Table 2 Key to symbols used

\(\left\{ {\left( {i,j} \right)} \right\}\)

Sets of O-D pairs

\({\mathbf{L}},\mathop {\mathbf{L}}\limits\)

Level of service vector, agreed minimum~

\(\left\{ \tau \right\}\)

Discrete fulfillment time windows

\(d\),\(\delta\),\(\delta_{ij}^{*}\)

Road distance, specific detour factor ≥ 1, detour factor i-j at equilibrium

\(\pi\),\(\pi ^{\prime}\)

Trip party size, extra car passengers taken

\(\alpha\),\(\alpha_{0}\),\(\alpha_{1}\)

Ridesharing supply adoption function and functional parameters

\(T\), \(\overline{T}\)

Person trip count per period, before/after DRT introduction

\(c_{O} ,c_{Eb} ,c_{E\pi ^{\prime}}\)

Unit vehicle operating, external unit costs

\(\vartheta\)

Proportion of non-elective users

\(r_{0} ,r_{1}\)

Passenger transport compensation (fix, unit)

\(P\)

Choice probability

\(w_{P} , w_{D}\)

Passengers’/drivers’ willingness-to-pay

\(V\)

Systematic/observable utility

\({\text{C}},{\overline{\text{C}}}\)

Choice sets before, after market entry

\(B\)

Budget needed to incentivize routes of public interest

\(\sigma_{{\mathbf{L}}} , \sigma_{T}\)

Step functions: relevance of supply, demand

\(m\)

Modal choice option

\(S\)

Supplier surplus if ridesharing is adopted

\({\text{R}}, {\text{R}}^{{\prime }} , {\text{R}}^{{\prime \prime }}\)

\(\left( {i,j,\tau } \right)\) Residuals, Option I

\(\tilde{U}\)

Expected received utility (E.R.U.)