A Hypercube Queueing Model for Facility Location and Redistricting in Urban Emergency Services

by Richard C. Larson

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A spatially distributed queueing model is developed to assist administrators of urban emergency services in locating vehicles and designing response districts. Computationally efficient algorithms are given that permit numerical evaluation of the performance characteristics of systems having up to 12 emergency response units. The measures of performance computed analytically by the model include the following: region-wide mean travel time, workload imbalance, and fractions of dispatches that are interdistrict dispatches; workloads of each response unit; mean travel time to each geographical atom and to each district; mean travel time of each response unit; fraction of responses into each district that are interdistrict; and fraction of responses of each response unit that are interdistrict. This mixture of performance measures allows one to focus simultaneously on several region-wide objectives, while assuring that spatial inequities in the delivery of service are maintained at an acceptable minimum.

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