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We construct an optimal execution strategy for the purchase of a large number of shares of a financial asset over a fixed interval of time. Purchases of the asset have a nonlinear impact on price, and this is moderated over time by resilience in the limit-order book that determines the price. The limit-order book is permitted to have arbitrary shape. The(More)
A queueing model has J ≥ 2 heterogeneous service stations, each consisting of many independent servers with identical capabilities. Customers of I ≥ 2 classes can be served at these stations at different rates, that depend on both the class and the station. A system administrator dynamically controls scheduling and routing. We study this model in the(More)
We consider scheduling and routing control problems for queueing models with I customer classes and J server pools, each consisting of many statistically identical, exponential servers. Customers require a single service that can be performed by a server from one of the pools; the service rate is ij ≥ 0, which depends on the customer’s class i and the(More)
A large number n of sensors (finite connected intervals) are placed randomly on the real line so that the distances between the consecutive midpoints are independent random variables with expectation inversely proportional to n. In this work we address two fundamental sensor allocation problems. Interference problem tries to reallocate the sensors from(More)
—We consider a problem of supplying electricity to a set of N customers in a smart-grid framework. Each customer requires a certain amount of electrical energy which has to be supplied during the time interval [0, 1]. We assume that each demand has to be supplied without interruption, with possible duration between and r, which are given system parameters(More)
This paper introduces and analyzes the notion of throughput suboptimality for many-server queueing systems in heavy traffic. The queueing model under consideration has multiple customer classes, indexed by a finite set I, and heterogenous, exponential servers. Servers are dynamically chosen to serve customers, and buffers are available for customers waiting(More)
—We consider a problem of supplying electricity to a network of electric demands, N , in a smart-grid framework. Each demand requires a random amount of electrical energy which has to be supplied during the time interval [0, 1]. We model this network by malleable rectangular shape demands, and then relate the resulted scheduling problem to well known Strip(More)