arXiv subjects

Markus Fidler

Publications and source records attributed to Markus Fidler.

At least 19 recordsLinked to original sources

arXiv2025

Performance and Stability of Barrier Mode Parallel Systems with Heterogeneous and Redundant Jobs

In some models of parallel computation, jobs are split into smaller tasks and can be executed completely asynchronously. In other situations the parallel tasks have constraints that require them to synchronize their start and possibly departure times. This is true of many parallelized machine learning workloads, and the popular Apache Spark processing engine has recently added support for Barrier Execution Mode, which allows users to add such barriers to their jobs. These barriers necessarily result in idle periods on some of the workers, which reduces their stability and performance, compared to equivalent workloads with no barriers. In this paper we will consider and analyze the stability and performance penalties resulting from barriers. We include an analysis of the stability of $(s,k,l)$ barrier systems that allow jobs to depart after $l$ out of $k$ of their tasks complete. We also derive and evaluate performance bounds for hybrid barrier systems servicing a mix of jobs, both with and without barriers, and with varying degrees of parallelism. For the purely 1-barrier case we compare the bounds and simulation results to benchmark data from a standalone Spark system. We study the overhead in the real system, and based on its distribution we attribute it to the dual event and polling-driven mechanism used to schedule barrier-mode jobs. We develop a model for this type of overhead and validate it against the real system through simulation.

cs.DC↗

arXiv2024

2D-AoI: Age-of-Information of Distributed Sensors for Spatio-Temporal Processes

The freshness of sensor data is critical for all types of cyber-physical systems. An established measure for quantifying data freshness is the Age-of-Information (AoI), which has been the subject of extensive research. Recently, there has been increased interest in multi-sensor systems: redundant sensors producing samples of the same physical process, sensors such as cameras producing overlapping views, or distributed sensors producing correlated samples. When the information from a particular sensor is outdated, fresh samples from other correlated sensors can be helpful. To quantify the utility of distant but correlated samples, we put forth a two-dimensional (2D) model of AoI that takes into account the sensor distance in an age-equivalent representation. Since we define 2D-AoI as equivalent to AoI, it can be readily linked to existing AoI research, especially on parallel systems. We consider physical phenomena modeled as spatio-temporal processes and derive the 2D-AoI for different Gaussian correlation kernels. For a basic exponential product kernel, we find that spatial distance causes an additive offset of the AoI, while for other kernels the effects of spatial distance are more complex and vary with time. Using our methodology, we evaluate the 2D-AoI of different spatial topologies and sensor densities.

cs.NI↗

arXiv2023

Statistical Age-of-Information Bounds for Parallel Systems: When Do Independent Channels Make a Difference?

This paper contributes tail bounds of the age-of-information of a general class of parallel systems and explores their potential. Parallel systems arise in relevant cases, such as in multi-band mobile networks, multi-technology wireless access, or multi-path protocols, just to name a few. Typically, control over each communication channel is limited and random service outages and congestion cause buffering that impairs the age-of-information. The parallel use of independent channels promises a remedy, since outages on one channel may be compensated for by another. Surprisingly, for the well-known case of M$\mid$M$\mid$1 queues we find the opposite: pooling capacity in one channel performs better than a parallel system with the same total capacity. A generalization is not possible since there are no solutions for other types of parallel queues at hand. In this work, we prove a dual representation of age-of-information in min-plus algebra that connects to queueing models known from the theory of effective bandwidth/capacity and the stochastic network calculus. Exploiting these methods, we derive tail bounds of the age-of-information of parallel G$\mid$G$\mid$1 queues. In addition to parallel classical queues, we investigate Markov channels where, depending on the memory of the channel, we show the true advantage of parallel systems. We continue to investigate this new finding and provide insight into when capacity should be pooled in one channel or when independent parallel channels perform better. We complement our analysis with simulation results and evaluate different update policies, scheduling policies, and the use of heterogeneous channels that is most relevant for latest multi-band networks.

cs.IT↗

arXiv2022

Age- and Deviation-of-Information of Time-Triggered and Event-Triggered Systems

Age-of-information is a metric that quantifies the freshness of information obtained by sampling a remote sensor. In signal-agnostic sampling, sensor updates are triggered at certain times without being conditioned on the actual sensor signal. Optimal update policies have been researched and it is accepted that periodic updates achieve smaller age-of-information than random updates. We contribute a study of a signal-aware policy, where updates are triggered by a random sensor event. By definition, this implies random updates and as a consequence inferior age-of-information. Considering a notion of deviation-of-information as a signal-aware metric, our results show, however, that event-triggered systems can perform equally well as time-triggered systems while causing smaller mean network utilization.

cs.NI↗

arXiv2022

The Tiny-Tasks Granularity Trade-Off: Balancing overhead vs. performance in parallel systems

Models of parallel processing systems typically assume that one has $l$ workers and jobs are split into an equal number of $k=l$ tasks. Splitting jobs into $k > l$ smaller tasks, i.e. using ``tiny tasks'', can yield performance and stability improvements because it reduces the variance in the amount of work assigned to each worker, but as $k$ increases, the overhead involved in scheduling and managing the tasks begins to overtake the performance benefit. We perform extensive experiments on the effects of task granularity on an Apache Spark cluster, and based on these, developed a four-parameter model for task and job overhead that, in simulation, produces sojourn time distributions that match those of the real system. We also present analytical results which illustrate how using tiny tasks improves the stability region of split-merge systems, and analytical bounds on the sojourn and waiting time distributions of both split-merge and single-queue fork-join systems with tiny tasks. Finally we combine the overhead model with the analytical models to produce an analytical approximation to the sojourn and waiting time distributions of systems with tiny tasks which include overhead. Though no longer strict analytical bounds, these approximations matched the Spark experimental results very well in both the split-merge and fork-join cases.

cs.DC↗

arXiv2021

A Min-plus Model of Age-of-Information with Worst-case and Statistical Bounds

We consider networked sources that generate update messages with a defined rate and we investigate the age of that information at the receiver. Typical applications are in cyber-physical systems that depend on timely sensor updates. We phrase the age of information in the min-plus algebra of the network calculus. This facilitates a variety of models including wireless channels and schedulers with random cross-traffic, as well as sources with periodic and random updates, respectively. We show how the age of information depends on the network service where, e.g., outages of a wireless channel cause delays. Further, our analytical expressions show two regimes depending on the update rate, where the age of information is either dominated by congestive delays or by idle waiting. We find that the optimal update rate strikes a balance between these two effects.

cs.NI↗

arXiv2016

Non-Asymptotic Delay Bounds for Multi-Server Systems with Synchronization Constraints

Multi-server systems have received increasing attention with important implementations such as Google MapReduce, Hadoop, and Spark. Common to these systems are a fork operation, where jobs are first divided into tasks that are processed in parallel, and a later join operation, where completed tasks wait until the results of all tasks of a job can be combined and the job leaves the system. The synchronization constraint of the join operation makes the analysis of fork-join systems challenging and few explicit results are known. In this work, we model fork-join systems using a max-plus server model that enables us to derive statistical bounds on waiting and sojourn times for general arrival and service time processes. We contribute end-to-end delay bounds for multi-stage fork-join networks that grow in $\mathcal{O}(h \ln k)$ for $h$ fork-join stages, each with $k$ parallel servers. We perform a detailed comparison of different multi-server configurations and highlight their pros and cons. We also include an analysis of single-queue fork-join systems that are non-idling and achieve a fundamental performance gain, and compare these results to both simulation and a live Spark system.

cs.PF↗

arXiv2016

A Benchmark for the Performance of Time-varying Closed-loop Flow Control with Application to TCP

Closed-loop flow control protocols, such as the prominent implementation TCP, are prevalent in the Internet, today. TCP has continuously been improved for greedy traffic sources to achieve high throughput over networks with large bandwidth delay products. Recently, the increasing use for streaming and interactive applications, such as voice and video, has shifted the focus towards its delay performance. Given the need for real-time communication of non-greedy sources via TCP, we present an estimation method for performance evaluation of closed-loop flow control protocols. We characterize an end-to-end connection by a transfer function that provides statistical service guarantees for arbitrary traffic. The estimation is based on end-to-end measurements at the application level that include all effects induced by the network and by the protocol stacks of the end systems. From our measurements, we identify different causes for delays. We show that significant delays are due to queueing in protocol stacks. Notably, this occurs even if the utilization is moderate. Using our estimation method, we compare the impact of fundamental mechanisms of TCP on delays at the application level: In detail, we analyze parameters relevant for network dimensioning, including buffer provisioning and active queue management, and parameters for server configuration, such as the congestion control algorithm. By applying our method as a benchmark, we find that a good selection can largely improve the delay performance of TCP.

cs.NI↗

arXiv2016

A Non-stationary Service Curve Model for Estimation of Cellular Sleep Scheduling

While steady-state solutions of backlog and delay have been derived for essential wireless systems, the analysis of transient phases still poses significant challenges. Considering the majority of short-lived and interactive flows, transient startup effects, as caused by sleep scheduling in cellular networks, have, however, a substantial impact on the performance. To facilitate reasoning about the transient behavior of systems, this paper contributes a notion of non-stationary service curves. Models of systems with sleep scheduling are derived and transient backlogs and delays are analyzed. Further, measurement methods that estimate the service of an unknown system from observations of selected probe traffic are developed. Fundamental limitations of existing measurement methods are explained by the non-convexity of the transient service and further difficulties are shown to be due to the super-additivity of network service processes. A novel two-phase probing technique is devised that first determines the shape of a minimal probe and subsequently obtains an accurate estimate of the unknown service. In a comprehensive measurement campaign, the method is used to evaluate the service of cellular networks with sleep scheduling (2G, 3G, and 4G), revealing considerable transient backlog and delay overshoots that persist for long relaxation times.

cs.NI↗

arXiv2016

On the Delay Performance of Interference Channels

A deep understanding of the queuing performance of wireless networks is essential for the advancement of future wireless communications. The stochastic nature of wireless channels in general gives rise to a time varying transmission rate. In such an environment, interference is increasingly becoming a key constraint. Obtaining an expressive model for offered service of such channels has major implications in the design and optimization of future networks. However, interference channels are not well-understood with respect to their higher layer performance. The particular difficulty for handling interference channels arises from the superposition of random fading processes for the signals of the transmitters involved (i.e., for the signal of interest and for the signals of the interferers). Starting from the distribution of the signal-to-interference-plus-noise ratio (SINR), we derive a statistical characterization of the underlying service process in terms of its Mellin transform. Then, we adapt a recent stochastic network calculus approach for fading channels to derive measures of the queuing performance of single- and multi-hop wireless interference networks. Special cases of our solution include noise-limited and interference-limited systems. A key finding of our analysis is that for a given average signal and average sum interference power, the performance of interfered systems not only depends on the relative strength of the sum interference with respect to the signal-of-interest power, but also on the interference structure (i.e., the number of interferers) as well as the absolute levels.

cs.NI↗

arXiv2015

Non-Asymptotic Delay Bounds for (k,l) Fork-Join Systems and Multi-Stage Fork-Join Networks

Parallel systems have received increasing attention with numerous recent applications such as fork-join systems, load-balancing, and l-out-of-k redundancy. Common to these systems is a join or resequencing stage, where tasks that have finished service may have to wait for the completion of other tasks so that they leave the system in a predefined order. These synchronization constraints make the analysis of parallel systems challenging and few explicit results are known. In this work, we model parallel systems using a max-plus approach that enables us to derive statistical bounds of waiting and sojourn times. Taking advantage of max-plus system theory, we also show end-to-end delay bounds for multi-stage fork-join networks. We contribute solutions for basic G|G|1 fork-join systems, parallel systems with load-balancing, as well as general (k,l) fork-join systems with redundancy. Our results provide insights into the respective advantages of l-out-of-k redundancy vs. load-balancing.

cs.PF↗

arXiv2015

A Non-stationary Service Curve Model for Performance Analysis of Transient Phases

Steady-state solutions for a variety of relevant queueing systems are known today, e.g., from queueing theory, effective bandwidths, and network calculus. The behavior during transient phases, on the other hand, is understood to a much lesser extent as its analysis poses significant challenges. Considering the majority of short-lived flows, transient effects that have diverse causes, such as TCP slow start, sleep scheduling in wireless networks, or signalling in cellular networks, are, however, predominant. This paper contributes a general model of regenerative service processes to characterize the transient behavior of systems. The model leads to a notion of non-stationary service curves that can be conveniently integrated into the framework of the stochastic network calculus. We derive respective models of sleep scheduling and show the significant impact of transient phases on backlogs and delays. We also consider measurement methods that estimate the service of an unknown system from observations of selected probe traffic. We find that the prevailing rate scanning method does not recover the service during transient phases well. This limitation is fundamental as it is explained by the non-convexity of non-stationary service curves. A second key difficulty is proven to be due to the super-additivity of network service processes. We devise a novel two-phase probing technique that first determines a minimal pattern of probe traffic. This probe is used to obtain an accurate estimate of the unknown transient service.

cs.NI↗

arXiv2015

Backlog and Delay Reasoning in HARQ Systems

Recently, hybrid-automatic-repeat-request (HARQ) systems have been favored in particular state-of-the-art communications systems since they provide the practicality of error detections and corrections aligned with repeat-requests when needed at receivers. The queueing characteristics of these systems have taken considerable focus since the current technology demands data transmissions with a minimum delay provisioning. In this paper, we investigate the effects of physical layer characteristics on data link layer performance in a general class of HARQ systems. Constructing a state transition model that combines queue activity at a transmitter and decoding efficiency at a receiver, we identify the probability of clearing the queue at the transmitter and the packet-loss probability at the receiver. We determine the effective capacity that yields the maximum feasible data arrival rate at the queue under quality-of-service constraints. In addition, we put forward non-asymptotic backlog and delay bounds. Finally, regarding three different HARQ protocols, namely Type-I HARQ, HARQ-chase combining (HARQ-CC) and HARQ-incremental redundancy (HARQ-IR), we show the superiority of HARQ-IR in delay robustness over the others. However, we further observe that the performance gap between HARQ-CC and HARQ-IR is quite negligible in certain cases. The novelty of our paper is a general cross-layer analysis of these systems, considering encoding/decoding in the physical layer and delay aspects in the data-link layer.

cs.IT↗

arXiv2012

H-Probe: Estimating Traffic Correlations from Sampling and Active Network Probing

An extensive body of research deals with estimating the correlation and the Hurst parameter of Internet traffic traces. The significance of these statistics is due to their fundamental impact on network performance. The coverage of Internet traffic traces is, however, limited since acquiring such traces is challenging with respect to, e.g., confidentiality, logging speed, and storage capacity. In this work, we investigate how the correlation of Internet traffic can be reliably estimated from random traffic samples. These samples are observed either by passive monitoring within the network, or otherwise by active packet probes at end systems. We analyze random sampling processes with different inter-sample distributions and show how to obtain asymptotically unbiased estimates from these samples. We quantify the inherent limitations that are due to limited observations and explore the influence of various parameters, such as sampling intensity, network utilization, or Hurst parameter on the estimation accuracy. We design an active probing method which enables simple and lightweight traffic sampling without support from the network. We verify our approach in a controlled network environment and present comprehensive Internet measurements. We find that the correlation exhibits properties such as long range dependence as well as periodicities and that it differs significantly across Internet paths and observation times.

cs.NI↗

arXiv2011

Non-equilibrium Information Envelopes and the Capacity-Delay-Error-Tradeoff of Source Coding

This paper develops an envelope-based approach to establish a link between information and queueing theory. Unlike classical, equilibrium information theory, information envelopes focus on the dynamics of sources and coders, using functions of time that bound the number of bits generated. In the limit the information envelopes converge to the average behavior and recover the entropy of a source, respectively, the average codeword length of a coder. In contrast, on short time scales and for sources with memory it is shown that large deviations from known equilibrium results occur with non-negligible probability. These can cause significant network delays. Compared to well-known traffic models from queueing theory, information envelopes consider the functioning of information sources and coders, avoiding a priori assumptions, such as exponential traffic, or empirical, trace-based traffic models. Using results from the stochastic network calculus, the envelopes yield a characterization of the operating points of source coders by the triplet of capacity, delay, and error. In the limit, assuming an optimal coder the required capacity approaches the entropy with arbitrarily small probability of error if infinitely large delays are permitted. We derive a corresponding characterization of channels and prove that the model has the desirable property of additivity, that allows analyzing coders and channels separately.

cs.PF↗

arXiv2010

A Foundation for Stochastic Bandwidth Estimation of Networks with Random Service

We develop a stochastic foundation for bandwidth estimation of networks with random service, where bandwidth availability is expressed in terms of bounding functions with a defined violation probability. Exploiting properties of a stochastic max-plus algebra and system theory, the task of bandwidth estimation is formulated as inferring an unknown bounding function from measurements of probing traffic. We derive an estimation methodology that is based on iterative constant rate probes. Our solution provides evidence for the utility of packet trains for bandwidth estimation in the presence of variable cross traffic. Taking advantage of statistical methods, we show how our estimation method can be realized in practice, with adaptive train lengths of probe packets, probing rates, and replicated measurements required to achieve both high accuracy and confidence levels. We evaluate our method in a controlled testbed network, where we show the impact of cross traffic variability on the time-scales of service availability, and provide a comparison with existing bandwidth estimation tools.

cs.NI↗

arXiv2009

Statistical End-to-end Performance Bounds for Networks under Long Memory FBM Cross Traffic

Fractional Brownian motion (fBm) emerged as a useful model for self-similar and long-range dependent Internet traffic. Approximate performance measures are known from large deviations theory for single queuing systems with fBm through traffic. In this paper we derive end-to-end performance bounds for a through flow in a network of tandem queues under fBm cross traffic. To this end, we prove a rigorous sample path envelope for fBm that complements previous approximate results. We find that both approaches agree in their outcome that overflow probabilities for fBm traffic have a Weibullian tail. We employ the sample path envelope and the concept of leftover service curves to model the remaining service after scheduling fBm cross traffic at a system. Using composition results for tandem systems from the stochastic network calculus we derive end-to-end statistical performance bounds for individual flows in networks under fBm cross traffic. We discover that these bounds grow in O(n (log n)^(1/(2-2H))) for n systems in series where H is the Hurst parameter of the fBm cross traffic. We show numerical results on the impact of the variability and the correlation of fBm traffic on network performance.

cs.NI↗

arXiv2008

Understanding Fairness and its Impact on Quality of Service in IEEE 802.11

The Distributed Coordination Function (DCF) aims at fair and efficient medium access in IEEE 802.11. In face of its success, it is remarkable that there is little consensus on the actual degree of fairness achieved, particularly bearing its impact on quality of service in mind. In this paper we provide an accurate model for the fairness of the DCF. Given M greedy stations we assume fairness if a tagged station contributes a share of 1/M to the overall number of packets transmitted. We derive the probability distribution of fairness deviations and support our analytical results by an extensive set of measurements. We find a closed-form expression for the improvement of long-term over short-term fairness. Regarding the random countdown values we quantify the significance of their distribution whereas we discover that fairness is largely insensitive to the distribution parameters. Based on our findings we view the DCF as emulating an ideal fair queuing system to quantify the deviations from a fair rate allocation. We deduce a stochastic service curve model for the DCF to predict packet delays in IEEE 802.11. We show how a station can estimate its fair bandwidth share from passive measurements of its traffic arrivals and departures.

cs.NI↗