From car traffic to production flows : a guided tour through solvable stochastic transport processes

The purpose of this thesis is to show on explicit examples how various theoretical concepts, ranging from statistical mechanics to stochastic control and from traffic theory to queuing systems, can be transferred to transport processes, encountered in particular in manufacturing systems, with benefic implications for their dynamical understanding, optimization and control. The thesis collects several articles where such implications are exposed [38]-[43]. We start with the observation that car traffic and production flows share several common dynamical properties (chapter 3). The main reason for the similarities are the presence of non-linear interactions in both settings. In traffic theory the interactions are between competing cars and originate from a trade off between safe and fast driving. They directly influence the speed of the cars. In production flow engineering the interactions are between cooperating work-cells forming the manufacturing system. They govern the production policy and hence the throughput of the manufacturing system. We exploit this analogy in case of a serial production line where the influence on the production rate of a work-cell is determined by the contents of its adjacent buffers (fig. 0.1) and derive a dictionary between the two fields. As a first result, this analogy allows the recognition of free-flow and jamming-flow regimes —well studied in traffic theory — in the context of production lines. Fig. 0.1. Above: Sketch of a serial production line composed of N machines Mi with production rates vi and N -1 buffers Bi with buffer content yi. Below: Sketch of a one-lane traffic system composed of N cars with velocities vi and headways xi. Dynamical similarities between cars and work-cells: the production rates and the car velocities, depend both on their environment e.g., the content of the next nearest buffers vi = vi(yi-1, yi) resp. the distances to the next nearest cars vi = vi(xi-1, xi). Applying a linear stability analysis to a given stationary flow regime, we draw a flow diagram which defines the boundary between the free and the jammed regime as a function of the control parameters. The relevant conclusions include the introduction of a dimensionless performance parameter, an enlightening connection between transient and stationary performance measures for production lines, a discussion of both the bull-whip effect and the stabilizing effect of pull production controls in serial production lines. The traffic models used in the analogy with serial production lines are socalled optimal-velocity car following models which assume that the velocity of a car is adapted to a distance dependent optimal velocity which reflects the safety requirements of two neighboring cars. This optimal velocity is chosen in an ad hoc fashion by traffic engineers and is not related to a cost functional which defines "optimality" via a minimization procedure. Here we calculate in the context of serial production lines the "optimal velo