Pre-congestion notification (PCN) provides feedback about load conditions in a network to its boundary nodes. The PCN working group of the IETF discusses the use of PCN to implement admission control (AC) and flow termination (FT) for prioritized realtime traffic in a DiffServ domain. Admission control (AC) is a well-known flow control function that blocks admission requests of new flows when they need to be carried over a link whose admitted PCN rate already exceeds an admissible rate. Flow termination (FT) is a new flow control function that terminates some already admitted flows when they are carried over a link whose admitted PCN rate exceeds a supportable rate. The latter condition can occur in spite of AC, e.g., when traffic is rerouted due to network failures. This survey gives an introduction to PCN and is a primer for this new technology. It presents and discusses the multitude of architectural design options in an early stage of the standardization process in a comprehensive and streamlined way before only a subset of them is standardized by the IETF. It brings PCN from the IETF to the research community and serves as historical record.

Abst,raet A discrete Bass model, which is a discrete analog of the Bass model, is proposed. This discrete Bass rnodel is defined as a difference equation that has an exact solution, The difference equation and the solution respectively t,elld to the differential equation whic:h the Bass model is defined as and the solution when the time interval tends to zero. The discrete Bass model conserves the characterist,ics of the Bass model because the differem, ce equation has am exact solution. Therefore, the discrete Bass model enables us to forecast the innovation diffusion of products and services without a eontinueus-time Bass model. The parameter estimattons of the discrete Bass model are very simple and precise. The difference equation itselfcan be used for the ordinary least squares procedure. Parameter estimation using the ordinary least squares procedure ls equa] Lo t,hat i]sing the nonlinear least squares procedure in the discrete Bass model. 'lihe ordinary least squares procedures iil the discrete Bass model overcome the three shortcomings of the ordinary Ieast squares procedure in the continuous Bass model: t/he time-interval bias, standard error, and multicollinearity.

We describe software reliability growth models that yield accurate parameter estimates in spite of a small amount of input data in an actual software testing. These models are based on discrete analogs of a logistic curve model. The models are described with two difference equations, one each proposed by Morishita and Hirota. The difference equations have exact solutions. The equations tend to a differential equation on which the logistic curve model is defined when the time interval tends to zero. The exact solutions also tend to the exact solution of the differential equation when the time interval tends to zero. The discrete models conserve the characteristics of the logistic model because the difference equations have exact solutions. Therefore, the proposed models provide accurate parameter estimates, making it possible to predict in the early development phase when software can be released.

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