# Waze Coverage Notes --- ### How to differentiate *no congestion* from *no wazer*? | | Congestion | No Congestion | |----------|:----------:|:-------------:| | Wazer | Signal | No Signal | | No wazer | **No Signal** | No Signal | --- We want to gauge the probability to observe a congestion $$P_w $$ which is strictly related with the existence of a wazer in the segment. --- $P_w \sim 1$ , then $P(\text{No Wazer and Congestion}) \sim 0$ $P_w \sim 0$ , then $P(\text{No Wazer and Congestion}) \sim 1$ --- Let's say that for a segment, $s$, there were $C$ true congestions, but only $C_w$ were observed by waze. Then, $$C_w = P_w C $$ --- ### Rule of Thumb Proposal: If the segment had few congestions during the year ($C_w$), than wazers in the segment are rare ($P_w$). $$P_w \propto C_w $$ --- ### Theoretical View: --- The probability of detecting a congestion is the probability of a wazer ($w$) to go through the congestion. Given the probability of a waze user in a vehicle (Waze density, $\rho$), then $$P_w = P(w \geq 1; v, \rho)= 1 - P(w = 0; v, \rho)$$ --- If each wazer is a bernoulli trial with probability $\rho$, then a repeated bernoulli trial can be written as binomial, thus, $$P_w = 1 - \binom{v}{0}\rho^0(1-\rho)^v $$ $$P_w = 1 - (1-\rho)^v $$ --- For a range of cars that might go through the segment in a given time ($v_{min}, v_{max}$), then $$P_w = \frac{\sum_{v=v_{min}}^{v_{max}} 1 - (1-\rho)^v}{v_{max}-v _{min}} $$ ---  --- Since we are interested in congestions of more important regions of the city, i.e. more traffic -> more vehicles. Even with Waze densities of 0.01 we have a good chance of identifiying the congestion