Strategic customer behavior in a queueing system with a loss subsystem

In the spirit of Little’s law \(L=\lambda W\) and its extension \(H=\lambda G\) we use sample-path analysis to give a general conservation law. For queueing models the law relates the asymptotic average workload in the system to the conditional asymptotic average sojourn time and service times distribution function. This law generalizes previously obtained conservation laws for both single- and multi-server systems, and anticipating and non-anticipating scheduling disciplines. Applications to single- and multi-class queueing and other systems that illustrate the versatility of this law are given. In particular, we show that, for anticipative and non-anticipative scheduling rules, the unconditional delay in a queue is related to the covariance of service times and queueing delays.     

Strategic behaviour in a tandem queue with alternating server

Queueing Systems - This paper considers an unobservable two-site tandem queueing system attended by an alternating server. We study the strategic customer behaviour under two threshold-based...     

High precision measurements of the temperature dependence of the sound velocity in selected liquid metals

The temperature dependence of the sound velocity in liquid lead, tin, bismuth and antimony has been measured with high precision (errors of less than 0.35%) by the ultrasonic pulse transmission technique. The measurements were performed from the melting temperature to approximately 1000 °C. A smooth temperature dependence of the sound velocity was found in liquid lead and antimony. In liquid lead, a linear dependence with a negative temperature coefficient was observed whereas for liquid antimony the sound velocity displays a distinct maximum. The high precision of the measurements enabled uncovering localized features in the temperature dependence of the sound velocity in liquid tin and bismuth. The measurements provide some information on the temperature dependent structure of the molten state of these four elements.     

Approximation Algorithms for Min–Max Tree Partition

We consider the problem of partitioning the node set of a graph intopequal sized subsets. The objective is to minimize the maximum length, over these subsets, of a minimum spanning tree. We show that no polynomial algorithm with bounded error ratio can be given for the problem unless P = NP. We present anO(n²) time algorithm for the problem, wherenis the number of nodes in the graph. Assuming that the edge lengths satisfy the triangle inequality, its error ratio is at most 2p − 1. We also present an improved algorithm that obtains as an input a positive integerx. It runs inO(2^{(p + x)p}n²) time, and its error ratio is at most (2 − x/(x + p − 1))p.     

Unconventional Josephson signatures of Majorana bound states

A junction between two topological superconductors containing a pair of Majorana fermions exhibits a "fractional" Josephson effect, 4π periodic in the superconductors' phase difference. An additional fractional Josephson effect, however, arises when the Majorana fermions are spatially separated by a superconducting barrier. This new term gives rise to a set of Shapiro steps which are essentially absent without Majorana modes and therefore provides a unique signature for these exotic states.     

Majorana fermions in equilibrium and in driven cold-atom quantum wires

We introduce a new approach to create and detect Majorana fermions using optically trapped 1D fermionic atoms. In our proposed setup, two internal states of the atoms couple via an optical Raman transition-simultaneously inducing an effective spin-orbit interaction and magnetic field-while a background molecular BEC cloud generates s-wave pairing for the atoms. The resulting cold-atom quantum wire supports Majorana fermions at phase boundaries between topologically trivial and nontrivial regions, as well as "Floquet Majorana fermions" when the system is periodically driven. We analyze experimental parameters, detection schemes, and various imperfections.     

Dynamic stimulation of quantum coherence in systems of lattice bosons

Thermal fluctuations tend to destroy long-range phase correlations. Consequently, bosons in a lattice will undergo a transition from a phase-coherent superfluid as the temperature rises. Contrary to common intuition, however, we show that nonequilibrium driving can be used to reverse this thermal decoherence. This is possible because the energy distribution at equilibrium is rarely optimal for the manifestation of a given quantum property. We demonstrate this in the Bose-Hubbard model by calculating the nonequilibrium spatial correlation function with periodic driving. We show that the nonequilibrium phase boundary between coherent and incoherent states at finite bath temperatures can be made qualitatively identical to the familiar zero-temperature phase diagram, and we discuss the experimental manifestation of this phenomenon in cold atoms.     

The minimum cost flow problem: A unifying approach to dual algorithms and a new tree-search algorithm

This paper is concerned with the minimum cost flow problem. It is shown that the class of dual algorithms which solve this problem consists of different variants of a common general algorithm. We develop a new variant which is, in fact, a new form of the ‘primal-dual algorithm’ and which has several interesting properties. It uses, explicitly only dual variables. The slope of the change in the (dual) objective is monotone. The bound on the maximum number of iterations to solve a problem with integral bounds on the flow is better than bounds for other algorithms. This paper is part of the author's doctoral dissertation submitted at Yale University.     

?/M/1: On the equilibrium distribution of customer arrivals

Each day a facility commences service at time zero. All customers arriving prior to time T are served during that day. The queuing discipline is First-Come First-Served. Each day, each person in the population chooses whether or not to visit the facility that day. If he decides to visit, he arrives at an instant of time such that his expected waiting time in the queue is minimal. We investigate the arrival rate of customers in equilibrium, where each customer is fully aware of the characteristics of the system. We show that the arrival rate is constant before opening time, but that in general it is not constant between opening and closing time. For the case of exponential distribution of service time, we develop a set of equations from which the equilibrium queue size distribution and expected waiting time can be numerically computed as functions of time.