Stability and performance of greedy server systems

Consider a queueing system in which arriving customers are placed on a circle and wait for service. A traveling server moves at constant speed on the circle, stopping at the location of the customers until service completion. The server is greedy: always moving in the direction of the nearest customer. Coffman and Gilbert conjectured that this system is stable if the traffic intensity is smaller than 1; however, a proof or counterexample remains unknown. In this review, we present a picture of the current state of this conjecture and suggest new related open problems.     

Structure determination of MnO2 films grown on single crystal α-Al2O3 substrates

Manganese oxide films have been grown by atomic layer deposition and investigated using electron diffraction and high-resolution electron microscopy (HREM). The films were deposited on the (001) surface of monocrystalline α-Al₂O₃. The films were found to consist of an ordered version of the hexagonal ε-MnO₂ (Akhtenskite) type. Using X-ray diffraction, the cell parameters were determined to be a?=?2.75(2)?Å and c?=?4.302(5)?Å. The films are epitaxial with a specific orientation relative to the Al₂O₃ substrate. The [210] and [001] axes of ε-MnO₂ are parallel to the [110] and [001] axes of α-Al₂O₃, respectively. Evidence of cation ordering was found by parallel beam electron diffraction. The ordered domains are needle shaped with widths of 2–10?nm. The unit cell of the ordered structure was found to be orthorhombic with cell dimensions a?=?2.75, b?=?4.76, c?=?4.302?Å and space group Pmnn (No. 58).     

A decision support model for establishing an air taxi service: a case study

Recent availability of relatively cheap small jet aircraft creates opportunities for a new air transport business: Air taxi, an on-demand service in which travellers call in one or a few days in advance to book transportation. In this paper, we present a methodology and simulation study supporting important strategic decisions, like for instance determining the required number of aircraft, for a company planning to establish an air taxi service in Norway. The methodology is based on a module simulating incoming bookings, built around a heuristic for solving the underlying dial-a-flight problem. The heuristic includes a separate method for solving the important subproblem of determining the best distribution of waiting time along a single aircraft schedule. The methodology has proved to provide reliable decision support to the company.     

Asymptotics for Sums of Random Variables with Local Subexponential Behaviour

We study distributions F on [0,) such that for some T , F ^*2(x, x+T] 2F(x, x+T]. The case T = corresponds to F being subexponential, and our analysis shows that the properties for T < are, in fact, very similar to this classical case. A parallel theory is developed in the presence of densities. Applications are given to random walks, the key renewal theorem, compound Poisson process and Bellman–Harris branching processes.     

On Optimality of the FCFS Discipline in Multiserver Queueing Systems and Networks

Siberian Mathematical Journal -