An M/M/1 queue with delayed feedback

We present some results for M/M/1 queues with finite capacities with delayed feedback. The delay in the feedback to an M/M/1 queue is modelled as another M-server queue with a finite capacity. The steady state probabilities for the two dimensional Markov process {N(t), M(t)} are solved when N(t) = queue length at server 1 at t and M(t) = queue length at server 2 at t. It is shown that a matrix operation can be performed to obtain the steady state probabilities. The eigenvalues of the operator and its eigenvectors are found. The problem is solved by fitting boundary conditions to the general solution and by normalizing. A sample problem is run to show that the solution methods can be programmed and meaningful results obtained numerically.     

The divisionalized firm revisited—A comment on Enzer's “the static theory of transfer pricing”

Three different solutions to a very simple transfer pricing problem are outlined and contrasted. These are labeled by their authors: Hirshleifer, Enzer, and Ronen and McKinney. Weaknesses associated with each solution are pointed out.     

On failure modeling

A promising approach to failure modeling, in particular to developing failure-time distributions, is discussed. Under this approach, system state or wear and tear is modeled by an appropriately chosen random process—for example, a diffusion process—and the occurrences of fatal shocks are modeled by a Poisson process whose rate function is state dependent. The system is said to fail when either wear and tear accumulates beyond an acceptable or safe level or a fatal shock occurs. This approach has significant merit. First, it provides revealing new insights into most of the famous and frequently used lifetime distributions in reliability theory. Moreover, it suggests intuitively appealing ways for enhancing those standard models. Indeed, this approach provides a means of representing the underlying dynamics inherent in failure processes. Reasonable postulates for the dynamics of failure should lend credence to the prediction and estimation of reliability, maintainability, and availability. In other words, accuracy of representation could lead to better, more reliable prediction of failure.     

Incorporation dynamic aspects and uncertainty in 1‐median location problems

In this paper we present several 1‐median formulations on a tree network which incorporate dynamic evolution and/or uncertainty of node demands and transportation costs over a planning horizon. Dynamic evolution is modeled using linear demand functions for the nodes and linear length functions for the edges. Uncertainty is modeled with the use of multiple scenarios, where a scenario is a complete specification of the uncertain node demands and/or edge lengths. We formulate our objective using minimax regret like criteria. We use two different criteria, namely, robust deviation and relative robustness. We discuss what motivated the introduction of these objectives, as well as their relation to existing literature and decision making practices. For all of the models presented, we provide low‐order polynomial time algorithms. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 147–168, 1999     

Expected waiting time rankings in extended machine-repair models

The present paper studies the relative magnitudes of expected waiting times in extended machine-repair models, when processing times are of two Erlang types. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 864–870, 1999