Abstract: Modern decision support methods handle uncertainty or hypothesis about operating conditions, using one of two techniques viz. probabilistic formulation and constraints based method, which is the subject of the present invention. A large number of applications use linear constraints to specify uncertainty. These linear constraints are the set of linear inequalities, which are used to define the demand/supply in the area of supply chains. The set of linear inequalities forms a polytope, the volume of which represents the information content. The present invention deals with the application of computational geometrical methods to find the set theoretic relationship—subset, intersection and disjointness among the polytopes and then present a visualization technique to represent these relationships among polytopes. This invention proposes a decision support system and method to visualize the relationship among the polytopes to help with decision support.

Abstract: Portable battery operated electronic devices often use a “sleep mode” for energy conservation. A key feature introduced in the IEEE 802 standard ensures power-efficient operation of these battery operated mobile devices. However, the standard fails to define what will trigger a device into the sleep mode while other systems define “waiting time threshold” as a time for which a Mobile Subscriber Station (MSS) waits before entering into sleep mode which has a constant duration. An embodiment of the present invention uses a unique method (1500) and algorithm for optimizing waiting time threshold (1509) according to traffic arrival pattern for uplink (UL) and downlink (DL) data packets. This leads to significant reduction in energy consumption with little increase in average waiting delay and acceptable end-to-end delay for non real time traffic.