Saulius Minkevičius

On the law of the iterated logarithm in open queueing networks

Abstract An open queueing network model in heavy traffic is developed. Such models are mathematical models of computer networks in heavy traffic. Laws of the iterated logarithm for the virtual waiting time of the customer in open queueing networks and homogeneous computer networks are proved.

On the law of the iterated logarithm in multiserver open queueing networks

The paper is devoted to the analysis of queueing systems in the context of the network and communication theory. We investigate a theorem on the law of the iterated logarithm for a queue of jobs in a multiserver open queueing network under heavy traffic conditions.

A law of the iterated logarithm for global values of waiting time in multiphase queues

The target of this research in the queueing theory is to prove the law of the iterated logarithm (LIL) under the conditions of heavy traffic in multiphase queueing systems. In this paper, the LIL for global extreme values (maximum and minimum) is proved in the phases of a queueing system studied for an important probability characteristic of system (waiting time of a customer).

On extreme values in open queueing networks

This paper presents heavy traffic limit theorems for the extreme virtual waiting time of a customer in an open queueing network. In this paper, functional limit theorems are proved for extreme values of important probability characteristics of the open queueing network investigated as the maximum and minimum of the total virtual waiting time of a customer, and the maximum and minimum of the virtual waiting time of a customer. Also, the paper presents the previous related works for extreme values in queues and the virtual waiting time in heavy traffic.

On the global values of the queue length in open queueing networks

The modern queueing theory is one of the powerful tools for a quantitative and qualitative analysis of communication systems, computer networks, transportation systems, and many other technical systems. Open queueing networks are of special interest both in theory and in practical applications (packet switch structures, cellular mobile networks, message switching systems, retransmission of video images, assembly lines, etc.). In this paper, we deal with approximations of an open queueing network and present a heavy traffic limit theorem for the global value of the queue length of customers in an open queueing network. A functional limit theorem is proved for the global value of the queue length of customers – an important probability characteristic of the queueing system under conditions of heavy traffic.

Python for scientific computing education: Modeling of queueing systems

In this paper, we present the methodology for the introduction to scientific computing based on model-centered learning. We propose multiphase queueing systems as a basis for learning objects. We use Python and parallel programming for implementing the models and present the computer code and results of stochastic simulations.

Simulation of reliability in multiserver computer networks

The performance in terms of reliability of computer multiserver networks motivates this paper. The probability limit theorem is derived on the extreme queue length in open multiserver queueing networks in heavy traffic and applied to a reliability model for multiserver computer networks where we relate the time of failure of a multiserver computer network to the system parameters.

The impact of overload conditions on computer network reliability

Performance in terms of reliability of computer networks motivates this paper. A limit theorem on the extreme queue length in open queueing networks in heavy traffic is derived and then applied to a reliability model for computer networks where we relate the time of failure of a computer network to the system parameters.

On Personalised Learning Units Evaluation Methodology

The aim of the paper is to present a methodology (i.e. model and method) to evaluate suitability, acceptance and use of personalised learning units/scenarios. Learning units/scenarios are referred here as methodological sequences of learning components (learning objects, learning activities, and learning environment). High-quality learning units should consist of the learning components optimised to particular students according to their personal needs, e.g. learning styles. In the paper, optimised learning scenarios mean learning scenarios composed of the components having the highest probabilistic suitability indexes to particular students according to Felder-Silverman learning styles model. Personalised learning units evaluation methodology presented in the paper is based on (1) well-known principles of Multiple Criteria Decision Analysis for identifying evaluation criteria; (2) Educational Technology Acceptance & Satisfaction Model (ETAS-M) based on well-known Unified Theory on Acceptance and Use of Technology (UTAUT) model, and (3) probabilistic suitability indexes to identify learning components’ suitability to particular students’ needs according to their learning styles. The methodology to evaluate personalised learning units presented in the paper is absolutely new in scientific literature. This methodology is applicable in real life situations where teachers have to help students to create and apply learning units that are most suitable for their needs and thus to improve education quality and efficiency.

SIMULIATION OF THE OPEN MESSAGE SWITCHING SYSTEM

The modern queueing theory is one of the powerful tools for a quantitative and qualitative analysis of communication systems, computer networks, transportation systems, and many other technical systems. The paper is designated to the analysis of queueing systems arising in the network theory and communications theory (called open queueing network). We present a theorem on the law of the iterated logarithm (LIL) for the virtual waiting time of a customer in an open queueing network and its application to the mathematical model of the open message switching system.