Sheldon M. Ross

A Random Graph.

Abstract : Let X(1),X(2), ..., X(n) be independent random variables such that P(X(i) = j) = P sub j , j = 1,2, ..., n, sum from j = 1 to n of P sub j = 1 and consider a graph with n nodes numbered 1,2, ..., n and the arcs (i,X(i)), i = 1,2, ..., n. We determine the probability that the above so-called random graph is connected and then develop a recursive formula for the distribution of C, the number of connected components it contains. We also derive expressions for the mean and variance of C. (Author)

On the Consecutive-k-of-n:F System

The linear (circular) k-of-n:F system has n linearly (circularly) ordered components. Each component either functions or fails. The system fails i.f.f.k consecutive components fail. This paper provides, in the i.i.d. case, recursive formulas and bounds for computing system reliability. It considers properties of system life distributions and, in the non i.i.d. case, questions of optimal system design.

An Optimal Algorithm for Monte Carlo Estimation

A typical approach to estimate an unknown quantity

Approximations in Finite Capacity Multi-Server Queues with Poisson Arrivals

\mu

Average delay in queues with non-stationary Poisson arrivals

is to design an experiment that produces a random variable Z, distributed in [0,1] with E[Z]=\mu

Software Reliability: The Stopping Rule Problem

, run this experiment independently a number of times, and use the average of the outcomes as the estimate. In this paper, we consider the case when no a priori information about Z is known except that is distributed in [0,1]. We describe an approximation algorithm

AVERAGE COST SEMI-MARKOV DECISION PROCESSES

{\cal A}{\cal A}

Bounds on the Delay Distribution in GI/G/1 Queues

which, given

Statistical Aspects of Quality Control

\epsilon

The Streetwalker’s Dilemma: A Job Shop Model

and