Brendan Patch

Performance of Faulty Loss Systems with Persistent Connections

We consider a finite capacity Erlang loss system that alternates between active and inactive states according to a two state modulating Markov process. Work arrives to the system as a Poisson process but is blocked from entry when the system is at capacity or inactive. Blocked jobs cost the owner a fixed amount that depends on whether blockage was due to the system being at capacity or due to the system being inactive. Jobs which are present in the system when it becomes inactive pause processing until the system becomes active again. A Laplace transform expression for the expected undiscounted revenue lost in [0, t] due to blocking is found. Further, an expression for the total time discounted expected lost revenue in [0,?) is provided. We also derive a second order approximation to the former that can be used when the computing power to invert the Laplace transform is not available. These expressions can be used to ascribe a value to four alternatives for improving system performance: (i) increasing capacity, (ii) increasing the service rate, (iii) increasing the repair rate, or (iv) decreasing the failure rate.

Networks of infinite-server queues with multiplicative transitions

This paper considers a network of infinite-server queues with the special feature that, triggered by specific events, the network population vector may undergo a linear transformation (a ‘multiplicative transition’). For this model we characterize the joint probability generating function in terms of a system of partial differential equations; this system enables the evaluation of (transient as well as stationary) moments. We show that several relevant systems fit in the framework developed, such as networks of retrial queues, networks in which jobs can be rerouted when links fail, and storage systems. Numerical examples illustrate how our results can be used to support design problems.

Modeling livelihood indicators and household resilience using Bayesian networks

The Bayesian network (BN) approach has garnered popularity in the field of environmental modeling because it is well-suited to representing relationships between the biophysical and societal factors critical to the success of natural resource management programs. BNs can be highly useful for structuring, clarifying, and communicating model results to stakeholders. This chapter introduces the BN methodology and its previous application to livelihood issues. The process used to construct a BN model relating the stocks of the livelihood capitals (e.g., social capital) held by households to their capacity to survive consecutive droughts (resilience) is described, followed by a demonstration of the model behavior and performance.

Exploring Implications of Climate, Land Use, and Policy Intervention Scenarios on Water Resources, Livelihoods, and Resilience

Abstract Integrated modeling methodologies have a greater potential than purely disciplinary approaches to support comprehensive assessment of social, economic, and biophysical aspects of complex natural resource management such as the Indian governments’ Integrated Watershed Management Program (IWMP). Climate and recharge estimates drive predictions assessment of the availability of surface and groundwater resources as impacted by IWMP, climate, and land use (i.e., water extractions). Water availability, land use mix, and crop productivity influence access to the available water resources, their usage, and, consequently, the decisions and resilience of households. This chapter draws together the science described in earlier chapters to allow scenario analysis of the likely impacts of selected climate, land use, IWMP, and other policy interventions on surface and groundwater resources, agricultural productivity, people’s livelihoods, and resilience. A brief recap of the biophysical and socioeconomic models is also provided, and their linkage within an integrated model is outlined. Examples of biophysical scenarios and social policy scenarios are used to demonstrate the value of the integrated and disciplinary models for assessing IWMP and other impacts on water resources and resilience.