Abstract: Systems and methods for measuring value-at-risk and profitability of hedging in relation to BMA debt obligations are provided using rigorous statistical solutions that address problems associated with municipalities involved in swap hedging face. Various embodiments permit users to quantify POL hedging basis risk through a VAR-style loss measurement and statistics measuring the profitability of a hedge, those statistics including gain durability and gain/loss ratio. Various aspects introduce significant innovation to risk management practices, particularly for tax-exempt issuers of debt. Certain embodiments of this disclosure facilitate better management of hedging risk, analysis of hedges using POL vs. BMA and provide guidance for analyzing the risk existing in an existing portfolio of POL swap hedges to better inform decision-making regarding use of hedging risk for profit or to lay off risk.

Abstract: Methods for measuring value-at-risk and profitability of hedging in relation to BMA debt obligations are provided using rigorous, statistical solutions that address problems associated with municipalities involved in swap hedging face. Various embodiments permit users to quantify POL hedging basis risk through a VAR-style loss measurement and statistics measuring the profitability of a hedge, those statistics including gain durability and gain/loss ratio. Various aspects introduce significant innovation to risk management practices, particularly for tax-exempt issuers of debt. Certain embodiments of this disclosure facilitate better management of hedging risk, analysis of hedges using POL vs. BMA and provide guidance for analyzing the risk existing in an existing portfolio of POL swap hedges to better inform decision-making regarding use of hedging risk for profit or to lay off risk.

Abstract: A method and apparatus for providing differentiated quality of service (QoS) within a GPRS/EGPRS network environment. The invention advantageously uses one or more of a microscheduling technique, a peak picking technique and other techniques and methodologies to provide differentiated quality of service levels to users while maximizing total network throughput.

Abstract: A method and apparatus are disclosed for monitoring and signaling a path restoration using pre-computed restoration paths following a detected fault on a primary service path in a communications network. A fault occurring inside the restorable portion of a network in heterogeneous or multiple network environments can be distinguished from faults occurring outside the restorable network in accordance with the ANSI Tandem Connection Maintenance standard, T1.105.05-1994. Path restoration is activated only when a fault causing path failure occurs inside the restorable portion of the network. Each conforming node in the restorable portion of the network has the necessary monitoring, signaling and cross-connect functionality and databases to participate actively in real time restoration. Additional non-conforming network elements can be positioned between the restoration nodes without preventing path restoration.

Abstract: Systems and methods for measuring value-at-risk and profitability of hedging in relation to BMA debt obligations are provided using rigorous statistical solutions that address problems associated with municipalities involved in swap hedging face. Various embodiments permit users to quantify POL hedging basis risk through a VAR-style loss measurement and statistics measuring the profitability of a hedge, those statistics including gain durability and gain/loss ratio. Various aspects introduce significant innovation to risk management practices, particularly for tax-exempt issuers of debt. Certain embodiments of this disclosure facilitate better management of hedging risk, analysis of hedges using POL vs. BMA and provide guidance for analyzing the risk existing in an existing portfolio of POL swap hedges to better inform decision-making regarding use of hedging risk for profit or to lay off risk.

Abstract: Capacity design of an optical network for demands of fast path restorable (FPR) connections forms a linear programming sizing problem for a optimal routing. A dual of the linear programming sizing problem is formed and solved with an approximation algorithm. Edge lengths are initialized based on i) the inverse of the edge's capacity and ii) a scalar constant. Then, the approximation algorithm proceeds in phases to route each commodity over the edges of a graph. During each phase, the demand's flow is sent from the source to destination via multiple iterations. During each iteration, the set of shortest disjoint paths from the source to the destination is determined, a portion of the flow is sent, and the lengths of the edges that carry the flow are updated. The value employed to scale the network is generated after the last phase from the maximum ratio of edge flow to edge capacity.

Abstract: A network element maintains failure information for a packet-based network and usage information for a backup path. Upon receipt of a new demand, with an associated bandwidth, d, the network element determines if the backup path can be shared as a function of the failure information and the usage information associated with the backup path.

Abstract: A method and apparatus for providing differentiated quality of service (QoS) within a GPRS/EGPRS network environment. The invention advantageously uses one or more of a microscheduling technique, a peak picking technique and other techniques and methodologies to provide differentiated quality of service levels to users while maximizing total network throughput.

Abstract: Capacity design of an optical network for demands of fast path restorable (FPR) connections forms a linear programming sizing problem for a optimal routing. A dual of the linear programming sizing problem is formed and solved with an approximation algorithm. Edge lengths are initialized based on i) the inverse of the edge's capacity and ii) a scalar constant. Then, the approximation algorithm proceeds in phases to route each commodity over the edges of a graph. During each phase, the demand's flow is sent from the source to destination via multiple iterations. During each iteration, the set of shortest disjoint paths from the source to the destination is determined, a portion of the flow is sent, and the lengths of the edges that carry the flow are updated. The value employed to scale the network is generated after the last phase from the maximum ratio of edge flow to edge capacity.

Abstract: A network element maintains failure information for a packet-based network and usage information for a backup path. Upon receipt of a new demand, with an associated bandwidth, d, the network element determines if the backup path can be shared as a function of the failure information and the usage information associated with the backup path.