Adjustment of freeway ramp metering rates to balance entrance ramp queues

IN A FREEWAY RAMP METERING SYSTEM THE VARIABLES WHICH CAN BE CONTROLLED ARE THE ENTRANCE RAMP RATES. IN ORDER TO AVOID CONGESTION ON THE FREEWAY THE RAMP RATES SHOULD BE KEPT BELOW CRITICAL LEVELS. TO CONTROL QUEUE BUILDUP, IT IS NECESSARY TO CONTROL THE DIFFERENCE BETWEEN DEMANDS AND RAMP RATES. SINCE DEMANDS ARE UNCONTROLLABLE, THIS IMPLIES THAT RAMP RATES SHOULD BE KEPT AS HIGH AS POSSIBLE TO LIMIT QUEUES. IT IS SHOWN THAT THESE CONFLICTING OBJECTIVES IN THE SELECTION OF RAMP RATES CAN BEST BE COMPROMISED BY SOLVING A QUADRATIC PROGRAMMING PROGRAM. THE RAMP RATES ARE SELECTED TO MINIMIZE THE SUM OF THE SQUARES OF THE DIFFERENCES BETWEEN THE RAMP RATES AND THE CORRESPONDING EQUIVALENT DEMANDS. AN EQUIVALENT DEMAND IS DEFINED AS THE ACTUAL DEMAND PLUS THE RATIO OF THE NUMBER OF QUEUED VEHICLES DIVIDED BY THE TIME BETWEEN ADJUSTMENTS OF THE RAMP RATES. THIS MINIMIZATION IS PERFORMED SUBJECT TO THE CONSTRAINT THAT THE RAMP RATES ARE KEPT LOW ENOUGH THAT NO FREEWAY CONGESTION OCCURS. /AUTHOR/