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Some electric power markets allow bidders to specify constraints on ramp rates for increasing or decreasing power production. We show in a small example that a bidder could use an overly restrictive constraint to increase profits, and explore the cause by visualizing the feasible region from the linear program corresponding to the power auction. We propose two penalty approaches to discourage bidders from such a tactic: one based on duality theory of Linear Programming, the other based on social cost differences caused by ramp constraints. We evaluate the two approaches using a simplified scaled model of the California power system, with actual 2001 California demand data.

Due to the increased role of statistics in current curriculum standards, there is at present a call for attention to secondary teachers' knowledge for teaching statistics in teacher education. This article reports the results of a study that answered this call by addressing mathematics teachers' knowledge for teaching graphing of bivariate categorical data. Novel curriculum materials to develop such knowledge were written then implemented with mathematics teachers in courses at four post-secondary schools. Results showed that prior to use of the materials, teachers' graphical competence was limited with teachers often utilizing frequencies when analyzing the data. Following use of the materials, they were more likely to correctly use relative frequencies in their analysis and expanded their knowledge of graphs to include segmented bar graphs. They also improved in their analysis of a student's graph and proposed response to the student, with more teachers noting the inappropriate use of frequencies and lack of label in the student-made graph post-instruction. Implications for development of teachers' knowledge for teaching statistics are discussed.

We consider an Erlang loss system (modem bank) with two streams of arriving customers, where arrival rates vary by time-of-day. We can observe one of the traffic streams (our customers), but we do not know how many servers the system has, or the characteristics of the other stream. Using detailed samplepath data, we construct a maximum likelihood estimator that makes good use of the data, but is slow to evaluate. As an alternative, we present an estimation system based on traffic data summarized by hour. This estimation system is much faster, and tends to produce good lower bounds on the size of the system and competing traffic.