This short note discusses open problems and partial solutions related to Sheldon M Ross's second conjecture about the classical single server queue subject a randomly time-varying rate arrival rate.

We make a novel connection between an energy-efficient wireless transmission scheduling problem and a multi-period, multi-item inventory control problem with stochastic convex ordering costs, deterministic demands, and a joint budget constraint. In the special case of a single item, we show that a state-dependent modified base-stock policy is optimal when the stochastic ordering costs are linea...

In this paper, we develop a uniied approach for stochastic load balancing on various multiserver systems. We expand the four partial orderings deened in Marshall and Olkin, by deening a new ordering based on the set of functions that are symmetric, L-subadditive and convex in each variable. This new partial ordering is shown to be equivalent to the previous four orderings for comparing determin...

In the present communication, stochastic comparison of a series (parallel) system having heterogeneous components with random lifetimes and series (parallel) system having homogeneous exponential components with random lifetimes has been studied. Further, conditions under which such a comparison is possible has been established. Keywords—Exponential distribution, Order statistics, Star ordering...

This paper presents a new formulation for warehouse inventory management in a stochastic situation. The primary source of this formulation is derived from FP model, which has been proposed by Fletcher and Ponnambalam for reservoir management. The new proposed mathematical model is based on the first and the second moments of storage as a stochastic variable. Using this model, the expected value...

Many procedures have been proposed to compute the nonparametric maximum likelihood estimates (NPMLEs) of survival functions under various stochastic ordering constraints. Each of the existing procedures is applicable only to a specific type of stochastic order constraint and often hard to implement. In this paper, we describe a method for computing the NPMLEs of survival functions, based on geo...

Social scientists often compare subclasses of populations or manipulatons. For example, in comparing task-completion times across two levels of a manipulations, if one group has faster overall mean response, it is natural to ask if the fastest 10% of the first group has a faster mean than the fastest 10% of the second group, and so on. Delta plots, a type of quantilequantile residual plot used ...