Highway system is experiencing increasing traffic congestion with fast-growing number of vehicles in metropolitan areas. Implementing management strategies such as utilizing the hard shoulder an extra lane could increase highway capacity without construction work. This paper presents a method determining optimal condition and speed limit opening shoulder. Firstly, states are clustered using K-M...

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 form of the optimal execution strategy i...

We propose a framework for studying optimal market making policies in a limit order book (LOB). The bid-ask spread of the LOB is modelled by a Markov chain with finite values, multiple of the tick size, and subordinated by the Poisson process of the tick-time clock. We consider a small agent who continuously submits limit buy/sell orders at best bid/ask quotes, and may also set limit orders at ...

Traditional methods for solving multiuser control problems in CDMA systems do not scale well as the number of users in the system increases. Indeed, the size and complexity of the control problem generally grows exponentially with the number of users. In order to find a tractable solution to these problems we develop a wideband limit approximation for dynamic programming problems in CDMA system...

Based on a recent L-L framework, we establish the acoustic limit of the Boltzmann equation for general collision kernels. The scaling of the fluctuations with respect to Knudsen number is optimal. Our approach is based on a new analysis of the compressible Euler limit of the Boltzmann equation, as well as refined estimates of Euler and acoustic solutions.

The theoretical limit of the minimal magnetization switching field and the optimal field pulse design for uniaxial Stoner particles are investigated. Two results are obtained. One is the existence of a theoretical limit of the smallest magnetic field out of all possible designs. It is shown that the limit is proportional to the damping constant in the weak damping regime and approaches the Ston...

We numerically determine the equilibrium trading strategies in a Continuous Double Auction (CDA). We consider heterogeneous and liquidity motivated agents, with private values and costs, that trade sequentially in random order under time constraints and are not aware of the type of the other agents in their session. We assume that they submit limit orders using a simple linear function of the c...

A crucial step in model checking Markov Decision Processes (MDP) is to translate the LTL specification into automata. Efforts have been made in improving deterministic automata construction for LTL but such translations are double exponential in the worst case. For model checking MDPs though limit deterministic automata suffice. Recently it was shown how to translate the fragment LTL\GU to expo...

We study numerically the optimal paths in two and three dimensions on various disordered lattices in the limit of strong disorder. We find that the length l of the optimal path scales with geometric distance r , as l approximately r (d(opt) ) with d(opt) =1.22+/-0.01 for d=2 and 1.44+/-0.02 for d=3 , independent of whether the optimization is on a path of weighted bonds or sites, and independen...

We study the problem of optimally liquidating a large portfolio position in a limit order book market. We allow for both limit and market orders and the optimal solution is a combination of both types of orders. Market orders deplete the order book, making future trades more expensive, whereas limit orders can be entered at more favorable prices but are not guaranteed to be filled. We model the...