A note on sojourn times in M/G/1 queues with instantaneous,bernoulli feedback

Queueing systems which include the possibility for a customer to return to the same server for additional service are called queueing systems with feedback. Such systems occur in computer networks for example. In these systems a chosen customer will wait in the queue, be serviced and then, with probability p, return to wait again, be serviced again and continue this process until, with probability (1 – p) = q, it departs the system never to return. The time of waiting plus service time, the nth time the customer goes through, we will call his nth sojourn time. The (random) sum of these sojourn times we will call the total sojourn time (abbreviated, sojourn time when there is no confusion which sojourn time we are talking about). In this paper we study the total sojourn time in a queueing system with feedback. We give the details for M/G/1 queues in which the decision to feedback or not is a Bernoulli process. While the details of the computations can be more difficult, the structure of the sojourn time process is unchanged for the M/G/1 queue with a more general decision process as will be shown. We assume the reader is familiar with Disney, McNickle and Simon [1].     

An empirical evaluation of further approximations to an approximate continuous review inventory model

This paper describes an empirical evaluation of several approximations to Hadley and Whitin's approximate continuous review inventory model with backorders. It is assumed that lead time demand is normally distributed and various exponential functions are used to approximate the upper tail of this distribution. These approximations offer two important advantages in computing reorder points and reorder quantities. One advantage is that normal tables are no longer required to obtain solutions, and a second advantage is that solutions may be obtained directly rather than iteratively. These approximations are evaluated on two distinct inventory systems. It is shown that an increase in average annual cost of less that 1% is expected as a result of using these approximations. The only exception to this statement is with inventory systems in which a high shortage cost is specified and ordering costs are unusually low.     

Multiple-facility loading under capacity-based economies of scope

Multiple-facility loading (MFL) involves the allocation of products among a set of finite-capacity facilities. Applications of MFL arise naturally in a variety of production scheduling environments. MFL models typically assume that capacity is consumed as a linear function of products assigned to a facility. Product similarities and differences, however, result in capacity-based economies or diseconomies of scope, and thus the effective capacity of the facility is often a (nonlinear) function of the set of tasks assigned to the facility. This article addresses the multiple-facility loading problem under capacity-based economies (and diseconomies) of scope (MFLS). We formulate MFLS as a nonlinear 0–1 mixed-integer programming problem, and we discuss some useful properties. MFLS generalizes many well-known combinatorial optimization problems, such as the capacitated facility location problem and the generalized assignment problem. We also define a tabu-search heuristic and a branch-and-bound algorithm for MFLS. The tabu-search heuristic alternates between two search phases, a regional search and a diversification search, and offers a novel approach to solution diversification. We also report computational experience with the procedures. In addition to demonstrating MFLS problem tractability, the computational results indicate that the heuristic is an effective tool for obtaining high-quality solutions to MFLS. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 229–256, 1997     

Efficient multinomial selection in simulation

Consider a simulation experiment consisting of v independent vector replications across k systems, where in any given replication one system is selected as the best performer (i.e., it wins). Each system has an unknown constant probability of winning in any replication and the numbers of wins for the individual systems follow a multinomial distribution. The classical multinomial selection procedure of Bechhofer, Elmaghraby, and Morse (Procedure BEM) prescribes a minimum number of replications, denoted as v*, so that the probability of correctly selecting the true best system (PCS) meets or exceeds a prespecified probability. Assuming that larger is better, Procedure BEM selects as best the system having the largest value of the performance measure in more replications than any other system. We use these same v* replications across k systems to form (v*)^k pseudoreplications that contain one observation from each system, and develop Procedure AVC (All Vector Comparisons) to achieve a higher PCS than with Procedure BEM. For specific small-sample cases and via a large-sample approximation we show that the PCS with Procedure AVC exceeds the PCS with Procedure BEM. We also show that with Procedure AVC we achieve a given PCS with a smaller v than the v* required with Procedure BEM. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 459–482, 1998     

Planning accelerated life tests for censored two‐parameter exponential distributions

We consider optimal test plans involving life distributions with failure‐free life, i.e., where there is an unknown threshold parameter below which no failure will occur. These distributions do not satisfy the regularity conditions and thus the usual approach of using the Fisher information matrix to obtain an optimal accelerated life testing (ALT) plan cannot be applied. In this paper, we assume that lifetime follows a two‐parameter exponential distribution and the stress‐life relationship is given by the inverse power law model. Near‐optimal test plans for constant‐stress ALT under both failure‐censoring and time‐censoring are obtained. We first obtain unbiased estimates for the parameters and give the approximate variance of these estimates for both failure‐censored and time‐censored data. Using these results, the variance for the approximate unbiased estimate of a percentile at a design stress is computed and then minimized to produce the near‐optimal plan. Finally, a numerical example is presented together with simulation results to study the accuracy of the approximate variance given by the proposed plan and show that it outperforms the equal‐allocation plan. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 169–186, 1999     

On gamma estimation via matrix kriging

In financial engineering, sensitivities of derivative prices (also known as the Greeks) are important quantities in risk management, and stochastic gradient estimation methods are used to estimate them given the market parameters. In practice, the surface (function) of the Greeks with respect to the underlying parameters is much more desired, because it can be used in real‐time risk management. In this paper, we consider derivatives with multiple underlying assets, and propose three stochastic kriging‐based methods, the element‐by‐element, the importance mapping, and the Cholesky decomposition, to fit the surface of the gamma matrix that can fulfill the time constraint and the precision requirement in real‐time risk management. Numerical experiments are provided to illustrate the effectiveness of the proposed methods.     

The Damoclean sword of offensive cyber: Policy uncertainty and collective insecurity

Cyberspace is a new domain of operation, with its own characteristics. Cyber weapons differ qualitatively from kinetic ones: They generate effects by non-kinetic means through information, technology, and networks. Their properties, opportunities, and constraints are comparable to the qualitative difference between conventional and nuclear weapons. New weapons and their target sets in a new domain raise a series of unresolved policy challenges at the domestic, bilateral, and international levels about deterrence, attribution, and response. They also introduce new risks: uncertainty about unintended consequences, expectations of efficacy, and uncertainty about both the target’s and the international community’s response. Cyber operations offer considerable benefits for states to achieve strategic objectives both covertly and overtly. However, without a strategic framework to contain and possibly deter their use, make state and non-state behavior more predictable in the absence of reciprocal norms, and limit their impact, an environment where states face persistent attacks that nonetheless fall below the threshold of armed conflict presents a policy dilemma that reinforces collective insecurity.     

A game with distorted information

This article considers a two-person game in which the first player has access to certain information that is valuable but unknown to the second player. The first player can distort the information before it is passed on to the second player. The purpose in distorting the information is to render it as useless as possible to the second player. Based on the distorted information received, the second player then maximizes some given objective. In certain cases he may still be able to use the distorted information, but sometimes the information has been so badly distorted that it becomes completely useless to him. © 1993 John Wiley & Sons, Inc.