The problem of simulating graphs (networks) subject to constraints has been studied extensively across several areas. Applications of this problem include modeling inter-bank financial networks, predator-prey ecological graphs, contingency tables, and even studying larger networks such as the Internet. In “Maximum Entropy Distributions with Applications to Graph Simulation,” P. Glasserman and E. Lelo de Larrea study the more general problem of sampling uniformly from product sets under linear constraints, which includes simulating bipartite, directed, and undirected graphs with given degree sequences. For this purpose, they consider two suitable probability distributions: one that maximizes the entropy of the system, and another that maximizes the minimum probability of hitting the desired target set. Although apparently different, the authors provide conditions under which both distributions coincide. In addition, they propose a simple sequential algorithm to sample medium-sized graphs with fixed degrees.

Most emergency medical services (EMS) systems send patients to the closest hospitals. This long-standing principle, while maximizing patient welfare in usual times, can lead to hospital overloading and negative patient outcomes during unusual EMS demand shifts caused by events such as the COVID-19 pandemic. This latter phenomenon was observed in New York City (NYC) during the spring of 2020 and overwhelmed many outer-borough hospitals. To prepare for a future potential incident surge, and to complement existing approaches to relieve congestion in emergency departments, Columbia University and the Fire Department of the City of New York collaborated to design a load-balancing optimization algorithm to transport 9-1-1 patients to hospitals. The algorithm automatically balances patient transport time and hospital capacity city-wide, by integrating daily-run optimization with data-driven prediction to proactively avoid hospital overload in advance of dispatch. We present the algorithm, explain how it enhances the existing system to guard against future unexpected incident surges, and discuss a range of implementation considerations. The load balancing rule was implemented in NYC's Computer Aided Dispatch system on January 13, 2021 through May 20, 2021 and again on December 31, 2021 through January 27, 2022.

Sudden periods of extreme and persistent changes in the distribution of medical emergencies can trigger resource planning inefficiencies for Emergency Medical Services, causing delayed responses and increased waiting times. Predicting such changes and reacting adaptively can alleviate these adversarial impacts. In this paper, we propose a simple framework to enhance historically calibrated call volume models, the latter a focus of study in the arrival estimation literature, to give more accurate short-term prediction by refitting their residuals into time series. We discuss some justification of our framework from the perspective of doubly stochastic Poisson processes. We illustrate our methodology in predicting the hourly call volume to the 911 call center during the Covid-19 pandemic in NYC, showing how it could improve the performance of baseline historical estimators by close to 50% measured by the out-of-sample prediction error for the next hour.

In most emergency medical services (EMS) systems, patients are transported by ambulance to the closest most appropriate hospital. However, in extreme cases, such as the COVID-19 pandemic, this policy may lead to hospital overloading, which can have detrimental effects on patients. To address this concern, we propose an optimization-based, data-driven hospital load balancing approach. The approach finds a trade-off between short transport times for patients that are not high acuity while avoiding hospital overloading. In order to test the new rule, we build a simulation model, tailored for New York City's EMS system. We use historical EMS incident data from the worst weeks of the pandemic as a model input. Our simulation indicates that 911 patient load balancing is beneficial to hospital occupancy rates and is a reasonable rule for non-critical 911 patient transports. The load balancing rule has been recently implemented in New York City's EMS system.

We propose an algorithm for simulating bipartite or directed graphs with given degree sequences, motivated by the study of financial networks with partial information. Our algorithm sequentially computes certain "maximum entropy" matrices, and uses the entries of these matrices to assign probabilities to edges between nodes. We prove the correctness of the algorithm, showing that it always returns a valid graph and that it generates all valid graphs with positive probability. We illustrate the algorithm in an example of an inter-bank network.