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Medium access control (MAC) is a challenging problem in vehicular environments due to a constantly changing topology due to vehicle's mobility and stringent delay requirements, especially for safety-related applications (e.g., for vehicular-to-vehicular communication). Consequently, topology-independent TDMA MAC policies that guarantee a number of successful transmissions per frame independently of the underlying topology, can be regarded as a suitable choice for the particular vehicular environment. One such policy (TiMAC) is revisited and considered in this paper for a vehicular environment and is also extended to one that considers disjoint frames depending on the vehicle's direction of movement (d-TiMAC). Both TiMAC and d-TiMAC are evaluated against VeMAC - a well-established TDMA MAC protocol in the area of vehicular networks - based on simulations. It is observed that throughput under the considered TiMAC policy is close to that induced by VeMAC, whereas the number of retransmissions is reduced leading to a smaller time delay. Furthermore, the proposed d-TiMAC appears to achieve a higher throughput than VeMAC, and an even lower number of retransmissions (when compared to TiMAC), suggesting that d-TiMAC yields an even smaller time delay. Eventually, this observation is also supported when d-TiMAC is compared against TiMAC showing a further reduced number of retransmissions. (C) 2018 Elsevier B.V. All rights reserved.