Why Smooth Weighted Round Robin Works: The Math Behind Balanced Load Distribution

Non-smooth weighted round robin

In a non‑smooth weighted round robin, servers with higher weight are selected consecutively, leading to bursts of traffic on the busy node and idle periods for others.

Smooth weighted round robin

The smooth algorithm maintains two weights for each node: a static weight and a dynamic currentWeight (initially 0). For each request it adds the static weight to currentWeight of every node, selects the node with the highest currentWeight, then subtracts the total weight sum from that node’s currentWeight. This produces a smooth distribution.

weight – constant configuration value

currentWeight – changes each round

Step‑by‑step example (weights A:B:C = 5:1:1)

First request: after adding weights, currentWeight = [5,1,1]; A is selected, then A’s currentWeight becomes 5‑7 = -2. Resulting weights: [-2,1,1].

Second request: add weights → [3,2,2]; A still highest, selected, then A’s currentWeight = 3‑7 = -4 → [-4,2,2].

Continuing this process for the third, fourth, … requests yields the selection order A → A → B → A → C → A → A, after which the pattern repeats, perfectly matching the 5:1:1 weight ratio without long bursts.

Mathematical proof of weight correctness

Let there be n nodes with weights w_i and total weight S = Σw_i. The algorithm starts with all currentWeight = 0. After each full round the sum of currentWeight values is 0. By induction, after S selections each node i has been chosen exactly w_i times, proving that the algorithm respects the configured weights.

Proof of smoothness

Because after a node is selected its currentWeight is reduced by S, it cannot be selected again until other nodes have accumulated enough weight to exceed it. Therefore the algorithm never selects the same node consecutively more than its weight permits, guaranteeing a smooth distribution.

Pseudocode

for each request:
    for node in nodes:
        node.currentWeight += node.weight
    selected = node with max currentWeight
    selected.currentWeight -= totalWeight

One more thing – source reference

The original article was removed, but an archived copy is available at https://web.archive.org/web/20210918075426/https://tenfy.cn/2018/11/12/smooth-weighted-round-robin/ .