Analysis and optimization of vacation and polling models with retrials

We study a vacation-type queueing model, and a single-server multi-queue polling model, with the special feature of retrials. Just before the server arrives at a station there is some deterministic glue period. Customers (both new arrivals and retrials) arriving at the station during this glue period will be served during the visit of the server. Customers arriving in any other period leave immediately and will retry after an exponentially distributed time. Our main focus is on queue length analysis, both at embedded time points (beginnings of glue periods, visit periods and switch- or vacation periods) and at arbitrary time points.Comment: Keywords: vacation queue, polling model, retrials Submitted for review to Performance evaluation journal, as an extended version of 'Vacation and polling models with retrials', by Onno Boxma and Jacques Resin

Transform-domain analysis of packet delay in network nodes with QoS-aware scheduling

In order to differentiate the perceived QoS between traffic classes in heterogeneous packet networks, equipment discriminates incoming packets based on their class, particularly in the way queued packets are scheduled for further transmission. We review a common stochastic modelling framework in which scheduling mechanisms can be evaluated, especially with regard to the resulting per-class delay distribution. For this, a discrete-time single-server queue is considered with two classes of packet arrivals, either delay-sensitive (1) or delay-tolerant (2). The steady-state analysis relies on the use of well-chosen supplementary variables and is mainly done in the transform domain. Secondly, we propose and analyse a new type of scheduling mechanism that allows precise control over the amount of delay differentiation between the classes. The idea is to introduce N reserved places in the queue, intended for future arrivals of class 1

Adaptive Resource Management for Uncertain Execution Platforms

Embedded systems are becoming increasingly complex. At the same time, the components that make up the system grow more uncertain in their properties. For example, current developments in CPU design focuses on optimizing for average performance rather than better worst case performance. This, combined with presence of 3rd party software components with unknown properties, makes resource management using prior knowledge less and less feasible. This thesis presents results on how to model software components so that resource allocation decisions can be made on-line. Both the single and multiple resource case is considered as well as extending the models to include resource constraints based on hardware dynam- ics. Techniques for estimating component parameters on-line are presented. Also presented is an algorithm for computing an optimal allocation based on a set of convex utility functions. The algorithm is designed to be computationally efficient and to use simple mathematical expres- sions that are suitable for fixed point arithmetics. An implementation of the algorithm and results from experiments is presented, showing that an adaptive strategy using both estimation and optimization can outperform a static approach in cases where uncertainty is high

Time Driven Priority Router Implementation and First Experiments

This paper reports on the implementation of Time-Driven Priority (TDP) scheduling on a FreeBSD platform. This work is part of a TDP prototyping and demonstration project aimed at showing the implications of TDP deployment in packet-switched networks, especially benefits for real-time applications. This paper focuses on practical aspects related to the implementation of the technology on a Personal Computer (PC)-based router and presents the experimental results obtained on a testbed network. The basic building blocks of a TDP router are described and implementation choices are discussed. The relevant results achieved and here presented can be categorized into two types: qualitative results, including the successful integration of all needed blocks and the insight obtained on the complexity related to the implementation of a TDP router, and quantitative ones, including measures of achievable network utilization and of jitter experienced on a fully-loaded TDP network. The outcome demonstrates the effectiveness of the presented implementation while confirming TDP points of strengt

Iterative approximation of k-limited polling systems

The present paper deals with the problem of calculating queue length distributions in a polling model with (exhaustive) k-limited service under the assumption of general arrival, service and setup distributions. The interest for this model is fueled by an application in the field of logistics. Knowledge of the queue length distributions is needed to operate the system properly. The multi-queue polling system is decomposed into single-queue vacation systems with k-limited service and state-dependent vacations, for which the vacation distributions are computed in an iterative approximate manner. These vacation models are analyzed via matrix-analytic techniques. The accuracy of the approximation scheme is verified by means of an extensive simulation study. The developed approximation turns out be accurate, robust and computationally efficient

Exploring a new Markov chain model for multiqueue systems.

Traditionally, Markov models have been used to study multiserver systems using exhaustive or gated service. In addition, exhaustive-limited and gate-limited models have also been used in communication systems to reduce overall latency. Recently the authors have proposed a new Markov Chain approach to study gate-limited service. Multiqueue systems such as polling systems, in which the server serves various queues have also been extensively studied but as a separate branch of queueing theory. This paper proposes to describe multiqueue systems in terms of a new Markov Chain called the Zero-Server Markov Chain (ZSMC). The model is used to derive a formula for the waiting times in an exhaustive polling system. An intuitive result is obtained and this is used to develop an appoximate method which works well over normal operational ranges