Showing papers by "J. Michael Harrison published in 1999"
TL;DR: A queueing system with r non‐identical servers working in parallel, exogenous arrivals into m different job classes, and linear holding costs for each class is considered, and the Brownian solution suggests the following: virtually all backlogged work should be held in one particular job class.
Abstract: We consider a queueing system with r non-identical servers working in parallel, exogenous arrivals into m different job classes, and linear holding costs for each class Each arrival requires a single service, which may be provided by any of several different servers in our general formulations the service time distribution depends on both the job class being processed and the server selected The system manager seeks to minimize holding costs by dynamically scheduling waiting jobs onto available servers A linear program involving only first-moment data (average arrival rates and mean service times) is used to define heavy traffic for a system of this form, and also to articulate a condition of overlapping server capabilities which leads to resource pooling in the heavy traffic limit Assuming that the latter condition holds, we rescale time and state space in standard fashion, then identify a Brownian control problem that is the formal heavy traffic limit of our rescaled scheduling problem Because of the assumed overlap in server capabilities, the limiting Brownian control problem is effectively one-dimensional, and it admits a pathwise optimal solution That is, in the limiting Brownian control problem the multiple servers of our original model merge to form a single pool of service capacity, and there exists a dynamic control policy which minimizes cumulative cost incurred up to any time t with probability one Interpreted in our original problem context, the Brownian solution suggests the following: virtually all backlogged work should be held in one particular job class, and all servers can and should be productively employed except when the total backlog is small It is conjectured that such ideal system behavior can be approached using a family of relatively simple scheduling policies related to the c\mu rule
240 citations
TL;DR: In this article, the authors used rainfall data from stations in South Africa that have not involved site relocations, but which have not been tested for inhomogeneities resulting from changes in instrumentation, a method of testing for changes in the intensity of extreme events is adopted.
Abstract: Extreme rainfall events can have severe impacts on society, so possible long-term changes in the intensity of extreme events are of concern. Testing for long-term changes in the intensity of extreme events is complicated by data inhomogeneities resulting from site and instrumentation changes. Using rainfall data from stations in South Africa that have not involved site relocations, but which have not been tested for inhomogeneities resulting from changes in instrumentation, a method of testing for changes in the intensity of extreme events is adopted. Significant increases in the intensity of extreme rainfall events between 1931-1960 and 1961-1990 are identified over about 70% of the country. The intensity of the 10-year high rainfall events has increased by over 10% over large areas of the country, except in parts of the north-east, north-west and in the winter rainfall region of the south-west. Percentage increases in the intensity of high rainfall events are largest for the most extreme events. While some inhomogeneities remain in the data used, the observed changes in the intensity of extreme rainfall events over South Africa are thought to be at least partly real.
237 citations
TL;DR: The model developed here explicitly incorporates both capacity investment decisions and production decisions, and is general enough to include reversible and irreversible investment, and highlights an important conceptual distinction between deterministic and stochastic environments.
179 citations