Quantiles and quantile related performance measures are common in modeling quality of service (QoS). Indeed, in the call center industry, QoS is typically measured by the fraction of services meeting a predefined service level, which can be expressed in terms of the fraction of customers that could be helped within a pre-specified time (e.g. 90 % of customers are helped within 10 minutes). In public transportation networks, QoS is measured by the achieved punctuality (e.g. 95 % of trains are no more delayed than 2 minutes). In risk analysis, value at risk and conditional value at risk are defined through quantiles.To improve or optimize the quantile related performance of a system, sensitivity analysis of quantiles with respect to changes in the parameters of the underlying model are essential.
In this talk we discuss sensitivity analysis for quantiles. Specifically, we propose a Monte Carlo estimator for the sensitivity of a quantile via Measure Valued Differentiation. We provide theory for continuous random variables. The resulting estimator has the interesting property that the weak derivative can be directly computed and no splitting of sample path is needed, which makes the estimator based on weak differentiation as efficient as sample path approaches such as infinitesimal perturbation analysis.
This is a joint work with Warren Volk-Makarewicz.