Time-dependent models are of great importance in highway engineering as they are appropriate for evaluating waiting times and queue lengths at intersections,which are integral parts of various activities in planning,verification and decision support for infrastructure.After reviewing the literature of the main time-dependent models based on the coordinate transformation method and a discussion about some computational issues in time-evolution profiles for non-signalised intersections,the paper identifies the re-quirements these models have to satisfy in order to be used as“basic”cases for analysing complex evolutionary situations.Three“basic”cases are presented with their time-dependent equations for vehicle waiting times and vehicle number;they have been completed and dimensionally homogenised in this paper.As they are recursive,these formulas can be applied for sequential intervals in the time domain in both vehicles and passenger car units.The closed-form expressions for state variables show to be mutually equivalent in comparison with discrete event simulation models and imbedded Markov chain results.For all the three models the paper presents a common deterministic simplification for average waiting time,with good approximation results in the tested cases.The proposed time-dependent formulas will contribute to a better adherence to the real phenomena,compared to the extremely simplified and unrealistic methods suggested by the international manuals for level of service assessment.The proposed formulas will be useful for current applications and possible future development in order to meet the emerging needs of road and transport engineering.