General Distributional Assumptions Research Articles

On the selection probabilities of two-stage decision procedures

Abstract This paper presents some general results on the selection probabilities of various two-stage decision procedures. Simple proofs are given for some least favorable configuration results which have hitherto required very intricate and complicated proofs. Furthermore, the results given here are more general than previous results because they allow more general distributional assumptions and more varied selection procedures. In addition, these results provide more information on the selection probabilities than has previously been available. Extensions to multistage decision procedures and stronger least favorable configuration results are discussed.

Processor-shared buffers with reneging

Motivated by buffer design questions in data networks, we consider a processor shared queue with finite buffer capacity and reneging. Reneging models events such as the timing-out of a communication path due to excessive delays, or decisions to preempt a path in order to re-route it according to some congestion control mechanism. The focus of the paper is on the asymptotic behavior of this system in a variety of regimes that correspond to large service rates (bandwidths). Congestion is measured by the blocking probability P, the mean number in system Q, and a cost function L giving the sum of the blocking and reneging rates normalized by the arrival rate. Convenient parameters of the analysis are the respective ratios ϱ and η of the arrival rate to the service rate and the service rate to the reneging rate. Fixing the relative rates at which η → ∞ and the buffer capacity N → ∞ in an exponential model, asymptotic estimates of P, Q, and L are derived as functions of η with ϱ a parameter. Similar results are obtained under a suitable scaling leading to heavy-traffic diffusion limits. These latter results are extended to more general distributional assumptions, and used in the solution of a problem in which bandwidth and reneging parameters must be chosen so as to minimize L.

Estimation of von Bertalanffy Growth Curve Parameters from Recapture Data

A simple method of constructing estimating functions for parameters in the von Bertalanffy growth model E[y(t)] = L[1 - exp(-Kt)] is presented for tag-recapture data when the age of the animal is unknown. The estimating functions are unbiased under very general distributional assumptions provided K does not vary between animals. Simulations of growth in lobsters and whelks indicate that the method performs well provided the initial capture times and recapture intervals vary over reasonable ranges. Comparison is made with methods based on least squares, which have been shown to be generally inconsistent.

On the Optimal Control of Two Queues with Server Setup Times and Its Analysis

Two queues are fed by independent, time-homogeneous Poisson arrival processes. One server is available to handle both. All service durations, in both queues, are drawn independently from the same distribution. A setup time is incurred whenever the server moves (switches) from one queue to the other. We prove that in order to minimize the sum of discounted setup charges and holdings costs, assumed linear in queue length and having the same rate at the two queues, the service at each queue should be exhaustive, A “threshold policy” is defined as a policy under which the server switches (from an empty queue) only when the other reaches a critical size. It is shown to be a likely candidate for the optimal policy, both for the discounted version and for the long-time average criterion. The steady-state performance of this policy (under somewhat more general distributional assumptions) and the optimal thresholds are determined for a number of cases.

Least-squares theory based on general distributional assumptions with an application to the incomplete observations problem

The linear regression modely=β′x+e is reanalyzed. Taking the modest position that β′x is an approximation of the “best” predictor ofy we derive the asymptotic distribution ofb andR 2, under mild assumptions. The method of derivation yields an easy answer to the estimation ofβ from a data set which contains incomplete observations, where the incompleteness is random.

Stochastic Modeling of Processor Scheduling with Application to Data Base Management Systems

This paper is concerned with the stochastic modeling of processor scheduling and of queuing due to contention for resources in data base management systems. The processing services rendered in searching the data base and retrieving and processing information are modeled explicitly, as is the algorithm used to schedule these services on the processor. The scheduling of the processor is based on a total priority ordering of a set of queues for processing service. A queuing model incorporating the processor scheduling algorithm for IMS (Information Management System) is formulated in order to illustrate the modeling ideas. The model is analyzed under rather general distributional assumptions, based on the observation that certain stochastic processes in the model are cumulative processes defined over the same embedded semi-Markov process. The model is not used in a performance study of IMS, nor is it proposed that the model developed here is one upon which a performance study of IMS should be undertaken. The model should be viewed as illustrative of stochastic models which can be constructed to incorporate algorithms for processor scheduling.

Letter to the Editor—Bruce's Spider and Renewal Theory

The theory of an alternating renewal process with absorption at the renewal points is examined. The problem is discussed in the context of the behavior of Bruce's spider that attempted to climb a smooth wall but repeatedly slipped back and had to start again; but it provides a model for many other processes, of which two typical examples are given. Results are obtained under fairly general distributional assumptions for the distribution of the time to absorption and for the probabilities, conditional upon no absorption having taken place, of the process being in one phase or the other of the alternating process.