Improved Rate-Based Pull and Push Strategies in Large Distributed Networks

Large distributed systems benefit from the ability to exchange jobs between nodes to share the overall workload. To exchange jobs, nodes rely on probe messages that are either generated by lightly-loaded or highly-loaded nodes, which corresponds to a so-called pull or push strategy. A key quantity of any pull or push strategy, that has often been neglected in prior studies, is the resulting overall probe rate. If one strategy outperforms another strategy in terms of the mean delay, but at the same time requires a higher overall probe rate, it is unclear whether it is truly more powerful. In this paper we introduce a new class of rate-based pull and push strategies that can match any predefined maximum allowed probe rate, which allows one to compare the pull and push strategy in a fair manner. We derive a closed form expression for the mean delay of this new class of strategies in a homogeneous network with Poisson arrivals and exponential job durations under the infinite system model. We further show that the infinite system model is the proper limit process over any finite time scale as the number of nodes in the system tends to infinity and that the convergence extends to the stationary regime. Simulation experiments confirm that the infinite system model becomes more accurate as the number of nodes tends to infinity, while the observed error is already around 1% for systems with as few as 100 nodes.