In single‑class queuing networks that are stable and operate under any work‑conserving scheduling discipline, the sum over all nodes of the product of each node's offered load (traffic intensity) and its mean delay is invariant; scheduling can redistribute delay among nodes but cannot change this weighted sum.

Principle

For a given set of arrival rates and service capacities in a single‑class, work‑conserving network, any admissible scheduling policy preserves the network‑wide weighted delay sum (offered load × mean delay) — scheduling only reallocates delay among nodes.

Demonstration

Illustrative scenario → A two‑node packet network with fixed per‑node service rates and a single traffic class is observed under FIFO scheduling and under a priority scheduling that favours node A. Recognition → Measured mean delays at A and B change. Action → Compute (offered load at A)×(mean delay at A) + (offered load at B)×(mean delay at B) for each scheduling. Consequence → The two sums are equal within statistical estimation error, showing invariance while individual node delays moved.

Misapplication

Assuming the law applies to multiclass traffic (multiple customer classes with different routing or service requirements), to non‑work‑conserving disciplines (e.g., deliberate idle periods), or to unstable networks; these are distinct regimes where the invariance does not generally hold.

Consequence

Designers can trade delay between locations or flows using scheduling without changing the conserved weighted sum; therefore, improving delay for one subset of packets must worsen delay for others unless service capacity is increased.

Reversal

If the network contains multiple service classes with class‑dependent routing, employs non‑work‑conserving service (intentional idling or rate shaping that changes total service offered), is transient or unstable, or includes stateful priority with class‑dependent arrival processes, the conservation relation need not hold.

Boundary

Applies to: single‑class, stable queuing networks; work‑conserving scheduling; steady‑state averages. Excludes: multiclass networks, non‑work‑conserving schedulers, networks outside steady state, and systems with stateful external control that alter offered load.

Semantic Tension

Fairness versus aggregate invariants — scheduling can satisfy fairness or latency targets for particular flows but must respect the conservation constraint that limits aggregate improvements without added capacity.

Synthesis

Kleinrock's law converts scheduling design into a redistribution problem: with fixed traffic and capacity, scheduling cannot create or destroy the network's weighted delay budget, only reallocate it among nodes or flows.