Performance analysis of networks on chips

Modules on a chip (such as processors and memories) are traditionally connected through a single link, called a bus. As chips become more complex and the number of modules on a chip increases, this connection method becomes inefficient because the bus can only be used by one module at a time. Networks on chips are an emerging technology for the connection of on-chip modules. In networks on chips, switches are used to transmit data from one module to another, which entails that multiple links can be used simultaneously so that communication is more efficient. Switches consist of a number of input ports to which data arrives and output ports from which data leaves. If data at multiple input ports has to be transmitted to the same output port, only one input port may actually transmit its data, which may lead to congestion. Queueing theory deals with the analysis of congestion phenomena caused by competition for service facilities with scarce resources. Such phenomena occur, for example, in traffic intersections, manufacturing systems, and communication networks like networks on chips. These congestion phenomena are typically analysed using stochastic models, which capture the uncertain and unpredictable nature of processes leading to congestion (such as irregular car arrivals to a traffic intersection). Stochastic models are useful tools for the analysis of networks on chips as well, due to the complexity of data traffic on these networks. In this thesis, we therefore study queueing models aimed at networks on chips. The thesis is centred around two key models: A model of a switch in isolation, the so-called single-switch model, and a model of a network of switches where all traffic has the same destination, the so-called network of polling stations. For both models we are interested in the throughput (the amount of data transmitted per time unit) and the mean delay (the time it takes data to travel across the network). Single-switch models are often studied under the assumption that the number of ports tends to infinity and that traffic is uniform (i.e., on average equally many packets arrive to all buffers, and all possible destinations are equally likely). In networks on chips, however, the number of buffers is typically small. We introduce a new approximation specifically aimed at small switches with (memoryless) Bernoulli arrivals. We show that, for such switches, this approximation is more accurate than currently known approximations. As traffic in networks on chips is usually non-uniform, we also extend our approximation to non-uniform switches. The key difference between uniform and nonuniform switches is that in non-uniform switches, all queues have a different maximum throughput. We obtain a very accurate approximation of this throughput, which allows us to extend the mean delay approximation. The extended approximation is derived for Bernoulli arrivals and correlated arrival processes. Its accuracy is verified through a comparison with simulation results. The second key model is that of concentrating tree networks of polling stations (polling stations are essentially switches where all traffic has the same output port as destination). Single polling stations have been studied extensively in literature, but only few attempts have been made to analyse networks of polling stations. We establish a reduction theorem that states that networks of polling stations can be reduced to single polling stations while preserving some information on mean waiting times. This reduction theorem holds under the assumption that the last node of the network uses a so-called HoL-based service discipline, which means that the choice to transmit data from a certain buffer may only depend on which buffers are empty, but not on the amount of data in the buffers. The reduction theorem is a key tool for the analysis of networks of polling stations. In addition to this, mean waiting times in single polling stations have to be calculated, either exactly or approximately. To this end, known results can be used, but we also devise a new single-station approximation that can be used for a large subclass of HoL-based service disciplines. Finally, networks on chips typically implement flow control, which is a mechanism that limits the amount of data in the network from one source. We analyse the division of throughput over several sources in a network of polling stations with flow control. Our results indicate that the throughput in such a network is determined by an interaction between buffer sizes, flow control limits, and service disciplines. This interaction is studied in more detail by means of a numerical analysis

Modeling developmental and linguistic relativity effects in color term acquisition

We model two patterns related to the acquisition of color termsin Russian and English: children produce overextension errorsfor some colors but not others, and language-specific distinc-tions affect color discrimination in a non-linguistic task. Botheffects, as well as a reasonable convergence with adult linguis-tic behavior, are shown by a Self-Organizing Map trained onnaturalistic input. We investigate the effect of different waysof representing colors, i.e., as perceptual features or in terms ofthe cognitive biases on categorization extracted from crosslin-guistic color naming data. We also consider the influence ofcolor term frequency. Our results suggest effects of all three ofterm frequency, cognitive biases, and perceptual features

A comparison of homonym meaning frequency estimates derived from movie and television subtitles, free association, and explicit ratings

First Online: 10 September 2018Most words are ambiguous, with interpretation dependent on context. Advancing theories of ambiguity resolution is important for any general theory of language processing, and for resolving inconsistencies in observed ambiguity effects across experimental tasks. Focusing on homonyms (words such as bank with unrelated meanings EDGE OF A RIVER vs. FINANCIAL INSTITUTION), the present work advances theories and methods for estimating the relative frequency of their meanings, a factor that shapes observed ambiguity effects. We develop a new method for estimating meaning frequency based on the meaning of a homonym evoked in lines of movie and television subtitles according to human raters. We also replicate and extend a measure of meaning frequency derived from the classification of free associates. We evaluate the internal consistency of these measures, compare them to published estimates based on explicit ratings of each meaning’s frequency, and compare each set of norms in predicting performance in lexical and semantic decision mega-studies. All measures have high internal consistency and show agreement, but each is also associated with unique variance, which may be explained by integrating cognitive theories of memory with the demands of different experimental methodologies. To derive frequency estimates, we collected manual classifications of 533 homonyms over 50,000 lines of subtitles, and of 357 homonyms across over 5000 homonym–associate pairs. This database—publicly available at: www.blairarmstrong.net/homonymnorms/—constitutes a novel resource for computational cognitive modeling and computational linguistics, and we offer suggestions around good practices for its use in training and testing models on labeled data

Approximation of discrete-time polling systems via structured Markov chains

We devise an approximation of the marginal queue length distribution in discrete-time polling systems with batch arrivals and fixed packet sizes. The polling server uses the Bernoulli service discipline and Markovian routing. The 1-limited and exhaustive service disciplines are special cases of the Bernoulli service discipline, and traditional cyclic routing is a special case of Markovian routing. The key step of our approximation is the translation of the polling system to a structured Markov chain, while truncating all but one queue. Numerical experiments show that the approximation is very accurate in general. Our study is motivated by networks on chips with multiple masters (e.g., processors) sharing a single slave (e.g., memory)

Remodelling complement coercion interpretation

Existing (experimental and computational) linguistic work uses participant paraphrases as a stand-in for event interpretation in complement coercion sentences (e.g. she finished the coffee \u3e she finished drinking the coffee). We present crowdsourcing data and modelling that supports broadening this conception. In particular, our results suggest that sentences where many participants do not give a paraphrase, or where many different paraphrases are given, are informative about to how complement coercion is interpreted in naturalistic contexts

End-to-end delays in polling tree networks

We consider a tree network of polling stations operating in discrete-time. Packets arrive from external sources to the network according to batch Bernoulli arrival processes. We assume that all nodes have a service discipline that is HoL-based. The class of HoL-based service disciplines contains for instance the Bernoulli and limited service disciplines, and hence also the classical exhaustive and 1-limited. We obtain an exact expression for the overall mean end-to-end delay, and an approximation for the mean end-to-end delay of packets per source. The study is motivated by Networks on Chips where multiple processors share a single memory