The Hanshin expressway21 serves the Osaka– Kobe area of Japan. Due to heavy congestion, the number of vehicles entering at each ramp j = 1,c, 38 of the expressway is controlled by a system that reevaluates the situation every 5 minutes based on current queue lengths qj at each ramp and estimated number of new entry-seeking arrivals dj over the next 5 minutes.

The system enforces end-of-period queue-length limits uj and total traffic capacities bi on 500-

meter segments i = 1,c, 23 of the highway.

Traffic entering at j affects only down-stream segments, and a part may exit before reaching any given i. Prior engineering studies have captured this behavior in estimated fractions fi, j of vehicles entering at j that persist to consume capacity at i. The system seeks the feasible control policy that permits the maximum total number of entry-seeking vehicles into the expressway during the next time period. Formulate an LP model of this traffic control problem using the decision variables 1j = 1,c, 382 xj ! number of vehicles allowed to enter at ramp j during the time period