Estimation of quantiles is one of the most fundamental real-time analysis tasks. Most real-time data streams vary dynamically with time and incremental quantile estimators document state-of-the art performance to track quantiles of such data streams. However, most are not able to make joint estimates of multiple quantiles in a consistent manner, and estimates may violate the monotone property of quantiles. In this paper we propose the general concept of *conditional quantiles* that can extend incremental estimators to jointly track multiple quantiles. We apply the concept to propose two new estimators. Extensive experimental results, on both synthetic and real-life data, show that the new estimators clearly outperform legacy state-of-the-art joint quantile tracking algorithm and achieve faster adaptivity in dynamically varying data streams.
Network monitoring in cellular networks requires the tracking of quantiles for data distributions of many evolving network measurements (e.g. number of high signaling subscribers per minute). Most quantile estimation algorithms are based on a summary of the empirical data distribution, using either a representative sample or a global approximation of the entire distribution. In contrast, by viewing data as a quantity from a random distribution, the stochastic approximation (SA) for quantile estimation does not keep a global approximation, but rather local approximations at the quantiles of interest, and therefore uses negligible memory even for estimating tail quantiles. However, the current stochastic approximation algorithm for quantile estimation tracks each quantile separately, and this may lead to a violation of the monotone property of quantiles. In this paper, we propose a stochastic approximation technique that enables the simultaneous tracking of multiple quantiles. Our technique maintains the monotone property of different quantiles, and is adaptive to changes in the data distribution. We evaluate its performance using real cellular provider datasets. Our results show that the technique is very efficient. Data are often collected in histogram form, especially in the context of computer simulation. While requiring less memory and computation than saving all observations, the grouping of observations in the histogram cells complicates statistical estimation of parameters of interest. In this paper the mean and variance of the cell midpoint estimator of the pth quantile are analyzed in terms of distribution, cell width, and sample size. Three idiosyncrasies of using cell midpoints to estimate quantiles are illustrated. The results tend to run counter to previously published results for grouped data. 