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Backpressure (BP) control was originally used for packet routing in communications networks. Since its first application to network traffic control, it has undergone different modifications to tailor it to traffic problems with promising results. Most of these BP variants are based on an assumption of perfect knowledge of traffic conditions throughout the network at all times, specifically the queue lengths (more accurately, the traffic volumes). However, it has been well established that accurate queue length information at signalized intersections is never available except in fully connected environments. Although connected vehicle technologies are developing quickly, we are still far from a fully connected environment in the real world. This paper test the effectiveness of BP control when incomplete or imperfect knowledge about traffic conditions is available. We combine BP control with a speed/density field estimation module suitable for a partially connected environment. We refer to the proposed system as a BP with estimated queue lengths (BP-EQ). We test the robustness of BP-EQ to varying levels of connected vehicle penetration, and we compared BP-EQ with the original BP (i.e., assuming accurate knowledge of traffic conditions), a real-world adaptive signal controller, and optimized fixed timing control using microscopic traffic simulation with field calibrated data. Our results show that with a connected vehicle penetration rate as little as 10%, BP-EQ can outperform the adaptive controller and the fixed timing controller in terms of average delay, throughput, and maximum stopped queue lengths under high demand scenarios.