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This lucid, accessible introduction to supervised machine learning presents core concepts in a focused and logical way that is easy for beginners to follow. The author assumes basic calculus, linear algebra, probability and statistics but no prior exposure to machine learning. Coverage includes widely used traditional methods such as SVMs, boosted trees, HMMs, and LDAs, plus popular deep learning methods such as convolution neural nets, attention, transformers, and GANs. Organized in a coherent presentation framework that emphasizes the big picture, the text introduces each method clearly and concisely “from scratch” based on the fundamentals. All methods and algorithms are described by a clean and consistent style, with a minimum of unnecessary detail. Numerous case studies and concrete examples demonstrate how the methods can be applied in a variety of contexts.
While in theory systems with traffic intensity rho > 1 blow up, in reality they are stabilized by abandonments. We study limiting results for many-server systems with abandonments.
We introduces some more general processing networks and the maximum pressure policy, which uses local information for decentralized control of the network. Maximum pressure policies can guarantee the stability of MCQN as well as of more general processing networks, under some simple structure conditions, whenever traffic intensity rho < 1.
We present the ingenious scheme devised by Loynes to show that G/G/1 with stationary arrival and service processes is stable when the traffic intensity rho < 1, and transient if rho > 1. Under the stronger assumption that interarrivals and services are i.i.d., we explore the connection of the GI/GI/1 queue with the general random walk and obtain an insightful upper bound on waiting time.
We discuss the case in which arrivals, service, and routing are all memoryless, which is the classic Jackson network, and some related systems. For all of these, the stationary distribution is obtainable and is of product form.
Because time is not scaled, limiting results for many-server scaling retains dependence on the service time distribution, as we saw in the scaling of M/GI/1. We extend these infinite server results to general time-dependent arrival streams.
We discuss the classic Jackson network with general i.i.d. interarrivals and service times, the generalized Jackson network. Like the GI/GI/1 system, the generalized Jackson network cannot be analyzed in detail, and we discuss fluid and diffusion approximations to the network process.
We consider Brownian problems of scheduling and admission control, where we force congestion to be kept at the least costly nodes, and use admission control to regulate congestion.
We define fluid limits and show that stability of the fluid limits implies stability of the stochastic queueing system. This enables us to study stability of MCQN under various policies.