Self-stabilizing K-out-of-L exclusion on tree network
  In this paper, we address the problem of K-out-of-L exclusion, a generalization of the mutual exclusion problem, in which there are $\ell$ units of a shared resource, and any process can request up to $\mathtt k$ units ($1\leq\mathtt k\leq\ell$). We propose the first deterministic self-stabilizing distributed K-out-of-L exclusion protocol in message-passing systems for asynchronous oriented tree networks which assumes bounded local memory for each process. 
Ajoy K. Datta (UNLV), St\'ephane Devismes (VERIMAG - IMAG), Florian   Horn (LIAFA), Lawrence L. Larmore (UNLV)