Efficient coordination of actuating elements is a prerequisite for modern automotive control units in order to deliver the requested torque for propulsion during all driving conditions. Embedded control requires fixed time step solution of the model equations. Literature lacks flexible fixed time step modeling solutions for multiple friction elements. This book proposes a solution to generic modeling of automotive step-ratio transmission topologies. A discontinuous event solver enables fixed time step execution in the presence of multiple friction elements. A generic observer concept sufficing with a single observer gain matrix enables system state and input disturbance estimation. Verification and validation of the modeling approach demonstrates the necessity and effectiveness of the discontinuous event solver to safely detect locking events of friction elements. Applications of the modeling approach implemented in a transmission control unit prove suitability for real-time execution and accuracy for driveability evaluation and control.