Internet Data Transport - From the Perspective of Discrete Mass Transport Modeling

In recent years a new class of one-dimensional cellular automata (CA) models has attracted much attention. These so-called mass transport models can be characterized as nonequilibrium stochastic processes. In the presented thesis a new model of this class, the Asymmetric Multi Occupation Process (AMOP) is considered. This CA model was first introduced with open boundary conditions to simulate Internet data transport. It is defined on a one-dimensional lattice equipped with buffers of finite size that can be occupied by at most B particles. The local dynamics are implemented by the totally asymmetric shift of discrete mass variables respectively particles under consideration of hard-core repulsion and parallel dynamics. In the first part of this work the AMOP with periodic boundary conditions is investigated by means of numerical as well as analytical considerations. Regarding deterministic model dynamics the influence of finite buffer and system sizes onto the fundamental diagram (FD), i.e., flow-density relation is analyzed. Furthermore, for stochastic movement the FDs obtained by numerical simulations are compared with analytical results derived by Mean-Field (MF) approaches and a 2-cluster approximation. In the second part the AMOP with open boundary conditions is investigated in the context of boundary induced phase transitions. In case of deterministic bulk dynamics an analytical exact representation of the system inflow as well as the outflow is presented in dependence of the buffer size. As a result the deterministic phase diagram derived by numerical simulations could be verified by analytical considerations. Regarding stochastic particle movement the phase diagram is obtained by Monte Carlo simulations. In both cases it is shown that the jammed phase is strongly enlarged for increasing buffer sizes. Finally, in the third part of this thesis the influence of interacting boundaries on the model dynamics is analyzed. Therefore, a new fall back inflow strategy is introduced in order to stabilize high flow states and thus prevent the system from a complete jamming. Precisely, the inflow is determined by the state of the last site of the system. As a result the phase diagrams of the deterministic and the stochastic model obtained by means of numerical simulations are presented. Two new phases could be identified a free-flow as well as a jammed phase both characterized by a striped microscopic pattern. Especially in the arising striped jammed regime system flow and mean velocity are drastically enlarged compared to generic inflow strategies. Here, the fall back strategy is capable to prevent the system from a complete jamming. Thus, the introduced inflow procedure represents an effective strategy for establishing reliable connections.


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