In this paper, we investigate the performance of networks built from single-channel devices that use wireless access in vehicular environment protocols. We consider several traffic combinations, each of which presents a mix of traffic classes, over control and service channels. Our results show that time switching between the channels causes synchronization of backoff processes, which increases the frame collision probability, in particular for small sizes of contention windows. We also evaluate the impact of the interruption of the backoff process by inactive channel time, which gives rise to a probability distribution with repeated tails and a coefficient of variation larger than 1. Our model can also be used to evaluate different sets of enhanced distributed channel access parameters and to select the channel duty cycle according to the policy of the network operator.