The Behavior of the Renewal Sequence in Case the Tail of the Waiting-Time Distribution Is Regularly Varying with Index -1

A second-order asymptotic result for the probability of occurrence of a persistent and aperiodic recurrent event is given if the tail of the distribution of the waiting time for this event is regularly varying with index -1

Single-leg airline revenue management with overbooking

Airline revenue management is about identifying the maximum revenue seat allocation policies. Since a major loss in revenue results from cancellations and no-show passengers, over the years overbooking has received a significant attention in the literature. In this study, we propose new models for static and dynamic single-leg overbooking problems. In the static case, we introduce computationally tractable models that give upper and lower bounds for the optimal expected revenue. In the dynamic case, we propose a new dynamic programming model, which is based on two streams of arrivals. The first stream corresponds to the booking requests and the second stream represents the cancellations. We also conduct simulation experiments to illustrate the proposed models and the solution methods

Two simple algorithms for bin covering

We define two simple algorithms for the bin covering problem and give their asymptotic performance

Order statistics and the linear assignment problem

Under mild conditions on the distribution functionF, we analyze the asymptotic behavior in expectation of the smallest order statistic, both for the case thatF is defined on (–, +) and for the case thatF is defined on (0, ). These results yield asymptotic estimates of the expected optiml value of the linear assignment problem under the assumption that the cost coefficients are independent random variables with distribution functionF

On Linear Programming Duality and Necessary and Sufficient Conditions in Minimax Theory

In this paper we discuss necessary and sufficient conditions for different minimax results to hold using only linear programming duality and the finite intersection property for compact sets. It turns out that these necessary and sufficient conditions have a clear interpretation within zero-sum game theory. We apply these results to derive necessary and sufficient conditions for strong duality for a general class of optimization problems

General models in min-max continous location

In this paper, a class of min-max continuous location problems is discussed. After giving a complete characterization of th stationary points, we propose a simple central and deep-cut ellipsoid algorithm to solve these problems for the quasiconvex case. Moreover, an elementary convergence proof of this algorithm and some computational results are presented

Kinematics of the Galactic Globular Cluster System: New Radial Velocities for Clusters in the Direction of the Inner Galaxy

HIRES on the Keck I telescope has been used to measure the first radial velocities for stars belonging to eleven, heavily-reddened globular clusters in the direction of the inner Galaxy. The question of kinematic substructuring among the Galactic globular cluster system is investigated using an updated catalog of globular cluster distances, metallicities and velocities. It is found that the population of metal-rich globular clusters shows significant rotation at all Galactocentric radii. For the metal-rich clusters within 4 kpc of the Galactic center, the measured rotation velocity and line-of-sight velocity dispersion are similar to those of bulge field stars. We investigate claims that the metal-rich clusters are associated with the central Galactic bar by comparing the kinematics of the innermost clusters to that of the atomic hydrogen in the inner Galaxy. The longitude-velocity diagram of both metal-rich and metal-poor clusters bears a remarkable similarity to that of the gas, including the same non-circular motions which have traditionally been interpreted as evidence for a Galactic bar, or, alternatively, a non-axisymmetric bulge. However, uncertainties in the existing three-dimensional Galactocentric positions for most of the clusters do not yet allow an unambiguous discrimination between the competing scenarios of membership in a rigidly rotating bar, or in a bulge which is an oblate isotropic rotator. We conclude that the majority of metal-rich clusters within the central 4 kpc of the Galaxy are probably associated with the bulge/bar, and not the thick disk. (ABRIDGED)Comment: 18 pages, including 7 of 13 postscript figures. Figures 1-6 available at http://astro.caltech.edu/~pc. Accepted for publication in the Astronomical Journa

Chemo-dynamical evolution of Globular Cluster Systems

We studied the relation between the ratio of rotational velocity to velocity dispersion and the metallicity (/\sigma_{v}-metallicity relation) of globular cluster systems (GCS) of disk galaxies by comparing the relation predicted from simple chemo-dynamical models for the formation and evolution of disk galaxies with the observed kinematical and chemical properties of their GCSs. We conclude that proto disk galaxies underwent a slow initial collapse that was followed by a rapid contraction and derive that the ratio of the initial collapse time scale to the active star formation time scale is \sim 6 for our Galaxy and \sim 15 for M31. The fundamental formation process of disk galaxies was simulated based on simple chemo-dynamical models assuming the conservation of their angular momentum. We suggest that there is a typical universal pattern in the /\sigma_{v}-metallicity relation of the GCS of disk galaxies. This picture is supported by the observed properties of GCSs in the Galaxy and in M31. This relation would deviate from the universal pattern, however, if large-scale merging events took major role in chemo-dynamical evolution of galaxies and will reflect the epoch of such merging events. We discuss the properties of the GCS of M81 and suggest the presence of past major merging event.Comment: 25 pages, 8 figures, Accepted for publication in the Astrophysical Journa

Hybrid next-fit algorithm for the two-dimensional rectangle bin-packing problem

We present a new approximation algorithm for the two-dimensional bin-packing problem. The algorithm is based on two one-dimensional bin-packing algorithms. Since the algorithm is of next-fit type it can also be used for those cases where the output is required to be on-line (e. g. if we open an new bin we have no possibility to pack elements into the earlier opened bins). We give a tight bound for its worst-case and show that this bound is a parameter of the maximal sizes of the items to be packed. Moreover, we also present a probabilistic analysis of this algorithm