Modern high-performance asynchronous circuits depend on timing constraints for correct operation, so timing analyzers are essential asynchronous design tools. In this paper we present a 13-valued abstract waveform algebra and a polynomial-time min-max timing simulation algorithm for use in efficient, approximate timing analysis of asynchronous circuits with bounded component delays. Unlike several previous approaches, our algorithm computes separate propagation delay bounds from each circuit input to each internal gate. This is useful for analyzing asynchronous circuits, where the relative transition times of the inputs may not be known a priori, unlike synchronous circuits. We also describe an efficient reconvergent fanout analysis technique that helps in increasing the accuracy of simulation. We have applied our algorithm to build an efficient timing analysis tool for extended burst-mode circuits (a class of timing-dependent asynchronous circuits) implemented in the 30 design style. Our tool analyzes gate-level 30 circuits assuming bounded component delays and determines safe timing constraints for correct operation. Although our results represent conservative approximations to the true timing requirements in the worst case, experiments indicate that our technique is efficient and fairly accurate in practice.