Abstract: In this work, we study the impact of dynamically
changing link slowdowns on the stability properties of packetswitched
networks under the Adversarial Queueing Theory
framework. Especially, we consider the Adversarial, Quasi-Static
Slowdown Queueing Theory model, where each link slowdown may
take on values in the two-valued set of integers {1, D} with D > 1
which remain fixed for a long time, under a (w, ¤ü)-adversary. In this
framework, we present an innovative systematic construction for the
estimation of adversarial injection rate lower bounds, which, if
exceeded, cause instability in networks that use the LIS (Longest-in-
System) protocol for contention-resolution. In addition, we show that
a network that uses the LIS protocol for contention-resolution may
result in dropping its instability bound at injection rates ¤ü > 0 when
the network size and the high slowdown D take large values. This is
the best ever known instability lower bound for LIS networks.
Abstract: 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 networks theory and communications theory
(called open queueing network). The authors of this research in the
sphere of queueing theory present the theorem about the law of the iterated logarithm (LIL) for the queue length of a customers in open
queueing network and its application to the mathematical model of
the open message switching system.
Abstract: In the queueing theory, it is assumed that customer
arrivals correspond to a Poisson process and service time has the
exponential distribution. Using these assumptions, the behaviour of
the queueing system can be described by means of Markov chains
and it is possible to derive the characteristics of the system. In the
paper, these theoretical approaches are presented on several types of
systems and it is also shown how to compute the characteristics in a
situation when these assumptions are not satisfied
Abstract: In this work, we study the impact of dynamically changing link slowdowns on the stability properties of packetswitched networks under the Adversarial Queueing Theory framework. Especially, we consider the Adversarial, Quasi-Static Slowdown Queueing Theory model, where each link slowdown may take on values in the two-valued set of integers {1, D} with D > 1 which remain fixed for a long time, under a (w, p)-adversary. In this framework, we present an innovative systematic construction for the estimation of adversarial injection rate lower bounds, which, if exceeded, cause instability in networks that use the LIS (Longest-in- System) protocol for contention-resolution. In addition, we show that a network that uses the LIS protocol for contention-resolution may result in dropping its instability bound at injection rates p > 0 when the network size and the high slowdown D take large values. This is the best ever known instability lower bound for LIS networks.
Abstract: Urban road network traffic has become one of the
most studied research topics in the last decades. This is mainly due to
the enlargement of the cities and the growing number of motor
vehicles traveling in this road network. One of the most sensitive
problems is to verify if the network is congestion-free. Another
related problem is the automatic reconfiguration of the network
without building new roads to alleviate congestions. These problems
require an accurate model of the traffic to determine the steady state
of the system. An alternative is to simulate the traffic to see if there
are congestions and when and where they occur. One key issue is to
find an adequate model for road intersections. Once the model
established, either a large scale model is built or the intersection is
represented by its performance measures and simulation for analysis.
In both cases, it is important to seek the queueing model to represent
the road intersection. In this paper, we propose to model the road
intersection as a BCMP queueing network and we compare this
analytical model against a simulation model for validation.