Abstract: A bandwidth management system combines a chance constrained optimization model with variable pricing as a tool for bandwidth management. Performance analysis and capacity planning are integrated with the pricing scheme. This is a discretized multi-time-period model, where the time t is specified in terms of multiples &tgr; of a fixed period length &Dgr;.

Abstract: A configuration management subsystem of a subsystem array system assigns heat producing devices to clusters such that the number of devices activated will not create overheating, regardless of which limited set of clusters is activated. The subsystem receives the dimensions of the disk array, the number of devices, the number of cluster groups and the maximum number of clusters that can be operated substantially simultaneously, and the dimensions of a critical box that defines an arrangement of the devices into cells such that, if a device is assigned to each cell of the critical box and all devices are operated simultaneously, then thermal operating restrictions of the devices will be exceeded. The system first executes simple numbering loop operations to determine, if they exist, dimensions of a building block subarray that meet certain requirements relative to the input parameters.