Abstract. The paper is aimed at a methodological development in biological pest control. The 10 considered one pest two-agent system is modelled as a verticum-type system. Originally, linear 11 verticum-type systems were introduced by one of the authors for modelling certain industrial 12 systems. These systems are hierarchically composed of linear subsystems such that a part of the 13 state variables of each subsystem affect the dynamics of the next subsystem. Recently, 14 verticum-type system models have been applied to population ecology as well, which required 15 the extension of the concept a verticum-type system to the nonlinear case. 16In the present paper the general concepts and technics of nonlinear verticum-type control 17 systems are used to obtain biological control strategies in a two-agent system. For the 18 illustration of this verticum-type control, these tools of mathematical systems theory are applied 19 to a dynamic model of interactions between the egg and larvae populations of the sugarcane 20 borer (Diatraea saccharalis) and its parasitoids: the egg parasitoid Trichogramma galloi and the 21 larvae parasitoid Cotesia flavipes. 22In this application a key role is played by the concept of controllability, which means that it is 23 possible to steer the system to an equilibrium in given time. In addition to a usual linearization, 24 the basic idea is a decomposition of the control of the whole system into the control of the 25 subsystems, making use of the verticum structure of the population system. The main aim of 26 this study is to show several advantages of the verticum (or decomposition) approach over the 27 classical control theoretical model (without decomposition). For example, in the case of 28 verticum control the pest larval density decreases below the critical threshold value much 29 quicker than without decomposition. Furthermore, it is also shown that the verticum approach 30 may be better even in terms of cost effectiveness. The presented optimal control methodology 31 also turned out to be an efficient tool for the "in silico" analysis of the cost-effectiveness of 32 different biocontrol strategies, e.g. by answering the question how far it is cost-effective to 33 speed up the reduction of the pest larvae density, or along which trajectory this reduction should 34 be carried out. 35 36

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SUMMARYWe present an approximation for the tail asymptotics in an infinite capacity single server queue serviced at a constant rate driven by general multifractal input process. We show that in the special and important case of the monofractal fractional Brownian motion input traffic our result gives the well-known Weibullian tail. We prove that the class of Gaussian processes with scaling properties is in the class of monofractal processes and we derive the related characterization functions. Our formula in the case of Gaussian input processes also gives a queueing result which is in good agreement with the theory of Gaussian processes. Applying the approximation we provide a new practical method for queueing performance estimation of general multifractal traffic. The validation of the method based on both analysis of simulations and measured network traffic have also been presented.

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