Mobile edge computing (MEC) is a promising computing paradigm for improving the quality of service (QoS) of a vehicular ad hoc network (VANET). The local delay is one of the major components in the delay for a node to transmit a data packet to another node. This project proposes the modeling and analysis of the downlink local delay in an MEC based highway road scenario. A theoretical model is built based on stochastic geometry for analyzing the average downlink local delay for a vehicle driving on a highway road to receive a data packet from an edge node along the highway road. In deriving the model, the spatial distributions of vehicle nodes and edge nodes are respectively modeled as an independent one-dimensional (1-D) homogeneous Poisson point process (PPP).A nearest transmitter model is used to determine the edge node for transmitting a computing result to the corresponding service requesting vehicle node. Moreover, a carrier sense multiple access (CSMA) mechanism is considered for channel access. The derived theoretical model is validated through simulation results and the impacts of major parameters on the average downlink local delay are investigated based on the derived model. The built model provides an insight into the deployment of edge nodes in order to reduce the downlink local delay and provide timely network services.