In this paper, we examine the operation of a node relaying packets from a number of users to a destination node. We assume that the relay does not have packets of its own, the traffic from the users is saturated and we have random access of the medium with slotted time. We study the impact of the relay node on the throughput per user and the aggregate throughput for the group of users. We obtain analytical expressions for the arrival and service rate of the queue of the relay, the stability conditions and the average length of the queue. We quantify the above, analytically and through simulations, for different numbers of users and different transmission characteristics of the users and the relay and give the conditions under which there are significant advantages from the deployment of the relay.