The Surge
Decision Explorer
Adjust the prior, distributions, fares, and your observed wait time to see exactly how each parameter shifts the posterior surge probability and your optimal decision. The key insight is often surprising: the wait time tells you less than you think.
The model
Wait times follow exponential distributions under each hypothesis. The exponential is the natural choice for arrival processes — it is memoryless, meaning the time you have already waited contains no information about how much longer you must wait.
Closed-form posterior
For exponential likelihoods the posterior simplifies to a logistic function of the wait time:
The decay rate (λ0−λ1) is always positive when surge slows arrivals, so longer waits always increase the posterior toward 1.
The decision rule
Book the ride if the expected total cost is below the alternative. The threshold wait w* is where the two are equal — an implicit equation solved numerically because the posterior itself depends on w.
Drag the sliders to explore how the threshold moves when fares, time value, or prior surge probability change. You may be surprised how robust the decision is to changes in prior belief, and how sensitive it is to changes in time value.
Surge Decision Calculator
Adjust parameters; the posterior and decision update in real time.