Edward Ignall

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.

The Output of A Two-Stage System with Unreliable Machines and Limited Storage

Abstract Buffer storage allows the decoupling of successive stages of large automatic production systems, which can be important when the machines sometimes fail. System designers should know how much added buffer capacity increases the hourly output of such systems. Previously available methods for predicting this increase treat systems with one machine in each stage. We present a computationally simple heuristic procedure for estimating hourly line output for two stage systems in which each stage may have several machines.

Using Simulation to Develop and Validate Analytic Models: Some Case Studies

Simulation models are generally costly tools to use in systems analyses. Whenever applicable, a simple analytic model is preferable. However, in many cases the conditions assumed by solvable analytic models do not hold in the real world; hence an analyst would hesitate to use them. A simulation can be used to suggest an appropriate approximate model and to determine how good an approximation a given analytic model is. We show how simulations of New York Citys fire and police operations have been used to develop and validate simple analytic models that are now being used to analyze the deployment of resources in these two services.

Optimal Dispatching of an Infinite-Capacity Shuttle: Control at a Single Terminal

We study the optimal control of a shuttle system consisting of a single infinite-capacity carrier transporting passengers between two terminals. Passengers arrive according to independent Poisson processes, and at only one of the terminals can the dispatcher hold the carrier for more passengers. Our objective: to determine dispatching rules that minimize the long-run average of a linear passenger-waiting-time cost and a charge per trip made by the carrier. When complete information about the system state is available, and travel times are not random, we prove that it is best to dispatch the carrier if, and only if, the total number of passengers waiting at both terminals is greater than a cutoff value. To compute this cutoff value, we propose an iterative method and find that we can approximate it quite well by a simple function of system costs and parameters similar to the economic-lot-size formula. We propose a dispatching rule which may not be optimal for the case when only the number of passengers waiting at one terminal is known, and we compare its efficiency to that of the optimal rule that uses complete information. We outline extensions to other optimality criteria and to the case of stochastic travel times.

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.

A Simulation Model of Fire Department Operations: Design and Preliminary Results

A simulation model designed to compare different policies for locating, relocating, and dispatching fire-fighting units is described. Issues treated include: the use of internal measures of performance as proxies for global ones; the use of analytical models for various subproblems to yield policies to be tested; the handling of loss of life and other important but rare events. The SIMSCRIPT 1.5 simulator and input and post-simulation analysis programs are described. Results that have been used by the Fire Department of the City of New York are presented and analyzed.

OPERATING CHARACTERISTICS OF A SIMPLE SHUTTLE UNDER LOCAL DISPATCHING RULES

We treat a transportation system with Poisson passenger arrivals at each of two terminals and a carrier of capacity one that shuttles back and forth between the terminals. We study the consequences of the control decision: how long should the carrier wait empty at a terminal? This dispatch decision is made without knowledge of the queue at the other terminal. Exact and approximate expressions are obtained for the number of carrier trips per unit time and average queue size at each terminal. They are used to show that it is best never to hold the carrier at the slow terminal and not to randomize in the decision process. Further, we show that holding the carrier at the fast terminal sometimes reduces both trip rate and the sum of the average queue sizes.

Fire Department Deployment Analysis: A Public Policy Analysis Case Study-- The RAND Fire Project.

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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.

ON USING SIMULATION TO EXTEND OR/MS THEORY: THE SYMBIOSIS OF SIMULATION AND ANALYSIS

Publisher Summary Simulation and analytic models are a package that has greatest prospects for giving new insights and knowledge when used together, often when used recursively. One advantage of simulation is the nearly limitless range of modeling detail and output that is possible. Whatever the complexities of the real system, they can be represented in a simulation, provided of course that the modeler understands what is going on. Simulation can produce as output a history of individual events or transactions as desired. Most simulations are logical models that imitate the event-by-event behavior of systems induced by exogeneous events that cannot be controlled or predicted exactly. One approach to dealing with such an environment is to model these exogeneous events as a stochastic process.