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In this paper, we consider network monitoring techniques to estimate communication qualities in wide-area mobile networks, where an enormous number of heterogeneous components such as base stations, routers, and servers are deployed. We assume that average delays of neighboring base stations are comparable, most of servers have small delays, and delays at core routers are negligible. Under these assumptions, we propose Heterogeneous Delay Tomography (HDT) to estimate the average delay at each network component from end-to-end round trip times (RTTs) between mobile terminals and servers. HDT employs a crowdsourcing approach to collecting RTTs, where voluntary mobile users report their empirical RTTs to a data collection center. From the collected RTTs, HDT estimates average delays at base stations in the Graph Fourier Transform (GFT) domain and average delays at servers, by means of Compressed Sensing (CS). In the crowdsourcing approach, the performance of HDT may be degraded when the voluntary mobile users are unevenly distributed. To resolve this problem, we further extend HDT by considering the number of voluntary mobile users. With simulation experiments, we evaluate the performance of HDT. key words: delay tomography, graph Fourier transform (GFT), compressed sensing (CS), crowdsourcing, mobile network

Heterogeneous Delay Tomography for Wide-Area Mobile Networks