Uncertainty in the Demand for Service - Faculty of Industrial ...

practical value in terms of accuracy. Moreover, he shows that the quality of the fluid approximation
improves as variability of the arrival rate increases.
Uncertainty in future call volume complicates the process of determining staffing levels. It
is then important to correctly model the stochastic nature of call arrivals, and in particular, to
make corect predictions of call arrivals. Operation Researchers have been developing planning
models for service systems for the last few decades. Channouf et al. [2] refers to the emergency
medical system and survey the academic literature regarding the planning models topic.
Next, they develop and evaluate time-series models for estimating and forecasting daily and
hourly arrival rates, and then compare the models in term of their quality of fit and forecasting
performance using historical observations of a major Canadian city’s emergency medical service.
Implementing the QED’s ”square-root staffing” rule (7) requires that forecasted arrival and
service rates adhere to a certain level of precision. The requirements for prediction accuracy
is that the estimated arrival rate must not exceed an order of square-root deviation from the
real arrival rate. Otherwise the QED rule will not be effective since, with a larger error, it will
either grossly over- or under- estimate the staffing level. Aldor [1] develops two variations of
Poisson process models, which are based on a mixed Poisson process approach, for predicting
the system loads, and then develops different goodness-of-fit criteria that help determine the
model performance under the QED regime. Her results, of analyzing an Israeli cellular phone
company data, show that during busy periods, when the QED regime ”square-root staffing” rule
is relevant, the system will be able to perform at a desired level commensurate with the actual
load. The results gives some evidence that one can ensure a pre-specified QED regime using
load forecasts that are sufficiently precise.
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