Throughput optimality of extended back-pressure traffic signal control algorithm

The back-pressure/max-pressure traffic signal control algorithm proposed in the existing literature is distributed, maximizes network throughput, and can be implemented without knowing traffic arrival rates. In this paper, we present an extended back-pressure traffic signal control algorithm, which can further handle bounded measurement/estimation noises in queue lengths and incorporate online estimation of turning ratios and saturated flow rates. Therefore, the extended back-pressure algorithm forms an important step towards the real application of distributed traffic signal control. We prove that under certain conditions, the extended back-pressure algorithm still achieves maximum throughput, i.e, the expected long-term average of total queues is bounded from above under the extended back-pressure algorithm for largest possible set of arrival vectors.