Reliability-Based Marginal Cost Pricing Problem Case with Both Demand Uncertainty and Travelers’ Perception Errors

Table 3

A summary of notations.

Notations	Explanations
𝑄^𝑤	Travel demand between OD pair 𝑤∈𝑊
𝑞^𝑤	Mean travel demand between OD pair 𝑤∈𝑊
𝜀^𝑤𝑞	Variance of travel demand between OD pair 𝑤∈𝑊
VMR𝑤	Variance-to-mean ratio (VMR) of the random travel demand
𝐹^𝑤𝑟	Route flow on path 𝑟∈𝑅𝑤
𝑓^𝑤𝑟	Mean traffic flow on path 𝑟∈𝑅𝑤
𝜀𝑓^𝑤,𝑟	Variance of traffic flow on path 𝑟∈𝑅𝑤
𝐟	Column vector of mean route flow, where 𝐟=𝑓^𝑤𝑟
𝑉𝑎	Traffic flow on link 𝑎∈𝐴
𝑣𝑎	Mean traffic flow on link 𝑎∈𝐴
𝜀^𝑎𝑣	Variance of traffic flow on link 𝑎∈𝐴
𝐯	Column vector of mean link flow, where 𝐯=𝑣𝑎
𝛿^𝑤𝑎,𝑟	Link-path incidence parameter; 1 if link 𝑎 on path 𝑟, zero otherwise
TT	Total travel time of the system, where TT=∑𝑎∈𝐴𝑉𝑎𝑇𝑎
VoR	Relative weight assigned to the travel time budget, that is, value of reliability
𝑇𝑎	Travel time on link 𝑎
𝑡𝑎	Mean travel time on link 𝑎
𝑇^𝑤𝑟	Perceived travel time on path 𝑟∈𝑅𝑤
𝑡^𝑤𝑟̃	Mean perceived travel time on path 𝑟∈𝑅𝑤
𝜀̃𝑡^𝑤,𝑟	Variance of perceived travel time on path 𝑟∈𝑅𝑤
𝑇𝑎	Perceived travel time on link 𝑎
𝑡𝑎̃	Mean perceived travel time on link 𝑎
𝜀^𝑎𝑡̃	Variance of perceived travel time on link 𝑎∈𝐴
𝑇𝑇	Total perceived travel time of the system, where 𝑇𝑇=∑𝑎∈𝐴𝑉𝑎𝑇𝑎
𝑡^0𝑎	Free-flow travel time on link 𝑎∈𝐴
𝑐𝑎	Capacity of link 𝑎∈𝐴
𝑦𝑎	Parameter, where 𝑦𝑎=1+VMR/𝑣𝑎
𝜀𝑎𝑇𝑎	Travelers’ perception errors on link 𝑎∈𝐴
𝑁𝜒,𝜛^2	Perception error distribution of traveler, in this study 𝑁𝜒,𝜛^2 follows a normal distribution with predefined and deterministic mean 𝜒 and variance 𝜛^2