Contention resolution with bounded delay

When distributed processes contend for a shared resource, we need a good distributed contention resolution protocol, e.g., for multiple-access channels (ALOHA, Ethernet), PRAM emulation, and optical routing. Under a stochastic model of request generation from n synchronous processes, Raghavan & Upfal (1995) have shown a protocol which is stable for a positive request rate; their main result is that for every resource request, its expected delay (time to get serviced) is O(log n). Assuming that the initial clock times of the processes are within a known bound of each other, we present a stable protocol, wherein the expected delay for each request is O(1). We derive this by showing an analogous result for can infinite number of processes, assuming that all processes agree on the time