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Enforcing Liveness in Autonomous Traffic Management Appendix: Proofs of the Theorems
 

Summary: Enforcing Liveness in Autonomous Traffic Management
Appendix: Proofs of the Theorems
Abstract
This file contains the proofs of the theorems in a paper en-
titled "Enforcing Liveness in Autonomous Traffic Manage-
ment" that appears in the proceedings of Twenty-Fifth Con-
ference on Artificial Intelligence (AAAI-11).
Liveness of the Batch Policy with Locking
Theorem 1 When an intersection manager in AIM uses the
batch policy with locking, a vehicle will eventually get a
reservation if every vehicle resends a request message after
receiving a reject message.
Proof. The cost function we used in the batch policy is
f(wait) = aŚ(wait)b
,
where a and b are positive constants and wait is the esti-
mated amount of time the vehicle has been waiting to enter
the intersection. This cost function is a monotonically in-
creasing function. Therefore, the cost strictly increases with
the time a vehicle spends waiting at the intersection. If a ve-

  

Source: Au, Tsz-Chiu - Department of Computer Sciences, University of Texas at Austin

 

Collections: Computer Technologies and Information Sciences