Approximations and Bounds for (n, k) Fork-Join Queues: A Linear Transformation Approach

Compared to basic fork-join queues, a job in (n, k) fork-join queues only needs its k out of all n sub-tasks to be finished. Since (n, k) fork-join queues are prevalent in popular distributed systems, erasure coding based cloud storages, and modern network protocols like multipath routing, estimating the sojourn time of such queues is thus critical for the performance measurement and resource plan of computer clusters. However, the estimating keeps to be a well-known open challenge for years, and only rough bounds for a limited range of load factors have been given. In this paper, we developed a closed-form linear transformation technique for jointly-identical random variables: An order statistic can be represented by a linear combination of maxima. This brand-new technique is then used to transform the sojourn time of non-purging (n, k) fork-join queues into a linear combination of the sojourn times of basic (k, k), (k+1, k+1), ..., (n, n) fork-join queues. Consequently, existing approximations for basic fork-join queues can be bridged to the approximations for non-purging (n, k) fork-join queues. The uncovered approximations are then used to improve the upper bounds for purging (n, k) fork-join queues. Simulation experiments show that this linear transformation approach is practiced well for moderate n and relatively large k.Comment: 10 page

Approximations for fork/join systems with inputs from multi-server stations.

Fork/join stations are commonly used to model synchronization constraints in queuing network models of computer and manufacturing systems. This paper presents an exact analysis of a fork/join station in a closed queuing network with inputs from multi-server stations with two-phase Coxian service distributions. The underlying queue length process is analyzed exactly to determine performance measures such as through put, and distributions of the queue length at the fork/join station. By choosing suitable parameters for the two-phase Coxian distributions, the effect of variability in inputs on system performance is studied. The study reveals that for several system configurations, analysis of the simpler system with exponential inputs provides efficient approximations for performance measures. Both, the exact analysis and the simple approximations of fork/join systems constitute useful building blocks for developing efficient methods for analyzing large queuing networks with fork/join stations.queueing; fork/join; synchronization; assembly systems; closed queuing networks;

Collaborative Uploading in Heterogeneous Networks: Optimal and Adaptive Strategies

Collaborative uploading describes a type of crowdsourcing scenario in networked environments where a device utilizes multiple paths over neighboring devices to upload content to a centralized processing entity such as a cloud service. Intermediate devices may aggregate and preprocess this data stream. Such scenarios arise in the composition and aggregation of information, e.g., from smartphones or sensors. We use a queuing theoretic description of the collaborative uploading scenario, capturing the ability to split data into chunks that are then transmitted over multiple paths, and finally merged at the destination. We analyze replication and allocation strategies that control the mapping of data to paths and provide closed-form expressions that pinpoint the optimal strategy given a description of the paths' service distributions. Finally, we provide an online path-aware adaptation of the allocation strategy that uses statistical inference to sequentially minimize the expected waiting time for the uploaded data. Numerical results show the effectiveness of the adaptive approach compared to the proportional allocation and a variant of the join-the-shortest-queue allocation, especially for bursty path conditions.Comment: 15 pages, 11 figures, extended version of a conference paper accepted for publication in the Proceedings of the IEEE International Conference on Computer Communications (INFOCOM), 201

Nested Fork-Join Queuing Networks and Their Application to Mobility Airfield Operations Analysis

A single-chain nested fork-join queuing network (FJQN) model of mobility airfield ground processing is proposed. In order to analyze the queuing network model, advances on two fronts are made. First, a general technique for decomposing nested FJQNs with probabilistic forks is proposed, which consists of incorporating feedback loops into the embedded Markov chain of the synchronization station, then using Marie\u27s Method to decompose the network. Numerical studies show this strategy to be effective, with less than two percent relative error in the approximate performance measures in most realistic cases. The second contribution is the identification of a quick, efficient method for solving for the stationary probabilities of the λn/Ck/r/N queue. Unpreconditioned Conjugate Gradient Squared is shown to be the method of choice in the context of decomposition using Marie\u27s Method, thus broadening the class of networks where the method is of practical use. The mobility airfield model is analyzed using the strategies described above, and accurate approximations of airfield performance measures are obtained in a fraction of the time needed for a simulation study. The proposed airfield modeling approach is especially effective for quick-look studies and sensitivity analysis

Blockchain For Food: Making Sense of Technology and the Impact on Biofortified Seeds

The global food system is under pressure and is in the early stages of a major transition towards more transparency, circularity, and personalisation. In the coming decades, there is an increasing need for more food production with fewer resources. Thus, increasing crop yields and nutritional value per crop is arguably an important factor in this global food transition. Biofortification can play an important role in feeding the world. Biofortified seeds create produce with increased nutritional values, mainly minerals and vitamins, while using the same or less resources as non-biofortified variants. However, a farmer cannot distinguish a biofortified seed from a regular seed. Due to the invisible nature of the enhanced seeds, counterfeit products are common, limiting wide-scale adoption of biofortified crops. Fraudulent seeds pose a major obstacle in the adoption of biofortified crops. A system that could guarantee the origin of the biofortified seeds is therefore required to ensure widespread adoption. This trust-ensuring immutable proof for the biofortified seeds, can be provided via blockchain technology

Coupled queues with customer impatience

Motivated by assembly processes, we consider a Markovian queueing system with multiple coupled queues and customer impatience. Coupling means that departures from all constituent queues are synchronised and that service is interrupted whenever any of the queues is empty and only resumes when all queues are non-empty again. Even under Markovian assumptions, the state space grows exponentially with the number of queues involved. To cope with this inherent state space explosion problem, we investigate performance by means of two numerical approximation techniques based on series expansions, as well as by deriving the fluid limit. In addition, we provide closed-form expressions for the first terms in the series expansion of the mean queue content for the symmetric coupled queueing system. By an extensive set of numerical experiments, we show that the approximation methods complement each other, each one being accurate in a particular subset of the parameter space. (C) 2017 Elsevier B.V. All rights reserved