Distributed Queuing in Dynamic Networks

We consider the problem of forming a distributed queue in the synchronous dynamic network model of Kuhn, Lynch, and Oshman (STOC 2010) in which the network topology changes from round to round but the network stays connected. Queue requests may arrive over rounds at network nodes and the goal is to eventually enqueue them in a distributed queue. We show that in 1-interval connected graphs, where the communication links change arbitrarily between every round, it is possible to solve the distributed queueing problem in O(nk) rounds using O(log n) size messages, where n is the number of nodes in the network and k <= n is the number of queue requests. Further, we show that for more stable graphs, e.g. T-interval connected graphs where the communication links change in every T >= 2 rounds, the distributed queuing problem can be solved in O (n + nk/min{alpha,T}) rounds using the same O(log n) size messages, where alpha > 0 is the concurrency level parameter that captures the minimum number of active queue requests in the system at any round. These results hold in any arbitrary arrival of queue requests and ensure correctness of the queue formed. To our best knowledge, these are the first solutions to the distributed queuing problem in highly dynamic networks.