4,343 research outputs found
The pseudo-self-similar traffic model: application and validation
Since the early 1990¿s, a variety of studies has shown that network traffic, both for local- and wide-area networks, has self-similar properties. This led to new approaches in network traffic modelling because most traditional traffic approaches result in the underestimation of performance measures of interest. Instead of developing completely new traffic models, a number of researchers have proposed to adapt traditional traffic modelling approaches to incorporate aspects of self-similarity. The motivation for doing so is the hope to be able to reuse techniques and tools that have been developed in the past and with which experience has been gained. One such approach for a traffic model that incorporates aspects of self-similarity is the so-called pseudo self-similar traffic model. This model is appealing, as it is easy to understand and easily embedded in Markovian performance evaluation studies. In applying this model in a number of cases, we have perceived various problems which we initially thought were particular to these specific cases. However, we recently have been able to show that these problems are fundamental to the pseudo self-similar traffic model. In this paper we review the pseudo self-similar traffic model and discuss its fundamental shortcomings. As far as we know, this is the first paper that discusses these shortcomings formally. We also report on ongoing work to overcome some of these problems
Queues and risk processes with dependencies
We study the generalization of the G/G/1 queue obtained by relaxing the
assumption of independence between inter-arrival times and service
requirements. The analysis is carried out for the class of multivariate matrix
exponential distributions introduced in [12]. In this setting, we obtain the
steady state waiting time distribution and we show that the classical relation
between the steady state waiting time and the workload distributions re- mains
valid when the independence assumption is relaxed. We also prove duality
results with the ruin functions in an ordinary and a delayed ruin process.
These extend several known dualities between queueing and risk models in the
independent case. Finally we show that there exist stochastic order relations
between the waiting times under various instances of correlation
A Mathematical Approach to Order Book Modeling
Motivated by the desire to bridge the gap between the microscopic description
of price formation (agent-based modeling) and the stochastic differential
equations approach used classically to describe price evolution at macroscopic
time scales, we present a mathematical study of the order book as a
multidimensional continuous-time Markov chain and derive several mathematical
results in the case of independent Poissonian arrival times. In particular, we
show that the cancellation structure is an important factor ensuring the
existence of a stationary distribution and the exponential convergence towards
it. We also prove, by means of the functional central limit theorem (FCLT),
that the rescaled-centered price process converges to a Brownian motion. We
illustrate the analysis with numerical simulation and comparison against market
data
A discrete-time Markov modulated queuing system with batched arrivals
This paper examines a discrete-time queuing system with applications to
telecommunications traffic. The arrival process is a particular Markov
modulated process which belongs to the class of discrete batched Markovian
arrival processes. The server process is a single server deterministic queue. A
closed form exact solution is given for the expected queue length and delay. A
simple system of equations is given for the probability of the queue exceeding
a given length.Comment: to appear Performance Evaluatio
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