Traffic Congestion Evaluation and Signal Control Optimization Based on Wireless Sensor Networks: Model and Algorithms

Table 1

Nomenclature and symbols.

𝑥∈[0,𝐿𝑒]	Location in road segment
𝑢(𝑥,𝑡)	Traffic flow speed
𝑥𝑖(𝑡)	Vehicle trajectory
𝑃(𝑥,𝑡)	Estimated traffic data
𝑢	Equilibrium speed
𝑝(𝜌)	Traffic pressure
𝑆(𝑘)	Sensor readings at time 𝑘
𝑡up,𝑡down	Time signals exceed threshold
Δ𝑡,Δ𝑥	Temporal-spatial scales
𝑒^𝑚𝑘	Error from sensor k of vehicle m
𝜂=(𝑠−𝑥𝑡)/𝜏	Self-similar variable
𝑔^𝑙𝑖,𝑔^𝑢𝑖	Min/max green time
𝐽𝑚(𝑘)	Cost function on lane m
𝑞^𝑗out(𝑘)	Outflow in phase j
𝑑𝑖(𝑘)	Demand flow in phase j
𝑆^𝑔𝑛𝑖	Saturation flow for green
𝜉𝑛𝑖(𝑘)	Existing phase state
𝑡∈[0,+∞)	Observation time
𝜌(𝑥,𝑡)	Traffic density
𝑝(𝑥,𝑡)	Traffic data
𝜌𝑀	Maximum traffic density
𝑢𝑓	Free speed on empty road
𝑠(𝑥,𝑡)	Flow production rate
ℎ(𝑘)	Vehicle detection threshold
𝑑(𝑘)	Detection flag
𝑢^𝑚𝑘	Speed of vehicle m at sensor k
𝐸𝑘	Mean square error (MSE)
𝐶^𝑖𝑐𝑓(𝑡)	Congestion factor of lane i
𝐺𝑖	Effective green time
𝑞^𝑗in(𝑘)	Inflow in phase j
𝑞^𝑖𝑠(𝑘)	Arrival traffic flow at stop line
𝑠𝑗(𝑘)	Exit flow in phase j
𝑆^𝑦𝑛𝑗	Saturation flow for yellow
𝑙𝑛𝑖(𝑘)	Queue length in phase i