A Model for the Dynamics of large Queuing Networks and Supply Chains

Abstract

We consider a supply chain consisting of a sequence of buffer queues and processors with certain throughput times and capacities. Based on a simple rule for releasing parts, i.e. batches of product or individual product items, from the buffers into the processors we derive a hyperbolic conservation law for the part density and flux in the supply chain. The conservation law will be asymptotically valid in regimes with a large number of parts in the supply chain. Solutions of this conservation law will in general develop concentrations corresponding to bottlenecks in the supply chain.

Optimization of order policies in supply networks

“…The inventory model used here essentially corresponds to replacing the inventory by a processor with a very short cycle time ε, and then using a version of the model for a production unit developed in [2] and [10]. Similar simple inventory models have been used in [1] and [3] in a different context.…”

A Fluid Dynamic Model for Telecommunication Networks with Sources and Destinations

“…|(α 3,1 (π)−α 3,1 (π))γ 1 +(α 3,2 (π)−α 3,2 (π))γ 2 , (α 4,1 (π)−α 4,1 (π))γ 1 +(α 4,2 (π)−α 4,2 (π))γ 2 | = |(α 3,1 (π) − α 3,1 (π), α 4,1 (π) − α 4,1 (π))γ 1 + (α 3,2 (π) − α 3,2 (π), α 4,2 (π) − α 4,2 (π))γ 2 …”

“…the percentages of packets going from a fixed source to a fixed destination. Assuming that packets velocity is independent from the source and the destination, the evolution of π follows a semilinear equation 2) hence inside transmission lines the evolution of π is influenced by the average speed of packets. The aim is then to consider networks in which many lines intersect.…”

“…(1.1) Recently, a conservation law model was obtained in [2] for supply chains, which have a dynamics somehow related to our case.…”

Production systems with limited repair capacity

“…During the last years several dynamic production models have been developed either describing the trajectory of each good through the network, which is called discrete event simulation [2], or by using so-called fluid models models, where averaged quantities are used to track goods, see [1-4, 7, 9, 13] for an overview. Based on these continuous production models, optimization problems have been introduced [8,10,11,14].…”