A Pipe-Stream Event-Based Mesoscopic LWR Model with Per-Lane Resolution and Class-Restricted Lanes

First-order network traffic models force an unhappy choice at motorway exits. Under strict first-in-first-out (FIFO), a queue on a one-lane off-ramp freezes every lane of the mainline; under relaxed FIFO, the same queue obstructs nobody. Field observations sit between these extremes. We remove the choice structurally. Pipe-stream is an event-based mesoscopic implementation of the Lighthill–Whitham–Richards kinematic wave model that partitions every link into pipes: parallel lane groups, down to single lanes, each solved as an independent kinematic wave stream with its own capacity, storage and backward wave. FIFO stays strict inside a pipe, where lane commitment makes it physically exact, and overtaking is free across pipes. Class permissions, movement restrictions and one friction coefficient φ complete the construction, and φ is the only parameter that requires calibration. Because the construction never leaves the stream formulation, the model keeps a single-stream ancestor and reducesto it bit for bit: a property enforced by trajectory checksums and confirmed against an independent implementation of that ancestor over 340 000 node passages. Solutions stay event-exact, nine closed-form LWR benchmarks passing at machine precision. On a blocked off-ramp the single-stream model collapses through service to the exit-interleaving rate, while the partition confines the queue to its lane and serves through traffic without delay. A microscopic simulator that resolves lanes and lane changes explicitly, sharing none of this model’s assumptions, agrees with the partition to within 1.2% of mainline throughput, while a mesoscopic queue model collapses with the single-stream engines: what separates the answers is lane resolution, not solver family. Lanes can be resolved without surrendering exactness.