Queue Length Simulations in a Finite Single-line Queueing System with Repeated Calls

2000 Mathematics Subject Classification: 60K25.

Study of Queuing Systems with a Generalized Departure Process

This work was supported by the Bulgarian National Science Fund under grant BY-TH-105/2005.

Single-Server Queueing System with Markov-Modulated Arrivals and Service Times

Key words: Markov-modulated queues, waiting time, heavy traffic.

On the Busy Period in One Finite Queue of M/G/1 Type with Inactive Orbit

The paper deals with a single server finite queuing system where the customers, who failed to get service, are temporarily blocked in the orbit of inactive customers. This model and its variants have many applications, especially for optimization of the corresponding models with retrials. We analyze the system in non-stationary regime and, using the discrete transformations method study, the busy period length and the number of successful calls made during it. ACM Computing Classification System (1998): G.3, J.7.

Evaluation of Pareto/D/1/k Queue by Simulation

The finding that Pareto distributions are adequate to model Internet packet interarrival times has motivated the proposal of methods to evaluate steady-state performance measures of Pareto/D/1/k queues. Some limited analytical derivation for queue models has been proposed in the literature, but their solutions are often of a great mathematical challenge. To overcome such limitations, simulation tools that can deal with general queueing system must be developed. Despite certain limitations, simulation algorithms provide a mechanism to obtain insight and good numerical approximation to parameters of queues. In this work, we give an overview of some of these methods and compare them with our simulation approach, which are suited to solve queues with Generalized-Pareto interarrival time distributions. The paper discusses the properties and use of the Pareto distribution. We propose a real time trace simulation model for estimating the steady-state probability showing the tail-raising effect, loss probability, delay of the Pareto/D/1/k queue and make a comparison with M/D/1/k. The background on Internet traffic will help to do the evaluation correctly. This model can be used to study the long- tailed queueing systems. We close the paper with some general comments and offer thoughts about future work.

Formation of Singularities for Weakly Non-Linear N×N Hyperbolic Systems

We present some results on the formation of singularities for C^1 - solutions of the quasi-linear N × N strictly hyperbolic system Ut + A(U )Ux = 0 in [0, +∞) × Rx . Under certain weak non-linearity conditions (weaker than genuine non-linearity), we prove that the first order derivative of the solution blows-up in finite time.

Optimization of Discrete-Time, Stochastic Systems

* This research was supported by a grant from the Greek Ministry of Industry and Technology.

Automata–based Method for Solving Systems of Linear Constraints in {0,1}

We consider a finite state automata based method of solving a system of linear Diophantine equations with coefficients from the set {-1,0,1} and solutions in {0,1}.

The Knowledge: Its Presentation and Role in Recognition Systems

The concept of knowledge is the central one used when solving the various problems of data mining and pattern recognition in finite spaces of Boolean or multi-valued attributes. A special form of knowledge representation, called implicative regularities, is proposed for applying in two powerful tools of modern logic: the inductive inference and the deductive inference. The first one is used for extracting the knowledge from the data. The second is applied when the knowledge is used for calculation of the goal attribute values. A set of efficient algorithms was developed for that, dealing with Boolean functions and finite predicates represented by logical vectors and matrices.

On OBDD Transformations Representing Finite State Automata

We present OBDD transformation problem representing finite labeled transition systems corresponding to some congruence relation. Transformations are oriented toward obtaining the OBDD of a minimized transition system for this congruence relation.

On Handling Replay Attacks in Intrusion Detection Systems

We propose a method for detecting and analyzing the so-called replay attacks in intrusion detection systems, when an intruder contributes a small amount of hostile actions to a recorded session of a legitimate user or process, and replays this session back to the system. The proposed approach can be applied if an automata-based model is used to describe behavior of active entities in a computer system.