement the power , which require a fair amount of computing resources.

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Requirements for a Well Behaved Congestion Function

Are there other types of congestion functions that are not (or are less) subject to the drawbacks of the BPR functions? If yes, how would such a ``designer'' volume-delay function look like? Let us first set forth some conditions these functions need to satisfy:

1. f(x) is strictly increasing. Necessary condition for the assignment to converge to a unique solution.
2. f(0) = 1 and f(1) = 2. These conditions ensure compatibility with the well known BPR type functions. The capacity is thus still defined as the volume at which congested speed is half the free flow speed.
3. f'(x) exists and is strictly increasing. This ensures convexity of the congestion function - not a necessary, but a most desirable property.
4. .

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