Estimating Service Territory Size

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Abstract
This paper considers the problem of allocating personnel to provide service that involves travel to demand locations distributed over a geographical area. Assuming that each individual server will be responsible for demand in a certain territory on a first come first served basis, formulas are determined for estimating the appropriate area per person. Demands for service are assumed to be Poisson arrivals with their locations distributed uniformly over the territory. Service time consists of travel to the call location plus “on-site” service time, which can be any random variable with known mean and variance. Area per server is determined as a function of call arrival rate, desired average response time, and service time parameters. Appropriate applications for the models are identified and discussed.

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