We present a non-local version of a scalar balance law modeling traffic flow with on-ramps and off-ramps. The source term is used to describe the traffic flow over the on-ramp and off-ramps. We approximate the problem using an upwind-type numerical scheme and we provide L^\infty and BV estimates for the sequence of approximate solutions. Together with a discrete entropy inequality, we also show the well-posedness of the considered class of scalar balance laws. Some numerical simulations illustrate the behaviour of solutions in sample cases.

翻译：我们提出一个非本地版的天平法,用以模拟在斜坡和离斜坡之间的交通流量。源词用来描述在斜坡和离斜坡之间的交通流量。我们使用上风类型的数字方法来比较问题,我们提供近似解决方案序列的L ⁇ infty和BV估计值。加上离散的环球不平等性,我们还展示了考虑的星际平衡法等级的稳妥性。一些数字模拟显示了抽样案例的解决方案行为。