Transient analysis of media access protocols by diffusion approximation

We present a transient analysis of media access control (MAC) protocols such as slotted ALOHA and CSMA/CD (Ethernet) by formulating their queueing behavior as an Ornstein-Uhlenbeck process X(t). We also derive an important result on the transient mean m_X(t)=E[X(t)l: if the drift coefficient β(x,t) is a linear function of the system congestion x=X(t), then m_X(t) obtained under the assumption of a homogeneous diffusion coefficient is an unbiased estimate of m_N(t), the mean of the original process N(t), and is independent of the diffusion coefficient α(x,t)