Vol. 35 No. 1 (194) (2001)

The article is a short review of a queuing model M_r|G_r|1|∞. First of all, methods for analysis of the M_r|G_r|1|∞ model’s characteristics with classic disciplines such as pre-emptive, head-of-the-line and alternating priorities are presented. A transition to analysis of parametric disciplines and further to class of conservative disciplines is justified and implemented. Special attention is paid to conditions for existence of stationary distributions and preservation laws. Particularly, two new preservation laws for stationary distributions of queue lengths are established. The range of optimization problems for the class of conservative disciplines and some of its subclasses are presented. Directions of asymptotic analysis under different traffic intensities are described. A new result for stationary waiting time distributions in terms of Laplace-Stilties transform is formulated in case of Kleinrock’s parametric discipline.

The problem of tuning of computer systems to specific tasks is considered. A review of existing tools that provide tuning on different levels for a specific class of computer systems named local area multicomputers is presented. A comparative analysis of considered tools is given according to their functional characteristics.

For a slowly varying function $L(t)$ a new integral representation is obtained:

$$L(t) = \mu(t)\int\limits_t_0 ^t b(x)d\ln x, t\geq t_{_}0> 0, $$

where $\mu(t)$ is measurable on $[t_0, +\infty), b(t)$ is continuous on $[t_0, +\infty)$ and

$\lim \limits_{t\ringrow + \infty}(b(t) / L(t))= 0.$

This representation allows to generalize D.D. Adamovich’s classical result on equivalent slowly varying functions and to extend the statement of A. A. Goldberg theorem.

The problem of vibrations of transversal-isotropic electroconductive plate in view of transversal shear strains and induced electromagnetic field at presence of constant longitudinal magnetic field is investigated.

In this paper considerations on conformal transformations of tensor-scalar theory are represented. It is shown that under certain conditions conformal transformed theory of Jordan–Brans–Dicke is equivalent to Einstein theory with a minimally bounded scalar field source.

In this paper we construct the weighted  $L_\mu ^q[-1, 1],  q \in[1, 4/3]\cup [4, +\infty],$ and Legander series $\sum \limits_{k=1} ^\infty c_pP_k(x)$, which is universal in $L_\mu ^q [-1, 1]$.

The behaviour of frequencies of vibrations of curvilinear tetragon with a rectilinear anisotropy is investigated.