This read-write value caps the number of cells belonging to this specific connection that may occupy the switch's shared cell memory at once, defaulting to half of the assumed 512K-cell total memory pool. It's a per-connection buffer-fairness control preventing one channel from monopolizing shared memory during a burst, which would otherwise starve other connections. An admin running many low-priority connections on one interface might lower bbChanMaxCellMemThreshold on each so no single connection's burst can exhaust the shared buffer pool.