an algorithm of lane change using two-lane nasch model in traffic networks 13/11/2013
TRANSCRIPT
NaSch model
• Step 1: Acceleration.• Step 2: Slowing down.• Step 3: Randomization. • Step 4: Vehicle motion.
Assumptions
• There are sufficient time and space to perform lane change • Each cell of the road has two states: occupied or not occupied
by a vehicle (at most one vehicle). • The maximum velocity of vehicles is one cell per timeslot
Three Algorithms
(1) Tail to Header Lane Change (THLC).(2) Header to Tail Lane Change (HTLC).(3) Random Lane Change (RLC).
Algorithm of THLC
• Input: I, an array of N ×2• Output: L, the operation of each row.• Part 1: from the tail to the header• Case A: uncertain vehicles• Case B:• Case C:• Part 2: from the header to the tail• With respect to Case A, determine which vehicles
should brake.
THLC is optimal
Proof:1)Assume there exists one optimal algorithm O, which is different from THLC.2)We construct O’, which is modified from O.3)We prove that O’ is not worse than O.4)It is contradictory to our assumption.5)Therefore, THLC is optimal• XTHLC = {N,N-1, …, i + 1, i,… , j,…, 1}(N > i > j > 1).
• XO = {N,N-1, ..., i +1, j,…, i,…}.
• XO ′= {N,N−1,..., i+1, i, j,...}
Conclusion
We introduce three lane change algorithms: THLC, HTLC, and RLC.
THLC is optimal, and we prove it.Through simulations, the performance of
THLC is improved by 75% than RLC, and 92% than HTLC.
Future work
• In the future, we would add more parameters, e.g., maximum velocity, maximum acceleration.
• And the range of research would be extended to multi-lane in highways and urban roads.