Grace M. Carter

Response Areas for Two Emergency Units

This paper gives a model in which two urban emergency service units such as fire engines or ambulances cooperate in responding to alarms or calls from the public in a specified region of a city. Given the home locations of the units and the spatial distribution of alarm rates, it is possible to specify which unit should respond to each alarm by defining a response area for each unit. The average response time to alarms and the workload of each unit are calculated as functions of the boundary that separates their response areas. The boundaries that minimize average response time and the ones that equalize workload are determined. Some boundaries can be dominated, in the sense that another boundary improves both workload balance and response time. The set of undominated boundaries is found.

Empirical Bayes Methods Applied to Estimating Fire Alarm Probabilities

Abstract An empirical Bayes approach is used to derive a Stein-type estimator of a multivariate normal mean when the components have unequal variances. This estimator is applied to estimating the probability that a fire alarm reported from a particular street box signals a structural fire rather than a false alarm or other emergency. The approach is to group alarm boxes into relatively homogeneous neighborhoods and to make empirical Bayes estimates of the “probability structural” for each box in the neighborhood from yearly (1967–1969) Bronx data. A dispatching rule based on the estimates is evaluated on 1970 data.

Urban problems

The panel examines several operational uses of simulation in the urban problem solving environment. Papers range from an attempt to develop a generalized urban planning model capable of managing substantive areas as varied as health and education, all the way through to a very specific example of a police patroling dispatching simulation. Other examples include an effort to understand, model and improve a portion of New Yorks troubled judicial system and a deployment model used by the New York Fire Department. The emphases throughout are serious and operational. Discussants have been chosen not only because of their technical qualifications to comment on model specification, construction and operation but also because they each have had considerable experience dealing with the specific substantive issues treated in the discussed simulations.

Queues with Service in Random Order

We consider two models, the GI/M/s queue and the M/G/1 queue, in which waiting customers are served in random order. For each model we derive expressions for the calculation of the stationary waiting-time distribution function. Our methods differ from those of previous authors in that we do not use transforms, and consequently our results may be better suited for calculation. We illustrate our methods by deriving previously known results for the M/M/s and M/D/1 random-service queues, and by making sample calculations for the M/Ek/1 random-service queue for various values of the utilization factor and the index k.

A simulation model of the New York city fire department: Its use in deployment analysis

This paper describes a simulation model developed as a tool to aid deployment decision-making for the New York City Fire Department. The model, written in Simscript I.5, has been used to evaluate alternative solutions to workload and response problems plaguing the City. These solutions involve new policies for locating, relocating and dispatching fire-fighting units to achieve a more effective utilization of resources. Several specific applications of the simulation are described. In addition, methodological issues concerning the design and use of the model are addressed.

Variations in cataract extraction rates in Medicare prepaid and fee-for-service settings.

OBJECTIVE To compare rates of cataract extraction in 2 prepaid health settings and in traditional fee-for-service (FFS) settings. DESIGN A cross-sectional analysis using 1993 health maintenance organization (HMO) Medicare claims and encounter files, the Health Care Financing Administration (HCFA) 5% Medicare Part B provider/supplier file, and the HCFA October 1992 100% Medicare population file. SETTING Southern California Medicare FFS settings and the staff-model and independent practice association (IPA) plans of a large California HMO. PATIENTS 1993 Medicare beneficiaries aged 65 years and older. The study included 43387 staff-model HMO enrollees, 19050 IPA enrollees, and 47 150 FFS beneficiaries (a 5% sample of all Southern California FFS beneficiaries). MAIN OUTCOME MEASURE Age and risk-factor adjusted rates of cataract extraction per 1000 beneficiary-years. RESULTS After controlling for age, sex, and diabetes mellitus status, FFS beneficiaries were twice as likely to undergo cataract extraction as were prepaid beneficiaries (P<.01). Female FFS beneficiaries were nearly twice as likely to undergo the procedure as were male FFS beneficiaries (P<.001); there were no extraction rate differences by sex in the prepaid settings. CONCLUSION Because of the potential implications for vision care in the elderly, the significantly different rates of cataract extraction in FFS and prepaid settings warrant further clinical investigation to determine whether there is overuse in FFS vs underuse in prepaid settings. Such investigations must assess the appropriateness of cataract surgery by evaluating its use relative to clinical need.