An Algorithm of Lane Change Using Two-Lane NaSch Model in Traffic Networks

13/11/2013

Additional road space when lane change is finished

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NaSch model

• Step 1: Acceleration.• Step 2: Slowing down.• Step 3: Randomization. • Step 4: Vehicle motion.

Three cases in one row of the road

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Two operations of Case A

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Two operations of Case B

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Operation of Case C

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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).

Results of Case A using two operations.

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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

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HTLC

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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,...}

Simulations

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ϕ: Additional road space (q = 100%).

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ψ: Number of times vehicles have to brake (q = 100%).

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ϕ: Additional road space when p varies with Density fixed (q =70%).

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ψ: Number of times vehicles have to brake when p varies with Density fixed (q = 70%).

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ψ: Number of times vehicles have to brake when q varies with p fixed (Density = 80%).

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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.

The End

• Thanks