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A class of queueing networks which may have an arbitrary topology, and consist of single-server fork-join nodes with both infinite and finite buffers is examined to derive a representation of the network dynamics in terms of max-plus algebra. For the networks, we present a common dynamic state equation which relates the departure epochs of customers from the network nodes in an explicit vector ...

Exotic semirings such as the “(max,+) semiring” (R ∪ {−∞},max,+), or the “tropical semiring” (N ∪ {+∞},min,+), have been invented and reinvented many times since the late fifties, in relation with various fields: performance evaluation of manufacturing systems and discrete event system theory; graph theory (path algebra) and Markov decision processes, Hamilton-Jacobi theory; asymptotic analysis...

In the modeling of human activities, in contrast to natural phenomena, quite frequently only the operations max (or min) and + are needed. A typical example is the performance evaluation of synchronized processes such as those encountered in manufacturing (dynamic systems made up of storage and queuing networks). Another typical example is the computation of a path of maximum weight in a graph ...

A fast learning method for morphological neural networks which are formulated based on max plus algebra, is proposed. The proposed fast learning method is deduced from the idempotent properties of max plus algebra and cost matrices. Through experiments using artificial training data sets, it is conformed that the computation time of the proposed method is decreased into 60.9-68.6% and 40.9 – 48...