We consider open networks of queues with Processor-Sharing discipline and signals. The signals deletes all the customers present in the queues and vanish instantaneously. The customers may be usual customers or inert customers. Inert customers do not receive service but the servers still try to share the service capacity between all the customers (inert or usual). Thus a part of the service capacity is wasted. We prove that such a model has a product-form steady-state distribution when the signal arrival rates are positive.

Hurricane Katrina demonstrated that a catastrophic event in the continental United States (US) can overwhelm domestic medical response capabilities. The recent focus on response planning for a catastrophic earthquake in the New Madrid Seismic Zone and the detonation of an improvised nuclear device also underscore the need for improved plans. The purpose of this analysis is to identify the potential role of foreign medical teams (FMTs) in providing medical response to a catastrophic event in the US. We reviewed existing policies and frameworks that address medical response to catastrophic events and humanitarian emergencies and assess current response capabilities by a variety of FMTs. While several policies and plans outline the role of the US in providing medical assistance during foreign disasters, further planning is necessary to identify how the US will integrate foreign medical assistance during a domestic catastrophic event. We provide an overview of considerations related to federal roles and responsibilities for managing and integrating FMTs into the overarching domestic medical response to a catastrophic disaster occurring in the continental US. (Disaster Med Public Health Preparedness. 2013;7:555-562)

This article analyzes an economy where both nonrenewable resources and a costly energy resource are essential inputs in production. The extraction of the nonrenewable resources leads to emissions that increase the probability of a catastrophe. We find that, in contrast to the constant-probability case, the endogenous probability of a catastrophe implies that some nonrenewable resources might optimally be left in the ground. The larger the effect of the fossil energy use on the probability of a catastrophe, the fewer nonrenewable resources should be extracted and the earlier should be the switch to the renewable substitute. The richer a country, the earlier it should shift to the energy substitute. In the trade-off between higher consumption and a higher probability of catastrophe, even small probability changes are likely to be more important for the planner than higher consumption.

A Markov decision model is considered for the control of a truncated general immigration process, which represents a pest population, by the introduction of total catastrophes. The optimality criterion is that of minimizing the expected long-run average cost per unit time. Firstly, a necessary and sufficient condition is found under which the policy of never controlling is optimal. If this condition fails, a parametric analysis, in which a fictitious parameter is varied over the entire real line, is used to establish the optimality of a control-limit policy. Furthermore, an efficient Markov decision algorithm operating on the class of control-limit policies is developed for the computation of the optimal policy.

This paper is concerned with the problem of controlling a simple immigration–birth process, which represents a pest population, by the introduction of catastrophes which, when they occur, reduce the population size to zero. The optimality criterion is that of minimising the long-term average cost per unit time of the process. Firstly, an optimal policy is found within a restricted class of stationary policies, which introduce catastrophes if and only if the population size is greater than or equal to some critical value x. The optimality of this policy within the wider class of all stationary policies is then verified by applying the general results of Bather (1976).