Improper functioning of traffic signals at the intersections result in extreme congestion leading to increase in overall journey time and wastage of precious fuel. Various algorithms have been proposed in literature for alleviating the problem of congestion. Fixed-time, non-preemptive and preemptive approaches work towards reduction of queue length at the intersections to decrease the overall waiting time on roads. High traffic volume on the road results in large queue length which takes huge amount of time to process using a single processor. Hence, there is a need for fast processing which can be obtained by parallelizing the algorithm. This paper proposes a parallel preemptive algorithm to reduce the average queue length resulting in decrease of overall waiting time. The implementation of parallel algorithm is done using Compute Unified Device Architecture (CUDA) by harnessing the power of Graphical Processing Units (GPUs). The performance of the proposed parallel preemptive algorithm is compared with fixed-time, non-preemptive and preemptive approaches. Obtained results show the reduction in queue length in case of the proposed algorithm which is also confirmed using T-test with 99% confidence. (C) 2016 Elsevier Inc. All rights reserved.