Wireless sensor networks (WSNs) consist of a large number of sensor nodes which communicate via wireless links for monitoring applications. In several applications, such as the monitoring of pipelines or roads, the network topology is linear. This type of WSN is called linear sensor network (LSN). Our goal is to improve the behavior of a MAC protocol for LSNs, by using a token approach. As usual, the possession of the token grants the node permission to transmit on the medium during a given amount of time. The payload of the token is used to propagate network parameters such as delay between tokens, sleep and wakeup calendar. In this paper, we study the behavior of this MAC protocol and we evaluate the impact of the node position on the packet delivery for two types of LSNs.