First Come First Served (FCFS) is a policy that is accepted for implementing fairness in a number of application domains such as scheduling in Operating Systems, scheduling web requests, and so on. We also have orthogonal applications of FCFS policies in proving correctness of search algorithms such as Breadth-First Search, the Bellman-Ford FIFO implementation for finding single-source shortest paths, program verification and static analysis. The data structure used to implementing FCFS policies, the queue, suffers from two principal drawbacks, viz., non-trivial verifiability and lack of scalability. In case of large distributed networks, maintaining an explicit queue to enforce FCFS is prohibitively expensive. The question of interest then, is whether queues are required to implement FCFS policies; this paper provides empirical evidence answering this question in the negative. The principal contribution of this paper is the design and analysis of a randomized protocol to implement approximate FCFS policies without queues. From the Software Engineering perspective, the techniques that are developed find direct applications in program verification, model checking, in the implementation of distributed queues and in the design of incremental algorithms for Shortest path problems.