Recently, the stationary state of a parallel-update totally asymmetric simple exclusion process with varying system length, which can be regarded as a queueing process with excluded-volume effect (exclusive queueing process), was obtained [C Arita and D Yanagisawa, J. Stat. Phys. 141, 829 (2010)]. In this paper, we analyze the dynamical properties of the number of particles $\langle N_t\rangle$ and the position of the last particle (the system length) $\langle L_t\rangle$, using an analytical method (generating function technique) as well as a phenomenological description based on domain-wall dynamics and Monte Carlo simulations. The system exhibits two phases corresponding to linear convergence or divergence of $\langle N_t\rangle$ and $\langle L_t\rangle$. These phases can both further be subdivided into high-density and maximal-current subphases. The predictions of the domain-wall theory are found to be in very good agreement quantitively with results from Monte Carlo simulations in the convergent phase. On the other hand, in the divergent phase, only the prediction for $\langle N_t\rangle$ agrees with simulations.

• Received 20 December 2010

DOI:https://doi.org/10.1103/PhysRevE.83.051128