Every request arriving at a busy web service has to be sent to one of several backend servers. The rule the load balancer uses to pick a server — its routing policy — has a big effect on how evenly work gets spread and how long users end up waiting, especially once requests take unpredictable amounts of time to finish.
"Power of two choices" (Mitzenmacher, 1996) is a classic result: randomly sampling just two servers and picking the less-loaded one reduces the worst-case queue length exponentially compared to picking one server at random, without the coordination overhead of checking every server for every request.
Requests stream in from a client node, get routed across a bank of backend servers, wait in a visible queue, and get processed — showing exactly how round robin, least connections and power-of-two-choices spread the load differently.
Round robin ignores current load and can pile requests onto a slow server; least connections always targets the shortest queue; power-of-two-choices gets nearly the same balance by sampling just two servers at random.
Pick a routing policy, raise the request rate or server count, and toggle uneven server speeds to see queues build up unevenly. Watch the per-server connection counts and average latency respond live.
Real load balancers such as NGINX, HAProxy and cloud application load balancers all ship variants of these exact three policies, because full global knowledge of every server's load is expensive to keep up to date at scale.