  We consider the problem of forming a distributed queue in the adversarial
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.
This is a synchronous model in which network nodes are assumed to be fixed, the
communication links for each round are chosen by an adversary, and nodes do not
know who their neighbors are for the current round before they broadcast their
messages. Queue requests may arrive over rounds at arbitrary nodes and the goal
is to eventually enqueue them in a distributed queue. We present two algorithms
that give a total distributed ordering of queue requests in this model. We
measure the performance of our algorithms through round complexity, which is
the total number of rounds needed to solve the distributed queuing problem. 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 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 in any round. These
results hold in any arbitrary (sequential, one-shot concurrent, or dynamic)
arrival of k queue requests in the system. Moreover, our algorithms ensure
correctness in the sense that each queue request is eventually enqueued in the
distributed queue after it is issued and each queue request is enqueued exactly
once. We also provide an impossibility result for this distributed queuing
problem in this model. To the best of our knowledge, these are the first
solutions to the distributed queuing problem in adversarial dynamic networks.
