Applied probability models in health, risk, queues and forestry

今年夏天，我们在双语呼叫中心方面的工作（仍在进行中）集中在双语呼叫中心模型上，该模型根据排队长度的差异分配双语代理。完成这一步骤后，我们打算研究三语呼叫中心，以便在使用三语人员之前，深入了解最佳分配不灵活（单语）和部分灵活（双语）代理的良好策略。然后，我们希望将从这方面获得的见解应用于多语言呼叫中心的分配程序。 谈到器官移植等候名单，几乎所有司法管辖区对可能受益的患者器官的需求都超过了稳定的供应。对于肾脏和肝脏来说，活体移植是一种越来越受到关注的选择，以填补差距。我们在这一领域的工作已经预测了在加拿大实现肝移植队列稳定所需的死者捐赠器官与活体捐赠器官的数量。未来的工作将包括对等待名单操作的详细模拟，以更全面地了解血型、健康水平、名单上的时间和其他因素对移植时间的影响。将开发一个理论优先队列模型，以反映随着患者健康水平随时间推移而下降的紧迫性。 未来的工作在该领域的风险理论将追求两个方面：应用流体流动技术尚未解决的方面扰动风险过程，如破产前的盈余，并启动调查的Gerber-Shiu函数的扰动风险过程和那些具有多层结构。在林业方面，我们将与省级消防局（安大略MNR）和国家消防专家（加拿大林业局）合作，使用红外摄像机，专家意见征集和其他技术研究火灾现场现象。

Our work this summer (still in progress) on Bilingual Call Centres has focused on bilingual call centre models that allocate bilingual agents on the basis of the difference in queue lengths. Upon completion of this step, we intend to study trilingual call centres to gain insight into good strategies for the optimal allocation of inflexible (unilingual) and partially-flexible (bilingual) agents, before using those who are trilingual. We then hope to apply insights gained from this aspect to allocation procedures for multilingual call centres. Turning to organ transplant waitlists, demand for organs from patients who could benefit exceeds the stable supply in almost all jurisdictions. For kidneys and livers, living-donor transplants are an option that is receiving increased attention to fill in the gap. Our work in this field has developed forecasts for the number of deceased donor organs vs. living donor organs required to achieve stability of the liver transplant queues in Canada. Future work will include a detailed simulation of waitlist operations, to more fully understand the impact of blood type, health level, time on list and other factors on time to transplantation. A theoretical priority queue model will be developed, to reflect increased urgency as a patient's health level decreases over time. Future work in the area of risk theory will pursue two fronts: applying fluid flow techniques to as yet unresolved aspects of perturbed risk processes such as the surplus prior to ruin, and initiating investigations of Gerber-Shiu functions for perturbed risk processes and those with a multi-layered structure. In Forestry, working with partners in provincial fire authorities (Ontario MNR) and national fire specialists (Canadian Forestry Service), we will study the fire spotting phenomenon, using infrared cameras, expert opinion elicitation, and other techniques.