Discrete flow networks: Bottleneck analysis and fluid approximations. (English) Zbl 0735.60095

Chen, Hong; Mandelbaum, Avi

Math. Oper. Res. 16, No. 2, 408-446 (1991).

The paper provides a detailed analysis of a deterministic discrete-flow network and its fluid approximation. The network models a dynamic system in which units are transferred individually between stations. Its properly rescaled versions can be described asymptotically by a so-called linear fluid model (with eventually constant flow rates). This approximation requires the existence of long-run averages; the determination of the asymptotic flow rates is equivalent to a bottleneck analysis of the original network. Applying the results to the sample paths of a stochastic Jackson network yields functional strong laws of large numbers.

Reviewer: W.Stadje (Osnabrück)

MSC:

60K20	Applications of Markov renewal processes (reliability, queueing networks, etc.)
60K25	Queueing theory (aspects of probability theory)
90B10	Deterministic network models in operations research
60F15	Strong limit theorems
60F17	Functional limit theorems; invariance principles
90B22	Queues and service in operations research
60G17	Sample path properties

Keywords:

oblique reflection; discrete-flow network; asymptotic flow; stochastic Jackson network; functional strong laws of large numbers; network models