Deadlock free buffer allocation in closed queueing networks

Blocking queueing networks are of much interest in performance analysis due to their realistic modeling capability. One important feature of such networks is that they may have deadlocks which can occur if the node capacities are not sufficiently large. A necessary and sufficient condition for the node capacities is presented such that the network is deadlock free. An algorithm is given for buffer allocation in blocking queueing networks such that no deadlocks will occur assuming that the network has the special structure called cacti-graph. Additional algorithm which takes linear time in the number of nodes, is presented to find cycles in cacti networks.