A. B. Macisaac

When to Renew Software Licences at HPC Centres? A Mathematical Analysis

In this paper we study a common problem faced by many high performance computing (HPC) centres: When and how to renew commercial software licences. Software vendors often sell perpetual licences along with forward update and support contracts at an additional, annual cost. Every year or so, software support personnel and the budget units of HPC centres are required to make the decision of whether or not to renew such support, and usually such decisions are made intuitively. The total cost for a continuing support contract can, however, be costly. One might therefore want a rational answer to the question of whether the option for a renewal should be exercised and when. In an attempt to study this problem within a market framework, we present the mathematical problem derived for the day to day operation of a hypothetical HPC centre that charges for the use of software packages. In the mathematical model, we assume that the uncertainty comes from the demand, number of users using the packages, as well as the price. Further we assume the availability of up to date software versions may also affect the demand. We develop a renewal strategy that aims to maximize the expected profit from the use the software under consideration. The derived problem involves a decision tree, which constitutes a numerical procedure that can be processed in parallel.

A Threaded Parallel Code for Pricing Discrete Asian Options on SMP Systems

This paper discusses the implementation and performance of a parallel algorithm for pricing discrete Asian options. Using a partial differential equation (PDE) based method, one attempts to solve simultaneously many PDEs on a Cartesian grid in the direction of underlying asset S then followed by an interpolation in the orthogonal direction A - average of the underlying - at each time step. This leads one to consider algorithms to perform such calculations in parallel. The interpolation is non-local, thus it requires a global data access to A. This requires that an efficient parallel implementation must minimize the cost of data movement among processes. We describe in this paper three implementations: one using message passing interface (MPI), one using OpenMP and one using POSIX threads through a high level FORTRAN API. We then discuss the performances of these three implementations on different platforms.