On the One Dimensional Poisson Random Geometric Graph

Figure 1

Queueing representation of the model. A down arrow denotes that user 𝑖 starts his service. An up arrow indicates that user 𝑖 leaves the system without having finished the service. A double up arrow illustrates that the service of user 𝑖 finishes. Beginning and end of the 𝑖th busy period, respectively, 𝐴_𝑖 and 𝐸_𝑖, are also shown.