In this paper we propose a prototype model for the problem of managing waiting lists for organ transplantations. Our model captures the double-queue nature of the problem: there is a queue of patients, but also a queue of organs. Both may suffer from “impatience”: the health of a patient may deteriorate, and organs cannot be preserved longer than a certain amount of time. Using advanced tools from queueing theory, we derive explicit results for key performance criteria: the rate of unsatisfied demands and of organ outdatings, the steady-state distribution of the number of organs on the shelf, the waiting time of a patient, and the long-run fraction of time during which the shelf is empty of organs.

A version of the classical secretary problem is studied, in which one is interested in selecting one of the b best out of a group of n differently ranked persons who are presented one by one in a random order. It is assumed that b ≥ 1 is a preassigned number. It is known, already for a long time, that for the optimal policy, one needs to compute b position thresholds (for instance, via backward induction). In this article we study approximate policies that use just a single or a double position threshold, albeit in conjunction with a level rank. We give exact and asymptotic (as n → ∞) results, which show that the double-level policy is an extremely accurate approximation.

A renewal model in risk theory is considered, where is the tail of the distribution of the deficit at ruin with initial surplus u and is the tail of the ladder height distribution. Conditions are derived under which the ratio is nondecreasing in u for any y≥0. In particular, it is proven that if the ladder height distribution is stable and DFR or phase type, then the above ratio is nondecreasing in u. As a byproduct of this monotonicity, an upper bound and an asymptotic result for are derived. Examples are given to illustrate the monotonicity results.

The generalized order statistics (GOS) model is a unified model that contains the well-known ordered random data such as order statistics and record values. In the present article, we investigate some stochastic ordering results and aging properties of the conditional GOS. The results of the article subsume some of the existing results, which recently are obtained in the literature, on conditional GOS. In particular, our results hold for the model of progressively type II right censored order statistics without any restriction on the censoring scheme.

The normal curve has been used to fit the rate of both world and US oil production. In this article we give the first theoretical basis for these curve fittings. It is well known that oil field sizes can be modeled by independent samples from a lognormal distribution. We show that when field sizes are lognormally distributed, the starting time of the production of a field is approximately a linear function of the logarithm of its size, and production of a field occurs within a small enough time interval, then the resulting total rate of production is close to being a normal curve.

We consider the problem of optimally allocating one/two active spares in series systems. Lifetimes of different configurations are compared with respect to the reversed failure rate order, the failure rate order, the increasing concave order, and the stochastic precedence order.

This article deals with Rényi entropies for the residual life and the inactivity time. Monotonic properties of the entropy in order statistics, record values, and weighted distributions are investigated, and the comparison on weighted random variables is studied in terms of residual Rényi entropy as well.

In this article notions of exponential dominance and uncertainty for weighted and unweighted distributions are explored and used to compare values of the informational energy function and the differential entropy. Stochastic inequalities and bounds for cross-discrimination and uncertainty measures in weighted and unweighted residual life distribution functions and related reliability measures are presented. Moment-type inequalities for the comparisons of weighted and unweighted residual life distributions are also presented.