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Register a new userBlockchain Queueing Theory
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Added by
Quan-Lin Li
Publication date
2018
fields
Informatics Engineering
and research's language is
English
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Blockchain has many benefits including decentralization, availability, persistency, consistency, anonymity, auditability and accountability, and it also covers a wide spectrum of applications ranging from cryptocurrency, financial services, reputation system, Internet of Things, sharing economy to public and social services. Not only may blockchain be regarded as a by-product of Bitcoin cryptocurrency systems, but also it is a type of distributed ledger technology through using a trustworthy, decentralized log of totally ordered transactions. By summarizing the literature of blockchain, it is found that more papers focus on engineering implementation and realization, while little work has been done on basic theory, for example, mathematical models (Markov processes, queueing theory and game models), performance analysis and optimization of blockchain systems. In this paper, we develop queueing theory of blockchain systems and provide system performance evaluation. To do this, we design a Markovian batch-service queueing system with two different service stages, while the two stages are suitable to well express the mining process in the miners pool and the building of a new blockchain. By using the matrix-geometric solution, we obtain a system stable condition and express three key performance measures: (a) The number of transactions in the queue, (b) the number of transactions in a block, and (c) the transaction-confirmation time. Finally, We use numerical examples to verify computability of our theoretical results. Although our queueing model is simple under exponential or Poisson assumptions, our analytic method will open a series of potentially promising research in queueing theory of blockchain systems.
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Cloud computing today is dominated by multi-server jobs. These are jobs that request multiple servers simultaneously and hold onto all of these servers for the duration of the job. Multi-server jobs add a lot of complexity to the traditional one-job-per-server model: an arrival might not fit into the available servers and might have to queue, blocking later arrivals and leaving servers idle. From a queueing perspective, almost nothing is understood about multi-server job queueing systems; even understanding the exact stability region is a very hard problem. In this paper, we investigate a multi-server job queueing model under scaling regimes where the number of servers in the system grows. Specifically, we consider a system with multiple classes of jobs, where jobs from different classes can request different numbers of servers and have different service time distributions, and jobs are served in first-come-first-served order. The multi-server job model opens up new scaling regimes where both the number of servers that a job needs and the system load scale with the total number of servers. Within these scaling regimes, we derive the first results on stability, queueing probability, and the transient analysis of the number of jobs in the system for each class. In particular we derive sufficient conditions for zero queueing. Our analysis introduces a novel way of extracting information from the Lyapunov drift, which can be applicable to a broader scope of problems in queueing systems.
In the todays Internet and TCP/IP-networks, the queueing of packets is commonly implemented using the protocol FIFO (First In First Out). Unfortunately, FIFO performs poorly in the Adversarial Queueing Theory. Other queueing strategies are researched in this model and better results are performed by alternative queueing strategies, e.g. LIS (Longest In System). This article introduces a new queueing protocol called interval-strategy that is concerned with the reduction from dynamic to static routing. We discuss the maximum system time for a packet and estimate with up-to-date results how this can be achieved. We figure out the maximum amount of time where a packet can spend in the network (i.e. worst case system time), and argue that the universal instability of the presented interval-strategy can be reached through these results. When a large group of queueing strategies is used for queueing, we prove that the interval-strategy will be universally unstable. Finally, we calculate the maximum time of the static routing to reach an universal stable and polynomial - in detail linear - bounded interval-strategy. Afterwards we close - in order to check this upper bound - with up-to-date results about the delivery times in static routing.
Traffic microscopic simulation applications are a common tool in road transportation analysis and several attempts to perform road safety assessments have recently been carried out. However, these approaches often ignore causal relationships between different levels of vehicle interactions and/or accident types and they lack a physical representation of the accident phenomena itself. In this paper, a new generic probabilistic safety assessment framework for traffic microscopic simulation tools is proposed. The probability of a specific accident occurring is estimated by an accident propensity function that consists of a deterministic safety score component and a random component. The formulation of the safety score depends on the type of occurrence, on detailed vehicle interactions and maneuvers and on its representation in a simulation environment. This generic model is applied to the case of an urban motorway and specified to four types of outcomes: non-accident events and three types of accidents in a nested structure: rear-end, lane-changing, and run-off-road accidents. The model was estimated and validated using simulated microscopic data. To obtained the consistent simulated data, a two-step simulation calibration procedure was adopted: (1) using real trajectories collected on site for detailed behavior representation; and (2) using aggregate data from each event used in safety model estimation. The final estimated safety model is able to identify and interpret several simulated vehicle interactions. The fact that these outcomes were extracted from simulated analysis shows the real potential of calibrated traffic microscopic simulation for detailed safety assessments.
In brittle fracture applications, failure paths, regions where the failure occurs and damage statistics, are some of the key quantities of interest (QoI). High-fidelity models for brittle failure that accurately predict these QoI exist but are highly computationally intensive, making them infeasible to incorporate in upscaling and uncertainty quantification frameworks. The goal of this paper is to provide a fast heuristic to reasonably estimate quantities such as failure path and damage in the process of brittle failure. Towards this goal, we first present a method to predict failure paths under tensile loading conditions and low-strain rates. The method uses a $k$-nearest neighbors algorithm built on fracture process zone theory, and identifies the set of all possible pre-existing cracks that are likely to join early to form a large crack. The method then identifies zone of failure and failure paths using weighted graphs algorithms. We compare these failure paths to those computed with a high-fidelity model called the Hybrid Optimization Software Simulation Suite (HOSS). A probabilistic evolution model for average damage in a system is also developed that is trained using 150 HOSS simulations and tested on 40 simulations. A non-parametric approach based on confidence intervals is used to determine the damage evolution over time along the dominant failure path. For upscaling, damage is the key QoI needed as an input by the continuum models. This needs to be informed accurately by the surrogate models for calculating effective modulii at continuum-scale. We show that for the proposed average damage evolution model, the prediction accuracy on the test data is more than 90%. In terms of the computational time, the proposed models are $approx mathcal{O}(10^6)$ times faster compared to high-fidelity HOSS.
A term structure model in which the short rate is zero is developed as a candidate for a theory of cryptocurrency interest rates. The price processes of crypto discount bonds are worked out, along with expressions for the instantaneous forward rates and the prices of interest-rate derivatives. The model admits functional degrees of freedom that can be calibrated to the initial yield curve and other market data. Our analysis suggests that strict local martingales can be used for modelling the pricing kernels associated with virtual currencies based on distributed ledger technologies.
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