A PROBLEM OF INTERFERENCE BETWEEN TWO QUEUES

A TWO-LANE ROAD IS ASSUMED TO BE OCCUPIED MAINLY BY PLATOONS OF CARS TRAVELLING ALONG THE TWO OPPOSITE DIRECTIONS AT CONSTANT SPEEDS. A SINGLE CAR IS ASSUMED TO TRY TO MOVE AT A SPEED HIGHER THAN THAT OF THE OTHER CARS MOVING IN ITS DIRECTION. IT CAN PASS ONLY WHEN THERE IS ENOUGH ROOM FOR IT WITHOUT BREAKING UP A PLATOON IN EITHER DIRECTION. THE SIZES OF THE PLATOONS ARE SUPPOSED TO BE GIVEN BY A BOREL DISTRIBUTION (E. BOREL, COMPTES RENDUS ACAD. SCI. PARIS, VOL. 214, 1942, PP. 452-456). AN INTERESTING RESULT IS THAT WHEN THE TRAFFIC FLOWS INCREASE BEYOND A CERTAIN LEVEL, APPRECIABLY BELOW THE THEORETICAL CAPACITY OF THE ROAD, THE "FAST" VEHICLE CANNOT MOVE ANY FASTER THAN THE OTHER VEHICLES. IT SPENDS MOST OF ITS TIME WAITING FOR AN OPPORTUNITY TO PASS, AND THE MEAN WAITING TIME UNTIL PASSING GOES TO INFINITY. THE AVERAGE SPEED WAS TABULATED AFTER NUMERICAL COMPUTATIONS CORRESPONDING TO A WIDE RANGE OF THE CONSTANTS OF THE MODEL. THESE NUMERICAL RESULTS LEAD TO TWO GENERAL CONCLUSIONS: FIRST, THAT INCREASING THE ACCELERATION CAPABILITY EVEN AT THE EXPENSE OF REDUCING THE MAXIMUM SPEED, (E.G., BY LOWERING THE TOP GEAR RATIO), WOULD RESULT IN INCREASED JOURNEY SPEEDS FOR MOST MODERN CARS UNDER TYPICAL TRAFFIC CONDITIONS. AND SECOND, THAT REDUCING THE SAFETY MARGINS IN PASSING WOULD NOT NORMALLY PROVIDE ANY WORTHWHILE INCREASE IN MEAN JOURNEY SPEED.

• Supplemental Notes:
  • Vol 40, pp 58-69
• Authors:
  • TANNER, J C
• Publication Date: 0

Media Info

• Serial:
  • Biometrika /UK/
  • Issue Number: 0

Subject/Index Terms

• TRT Terms: Passing; Queuing; Traffic congestion; Traffic flow; Traffic platooning; Traffic speed; Two lane highways; Waiting time
• Old TRIS Terms: Traffic interference
• Subject Areas: Highways; Operations and Traffic Management;

Filing Info

• Accession Number: 00225264
• Record Type: Publication
• Files: TRIS
• Created Date: Feb 16 1970 12:00AM