Peter Kubat

Optimal Release Time of Computer Software

A decision procedure to determine when computer software should be released is described. This procedure is based upon the cost-benefit for the entire company that has developed the software. This differs from the common practice of only minimizing the repair costs for the data processing division. Decision rules are given to determnine at what time the system should be released based upon the results of testing the software. Necessary and sufficient conditions are identified which determine when the system should be released (immediately, before the deadline, at the deadline, or after the deadline). No assumptions are made about the relationship between any of the models parameters. The model can be used whether the software was developed by a first or second party. The case where future costs are discounted is also considered.

Design of partially survivable networks for cellular telecommunication systems

Abstract In cellular networks, cells are connected to the mobile telephone switching office (MTSO) directly or via hubs. It may also be desirable for some cells to split their traffic to two or more hubs for partial survivability in the case of equipment failures; such cells are said to have a diversity requirement greater than one. Assuming that hubs are connected to the MTSO via self-healing rings, as is common in current cellular implementations, the objective is to find the assignment of cells to hubs – including the MTSO – that meets demand as well as survivability requirements at minimum cost. With the increasing use of fiber for high capacity backbone transmission, networks have become sparser, and the consequences of link failures much more serious. Hence network survivability has taken on added urgency. Our paper models this problem in the context of cellular networks.

Modular product design and product support

Abstract A modular design for a product or system can be an effective approach to support of the product if total replacement and repair times can be reduced by modular replacement. On the other hand, modular designs may involve higher costs of replacement and inventory holding. Cost models are developed for the evaluation of a modular design, and the distinction between integrated modules and replaceable subassemblies is discussed. Numerical examples are given to illustrate the tradeoffs to be made.

Managing Test-Procedures to Achieve Reliable Software

Quantitative decision-making procedures are proposed to aid software project managers to manage effectively the testing stage during software project development. The module and integration testing phases are thoroughly investigated. Decision procedures which maximize the reliability and/or minimize some cost-benefit objective subject to a time and/or budget constraint are suggested. These procedures optimally allocate test time to the modules for module testing and select the optimal data mixture for integration testing. Testing of computer software is a major component of the software development effort. An efficient allocation of computer time among various modules during testing can appreciably improve reliability and shorten the testing stage. Using decision models presented in this paper, a project manager can effectively allocate test time during module testing and select the best data mixture for integration testing. The models are based upon software failure data that are collected during testing. These decision models can be valuable not only for the project manager but for the group responsible for generating the appropriate test data.

Design of cellular networks with diversity and capacity constraints

This paper presents three mathematical models for network design of cellular networks. The models reflect varying degrees of complexity. Model 1 is a 1-period fixed-link capacity model. Three heuristics are used for solving this problem. All the heuristics first use linear programming relaxations to yield the near-optimal integer solution, then use clever rounding-schemes to find the final solution. The three heuristics are compared with an integer branch-and-bound algorithm to show the efficacy of the heuristics and the speed with which they achieve their solution. The first heuristic is the best. An appendix presents a detailed algorithmic description of the first heuristic. Model 2 allows the capacities of the links to vary. This is a much more difficult mathematical programming problem, yet certain features of the problem reveal valuable characteristics of the linear programming relaxations. Two heuristics are generated; the first heuristic is superior to the second. The heuristics are compared with an optimal branch-and-bound algorithm. Model 3 presents a multi-period demand problem. This is a very complex problem and, while no heuristics are developed and no computational experiments are shown, the structure of the final problem is similar to models 1 and 2; thus linear programming relaxations should be a viable strategy for its solution.

Stochastic Allocation Rules

This paper considers the allocation of a fixed amount of resource across competing activities, where the rate of use of the allocated amounts is stochastic. The allocated amounts are said to have run out when the first of the allocations is used up and another distribution must then be considered. This problem arises in the allocation of stocks of a commodity to branch warehouses and in the allocation of production time to items that are jointly produced. It also occurs in the allocation of spares to subsystems when the total number of spares is constrained by volume or cost and when failure of one subsystem causes a failure of the whole system. Two alternative formulations are presented: the Maximization of Expected Time to Runout and the Minimization of Expected Discounted Time to Runout. Bounds are developed on the problems by using deterministic and exponential models for the time to runout. The case of two competing processes is investigated numerically, and it appears that the solutions to the bounding problems provide effective heuristics at least for such small problems.

Estimation of Quantiles of Location-Scale Distributions Based on Two or Three Order Statistics

Linear asymptotically unbiased estimators of ξ quantiles, x ξ 0 < ξ < 1, of location-scale distributions are considered. These are based on two or three order statistics suitably selected in a neighborhood of the sample quantile X (N), N = [nξ] + 1, where n is the sample size. The estimators are easy to calculate and are substantially more efficient than the nonparametric estimator ξ = X (N). The estimators are tabulated for selected values of ξ for the normal and extreme value (Gumbel) distributions. Also given are the asymptotic relative efficiencies of these estimators when compared with the maximum likelihood estimator of x ξ based on all n observations.

Diagnostics design: A product support strategy

Abstract The use of automated built-in diagnostics in a durable product reduces the cost of product failure in two ways. It reduces the users downtime cost by reducing the diagnosis time. A service representative visit may also in some cases be eliminated. The benefits are countervailed by the incremental production cost of the new design. Models are developed to study the tradeoffs involved in designing a product with added diagnostics technology. This strategy is also evaluated from the system performance point of view.

The Value of Loaners in Product Support

Abstract Reducing the customers risk of down time is becoming increasingly important in the support of industrial and consumer durable equipment, whether sold or leased. Traditionally, improved support has meant improvements in diagnosis, repair, and spare part availability. However, these approaches eventually have diminishing returns. In many cases, dedicated loaners can be cost effective in eliminating or reducing down time. In this paper, models are developed to examine the trade-offs involved in decisions about loaners. Alternative loan policies are discussed, and the application of these policies is illustrated.

Balancing Traffic Flows in Resilient Packet Rings

Resilient Packet Ring (RPR) is a new telecommunication transport technology that combines (a) high bandwidth utilization usually associated with Ethernet and (b) the 50ms protection schemes (in the case of segment /node failures) associated with SONET rings. The RPR is in essence, a distributed Ethernet switch, in which the RPR nodes are connected with two counter-rotating rings (clockwise and counter-clockwise ring). The ring spans are either SONET of Gbit Ethernet. The (unidirectional) point-to-point traffic demands (10/100/1000 Ethernet and/or TDM) can be carried on either ring.