Pull versus push mechanism in large distributed networks: Closed form results

In this paper we compare the performance of the pull and push strategy in a large homogeneous distributed system. When a pull strategy is in use, lightly loaded nodes attempt to steal jobs from more highly loaded nodes, while under the push strategy more highly loaded nodes look for lightly loaded nodes to process some of their jobs. Given the maximum allowed overall probe rate R and arrival rate λ, we provide closed form solutions for the mean response time of a job for the push and pull strategy under the infinite system model. More specifically, we show that the push strategy outperforms the pull strategy for any probe rate R > 0 when λ < φ − 1, where φ = (1 + V5)/2 ≈ 1.6180 is the golden ratio. More generally, we show that the push strategy prevails if and only if 2λ < √(R+1)
²
+ 4(R+1) − (R+1). We also show that under the infinite system model, a hybrid pull and push strategy is always inferior to the pure pull or push strategy. The relation between the finite and infinite system model is discussed and simulation results that validate the infinite system model are provided.