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;

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

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

Analysis of Aircraft Sortie Generation with Concurrent Maintenance and General Service Times

The primary objective of this study was to develop an analytical methodology for evaluating an aircraft sortie generation process. The process is modeled as a closed network of general service queues with a fork join node to model concurrent servicing. The model uses the Mean Value Analysis (MVA) algorithm and general queueing network analysis by decomposition to approximate network performance measures including resource utilization and the overall sortie generation rate. The results of the study show that the analytical approximation\u27s accuracy decreases as server utilization increases. However, when server utilization is kept in realistic ranges, the approximation is very accurate. When applied to a closed system of single server queues and delay stations, the approximation performs significantly better than a pure MVA-based approach. For closed or capacitated open systems with multiserver queues, the approximation can still be applied to provide upper and lower bounds on system performance

Taming tail latency for erasure-coded, distributed storage systems

Nowadays, in distributed storage systems, long tails of responsible time are of particular concern. Modern large companies like Bing, Facebook and Amazon Web Service show that 99.9th percentile response times being orders of magnitude worse than the mean. With the advantages of maintaining high data reliability and ensur- ing enough space eciency, erasure code has become a popular storage method in distributed storage systems. However, due to the lack of mathematical models for analyzing erasure-coded based distributed storage systems, taming tail latency is still an open problem. In this research, we quantify tail latency in such systems by deriving a closed upper bounds on tail latency for general service time distribution and heterogeneous files. Later we specified service time to shifted exponentially distributed. Based on this model, we developed an optimization problem to minimize weighted tail latency probability of deriving all files. We propose an alternating minimization algorithm for this problem. Our simulation results have shown significant reduction on tail latency of erasure-coded distributed storage systems with realistic environment workload