Job assignment in large-scale service systems with affinity relations

We consider load balancing in service systems with affinity relations between jobs and servers. Specifically, an arriving job can be assigned to a fast, primary server from a particular selection associated with this job or to a secondary server to be processed at a slower rate. Such job–server affinity relations can model network topologies based on geographical proximity, or data locality in cloud scenarios. We introduce load balancing schemes that assign jobs to primary servers if available, and otherwise to secondary servers. A novel coupling construction is developed to obtain stability conditions and performance bounds. We also conduct a fluid limit analysis for symmetric model instances, which reveals a delicate interplay between the model parameters and load balancing performance.

     

Lines,Trees, and Branch Spaces

In this paper we examine the interactions between the topology of certain linearly ordered topological spaces (LOTS) and the properties of trees in whose branch spaces they embed. As one example of the interaction between ordered spaces and trees, we characterize hereditary ultraparacompactness in a LOTS (or GO-space) X in terms of the possibility of embedding the space X in the branch space of a certain kind of tree.     

Mathematics Assessment: Practices and Reporting Methods

The curriculum, teaching, and assessment Standards of the National Council of Teachers of Mathematics advocate the use of various assessment techniques in mathematics, K-12. Practitioners from 35 school districts in two regions of a midwestern state completed a questionnaire and reported information about their assessment practices, reporting methods, and other issues that affect change in mathematics. The results of the survey suggest that current reporting practices are limiting the use of alternative classroom assessment practices. Delays in the use of alternative mathematics assessment practice can probably be expected until the reporting systems used in school districts become consistent with the assessment systems and teachers participate in ongoing professional development programs to learn more about alternative assessment practices.