Lineary MAX-Plus Models Applyng in Traffic Management Tasks

V.M. Lozynska

Donetsk national technical university in Krasnoarmiysk

Development of next generation networks concept let to reconfigure the most of existing traffic controls at telecommunication node. Necessity of its modification causes of low efficient network resources usage. Among of frequently used traffic controls at telecommunication node are service queues schedulers. This is due to traffic “conditioning” feature and as result opportunity of decreasing data lost level. For modern telecommunication devices most common are schedulers with fair and hybrid queue servicing. Limitation of existing algorithms can be explained by it static character at the same time with dynamic changing character of incoming traffic and it non-controllability. For modification of these algorithms, formalized an optimization problem, limitations of which are quality of service parameters. Also being of more than one queue at one network device suggests packet service synchronization. All these tasks can be solved with two ways, presented in the paper: discrete-event models and Max-plus algebra linear models. For every model was find state space equations by conversion into Max-plus algebra basis. Control functions in represented models execute vectors of incoming request delays and requests’ service time. The solving of the given optimization problem is in finding of adjustments vector, which in fact shows the required queue buffer space size for every computing cycle. Thus, in represented article for the first time the max-plus algebra applications is showed for the solving traffic management tasks.
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