Gipps' model is a mathematical model for describing car-following behaviour by motorists in the United Kingdom.

The model is named after Peter G. Gipps who developed it in the late-1970s under S.R.C. grants at the Transport Operations Research Group at the University of Newcastle-Upon-Tyne and the Transport Studies Group at the University College London.

Gipps' model is based directly on driver behavior and expectancy for vehicles in a stream of traffic. Limitations on driver and vehicle parameters for safety purposes mimic the traits of vehicles following vehicles in the front of the traffic stream. Gipps' model is differentiated by other models in that Gipps uses a timestep within the function equal to ${\displaystyle \tau }$ to reduce the computation required for numerical analysis.

The method of modeling individual cars along a continuous space originates with Chandler et al. (1958), Gazis et al. (1961), Lee (1966) and Bender and Fenton (1972), though many other papers proceeded and have since followed. In turn, these papers have bases in several works from the mid-1950s. Of special importance are a few that have analogies to fluid dynamics and movement of gases (Lighthill and Whitman (1955) and Richards (1956) postulated the density of traffic to be a function of position; Newell (1955) makes an analogy between vehicle motion along a sparsely populated roadway and the movement of gases). First mention of simulating traffic with “high speed computers” is given by Gerlough and Mathewson (1956) and Goode (1956).

The impetus for modeling vehicles in a stream of traffic and their subsequent actions and reactions comes from the need to analyze changes to roadway parameters. Indeed, many factors (to include driver, traffic flow and roadway conditions, to name a few) affect how traffic behaves. Gipps (1981) describes models current to that time to be in the general form of:

which is defined primarily by one vehicle (noted by subscript n) following another (noted by subscript n-1); reaction time of the following vehicle ${\displaystyle \tau }$; the locations ${\displaystyle x_{n}(t)}$, ${\displaystyle x_{n-1}(t)}$ and speeds ${\displaystyle v_{n}(t)}$, ${\displaystyle v_{n-1}(t)}$ of the following and preceding vehicle; acceleration ${\displaystyle a_{n}(t+\tau )}$ of the following vehicle at time ${\displaystyle (t+\tau )}$; and finally, model constants ${\displaystyle l_{n}}$, ${\displaystyle k}$, ${\displaystyle m}$ to adjust the model to real-life conditions. Gipps states that it is desirable for the interval between successive recalculations of acceleration, speed and location to be a fraction of the reaction time which necessitates the storage of a considerable quantity of historical data if the model is to be used in a simulation program. He also points out that the parameters ${\displaystyle l_{n}}$, ${\displaystyle k}$ and ${\displaystyle m}$ has no obvious connection with identifiable characteristics of driver or vehicle. So, he introduces a new and improved model.

Gipps’ model should reflect the following properties:

Gipps sets limitations on the model through safety considerations and assuming a driver would estimate his or her speed based on the vehicle in front to be able to come to a full and safe stop if needed (1981). Pipes (1953) and many others have defined following characteristics placed into models based on various driver department codes defining safe following speeds, known informally as a “2 second rule,” though is formally defined through code.