Phase Transitions in Stochastic Networks

Calls arrive in the network as a Poisson process and will be rejected or blocked if they cannot be served immediately due to insufficient capacities in the required links. Network performance is assessed by the probability that a call is blocked or lost (blocking probability). Such a network is considered as fair if the blocking probability for a certain type of call is uniform across the network space, however, phase transition effects can lead to unfairness or poor performance of the system. The critical questions are: When do phase transitions occur? How might they be avoided? Earlier work showed that phase transitions can occur in such networks with a symmetric tree structure and, more recently, that those phase transitions can be nonmonotone in the arrival rate of multilink connections at a node [1, 2].