Tadeusz Czachórski

Performance evaluation of fork and join synchronization primitives

SummaryThe paper presents a performance model of fork and join synchronization primitives. The primitives are used in parallel programs executed on distributed systems. Three variants of the execution of parallel programs with fork and join primitives are considered and queueing models are proposed to evaluate their performance on a finite number of processors. Synchronization delays incurred by the programs are represented by a state-dependent server with service rate depending on a particular synchronization scheme. Closed form results are presented for the two processor case and a numerical method is proposed for many processors. Fork-join queueing networks having more complex structure i.e., processors arranged in series and in parallel, are also analyzed in the same manner. The networks can model the execution of jobs with a general task precedence graph corresponding to a nested structure of the fork-join primitives. Some performance indices of the parallel execution of programs are studied. The results show that the speedup which can be obtained theoretically in a parallel system may be decreased significantly by synchronization constraints.

The drop-from-front strategy in AQM

The article investigates the influence of the way packets are chosen to be dropped (end of the tail, head of the tail) on the performance, i.e. response time for in case of RED and DSRED queues - two representative active queue management mechanisms used in IP routers. In particular, the self-similar traffic is considered. The quantitative analysis is based on simulation and Markov chain models solved numerically.

Diffusion Approximation Model of Multiserver Stations with Losses

The article presents a diffusion approximation model of a G/G/N/N station -N parallel servers without queueing. Diffusion approximation allows us to include in queueing models fairly general assumptions. First of all it gives us a tool to consider in a natural way transient states of queues, which is very rare in classical queueing models. Then we may consider input streams with general interarrival time distributions and servers with general service time distributions. Single server models may be easily incorporated into a network of queues. Here, we apply the diffusion approximation formalism to study transient behaviour of G/G/N/N station and use it to construct a model of a typical call centre and to study the sliding window mechanism, a popular Call Admission Control (CAC) algorithm.

Diffusion Approximation Model for the Distribution of Packet Travel Time at Sensor Networks

We propose a model to estimate the probability density function of the distribution of a packet travel time in a multihop wireless sensor network. The model is based on diffusion approximation and it takes into consideration the heterogeneity of the propagation medium and of the distribution of relay nodes. The modeled system parameters, e.g. the packet loss probability or the network topology, may depend on time.

Diffusion model of the push-out buffer management policy

A method for modeling a spatial priority mechanism called the push-out buffer management policy is proposed. It is a known mechanism which takes into account two kinds of cells: vital and ordinary ones. It also ensures a high degree of flexibility for asynchronous transfer mode (ATM) services. The use of the diffusion approximation allows modeling general interarrival and service time distributions. The developed transient solution helps describe the burstiness of the flow of cells arriving at a node. The model may be useful for dimensioning network buffers within ATM networks.<<ETX>>

Internet traffic source based on hidden Markov model

This article shows how to use Hidden Markov Models to generate self-similar traffic. The well-known Bellcore traces are used as a training sequence to learn HMM model parameters. Performance of trained model are tested on the remaining portions of the sequences. Then we can use the HMM trained with the Bellcore data as the traffic source model.

The Impact of Self-similarity on Traffic Shaping in Wireless LAN

IEEE 802.11 MAC protocol ist the de facto standard for wireless local area networks (WLANs). In todays Internet, the emerging widespread use of real-time voice, audio, and video applications makes QoS (Quality of Service) a key problem. At the MAC layer, 802.11e defines extensions to enhance the QoS performance of 802.11 WLAN. This MAC layer solution leaves such issues of QoS as QoS guarantee and admission control to the traffic control systems at the higher layers. This article tries to show that implementation of some mechanisms of traffic shaping causes some improvement of the level of QoS in WLANs. First we analyse the influence of the traffic shaping in WLANs stations by the mechanism of token bucket filter. Next the analysis of the behaviour of Access Point with AQM mechanism was carried out. The conducted research has shown that it is possible to achieve certain level of QoS thanks to the implementation of traffic shaping mechanisms. We make our experiments comparatively for the traffic sources with self-similarity and without it. Our results confirm the necessity of taking into account the self-similar character of wireless traffic.

Diffusion approximation as a modelling tool

Diffusion theory is already a vast domain of knowledge. This tutorial lecture does not cover all results; it presents in a coherent way an approach we have adopted and used in analysis of a series of models concerning evoluation of some traffic control mechanisms in computer, especially ATM, networks. Diffusion approximation is presented from engineers point of view, stressing its utility and commenting numerical problems of its implementation. Diffusion approximation is a method to model the behavior of a single queueing station or a network of stations. It allows one to include in the model general sevice times, general (also correlated) input streams and to investigate transient states, which, in presence of bursty streams (e.g. of multimedia transfers) in modern networks, are of interest.

Stability and dynamics of TCP-NCR(DCR) protocol in presence of UDP flows

The fluid-flow approximation models investigate with much success the dynamics and stability of TCP/RED connections. Their main assumption is that the fluctuations of variables characterizing the behaviour of the connections are relatively small, that enables the linearization of model and the use of traditional control analysis tools to obtain such measures as Bode gain, phase margins, tracking error or delay margin. In this article, preserving linear fluid-flow model, we propose its extension to the case when a network is composed of wired and wireless part. We consider a variant of TCP algorithm (TCP-DCR or its new version TCP-NCR) and fluid-flow differential equations representing the size of congestion window, mean queue at the bottleneck router and loss probability at a RED queue are supplemented with terms representing constant loss probability due to transmission in wireless part and probability that a fraction of these errors is recovered by a link level mechanism. The decrease of congestion window due to TCP mechanism is delayed to allow the link protocol to deal with the errors. The model considers the presence of uncontrollable UDP flows.

Markovian model of RED mechanism

The IP networks are faced today with difficult task of satisfying the needs of connections requiring different QoS by sharing the same physical resources, e.g. bandwidth and buffers. Buffers are a key component of packet-switched network, as they absorb burst arrivals of packets and hence reduce losses. Larger buffers can absorb larger bursts but they tend to build up high load and increase queueing delays. The traditional technique for managing delay is to set a maximum length for each buffer queue, accept packets in the queue until the maximum length is reached. Distributed computational grids depend on TCP to ensure reliable end-to-end communication between nodes across the wide area network (WAN). In the core of network (routers), it is believed that random early detection (RED) will alleviate problems related to synchronization of flows and also provide some notion of QoS by intelligent dropping. In this paper we develop simple Markovian model for the RED buffer management schemes, and use these models to quantify the benefits brought about by RED. In particular we examine the impact of RED on the loss rate and the mean delay. We analyse the transient and stationary states, using Markovian model. We show that the loss probability is the same for TCP and UDP traffics if RED algorithm is used. This loss rate of a flow going through a RED router does not depend of the burstiness of this flow, but only on the load it generates.