An analysis of symmetric polling systems with two priority classes

A cyclic multiqueue system consists of several stations in which messages are enqueued for transmission, and which are served sequentially in cyclic order by a single server. The arrivals at each queue are independent Poisson processes, and the transmission times are generally distributed. Moreover, there is a nonzero switchover time from one station to the next, which is also generally distributed. Messages can be at either of two priority levels: priority 1 (low) or priority 2 (high), and polling occurs either at low priority, in which case both priority 1 and priority 2 messages can be transmitted, or at high priority, in which case only priority 2 messages are transmitted. The service disciplines considered are the exhaustive service discipline and the gated service discipline. In both cases the performance, as measured by the expected delay for high- and for low-priority messages, is evaluated. Part of the analysis is approximate, and simulation results are presented to validate the approximation.     

On structured perturbations for two classes of linear infinite-dimensional systems

This paper considers two classes of infinite-dimensional systems described by an abstract differential equationx (t) = (A + BC)x(t),x(0) =x ₀, on a Hilbert space, whereA, B, C are linear, possibly unbounded operators and is an unknown, linear, bounded perturbation. The two classes of systems are defined in terms of properties imposed on the triple (A, B, C). It is proved that for every the perturbed system (A + EF, B, C) inherits all the properties of the unperturbed system {A, B, C}) if (A, E, F) and {A, B, F} are in the same class.     

On the billing vulnerabilities of SIP-based VoIP systems

For commercial VoIP services, billing is crucial to both service providers and their subscribers. One of the most basic requirements of any billing function is that it must be accurate and trustworthy. A reliable VoIP billing mechanism should only charge VoIP subscribers for the calls they have really made and for the durations they have called.Existing VoIP billing is based on the underlying VoIP signaling and media transport protocols. Hence, vulnerabilities in VoIP signaling and media transports can be exploited to compromise the trustworthiness of the billing of VoIP systems. In this paper, we analyze several deployed SIP-based VoIP systems, and present three types of billing attacks: call establishment hijacking, call termination hijacking and call forward hijacking. These billing attacks can result in charges on the calls the subscribers have not made or overcharges on the VoIP calls the subscribers have made. Such billing attacks essentially cause inconsistencies between what the VoIP subscribers have received and what the VoIP service provider has provided, which would create hard to resolve disputes between the VoIP subscribers and service providers. Our empirical results show that VoIP subscribers of Vonage, AT&T and Gizmo are vulnerable to these billing attacks.     

Relations between the stabilization properties of two classes of hereditary linear systems with commensurate delays

Two classes of hereditary linear systems each subjected to two alternative controller structures (one of a free delay dynamic nature while the other one includes delays under integral forms) are analysed from a stabilizability viewpoint. The first class of plants has pure commensurate delays in both state and input while the second has its time delayed contributions to the dynamics under integral form in the differential equations. Under certain weak conditions, the four closed-loop systems resulting from combining each open-loop plant structure with each controller structure can lead to identical state/output trajectories for appropriately related controller parametrizations. This allows the derivation of stabilizability results for any of the four closed-loop combinations of open-loop system plus controller by using results from the literature, each one being originally applicable to just one of the above combinations     

New classes of stabilizable uncertain systems

Consideration was given to the new classes of continuous and discrete uncertain systems where the elements of the control plant matrix represent physically realizable arbitrary functionals with only the boundaries of their variation known. The stabilizing controls robust in the elements of the control plant matrix were constructed using special quadratic Lyapunov functions.     

Connectivity properties of classes of linear systems

The number of pathwise-connected components of various classes of linear systems is determined. The proofs are based on the representation of these classes of systems in terms of balanced realizations. This provides a unified way of deriving well-known results as well as the new results presented here.     

On diffeomorphisms between classes of linear systems

In this paper, we show that the following classes of linear dynamical systems are diffeomorphic to each other: fixed order, asymptotically stable, strictly bounded real, strictly positive real, stable and minimum phase, and invertible. These results are then used to prove the diffeomorphisms between the state bundles associated with these classes of systems, and between their associated principal fibre bundles. We shall conclude this paper by discussing how these results can be used to deduce geometric properties of other classes of linear systems, and to construct overlapping parametrizations.     

BIBO stability of some classes of delay systems and fractional systems

A new test is presented for the BIBO stability of delay systems of neutral type with a single delay, specified in terms of their transfer functions, enabling us to decide on some cases that were previously open. Next, a class of fractional systems is considered, and a method is given for determining the stability intervals for such systems.     

Solving large classes of nonlinear systems of PDEs

It is shown that large classes of nonlinear systems of PDEs, with possibly associated initial and/or boundary value problems, can be solved by the method of order completion. The solutions obtained can be assimilated with Hausdorff-continuous functions. The usual Navier–Stokes equations, as well as their various modifications aiming at a realistic modeling, are included as particular cases. The same holds for the critically important constitutive relations in various branches of Continuum Mechanics. The solution method does not involve functional analysis, nor various Sobolev or other spaces of distributions or generalized functions. The general and type independent existence and regularity results regarding solutions presented here have recently been introduced in the literature.

“... provided also if need be that the notion of a solution shall be suitably extended...” cited from Hilbert’s 20th Problem

     

Two classes of passive time-varying well-posed linear systems

We investigate two classes of time-varying well-posed linear systems. Starting from a time-invariant scattering-passive system, each of the time-varying systems is constructed by introducing a time-dependent inner product on the state space and modifying some of the generating operators. These classes of linear systems are motivated by physical examples such as the electromagnetic field around a moving object. To prove the well-posedness of these systems, we use the Lax–Phillips semigroup induced by a well-posed linear system, as in scattering theory.     

A review on some classes of algebraic systems

ABSTRACT

In this paper, we review some algebraic control system. Precisely, linear and bilinear systems on Euclidean spaces and invariant and linear systems on Lie groups. The fourth classes of systems have a common issue: to any class, there exists an associated subgroup. From this object, we survey the controllability property. Especially, from those coming from our contribution to the theory.     

Characterizations of some classes of spiking neural P systems

We look at the recently introduced neural-like systems, called SN P systems. These systems incorporate the ideas of spiking neurons into membrane computing. We study various classes and characterize their computing power and complexity. In particular, we analyze asynchronous and sequential SN P systems and present some conditions under which they become (non-)universal. The non-universal variants are characterized by monotonic counter machines and partially blind counter machines and, hence, have many decidable properties. We also investigate the language-generating capability of SN P systems.     

Representation of some classes of algebraic systems in G-algebra

Representation of finite algebraic systems in terms of a special universal algebra (G-algebra) is considered. Software is described for technological database support using procedures that implement the operations of G-algebra.Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 144–149, November–December, 1991.     

Invariant stabilization of classes of uncertain systems with delays

This paper deals with uncertain systems with delayed argument and having the property that the entries of the state matrix are functionals of arbitrary nature with the only available information being the bounds on their variations. Using quadratic Lyapunov-Krasovskii functionals of the special form, the control is designed such that it is robust against the variations in the plant matrix, the system output decays exponentially no matter what the persistent exogenous disturbance is, and the state vector remains bounded.