Sim time0.0 s

Mean delay-

Loss0.0 %

Throughput0 pkt/s

Click or tap a cable to cut / restore it. The bar at a cable's sending end is its queue.

Link load (utilisation)

065 %100 %

Switch to 3D

Packet Path Diorama: 2D Network Map and Queue Phase Plane

The 2D companion shows what the 3D scene hides: every cable's load against the queueing curve, and delay and loss over time.

Phase plane: load vs queue length

Each dot is one direction of one cable. The white curve is the M/M/1 average number in the system, ρ/(1-ρ). Dots near the curve behave like textbook queues; dots below it have a small buffer and drop packets instead of queueing.

Delay and loss over time

■ mean delay (s) ■ loss % per second ■ M/M/1 prediction

Mean delay (20 s window)- Fluid + M/M/1 prediction- 95th percentile delay- Offered / delivered- Loss (buffer + failures)- Busiest link- Packets in flight / queued-

Traffic and routing

Routing

Buffer / link

Service

Speed1x

Experiment: which routing wins?

Replays the current traffic, buffer and cut cables for 120 s under each policy with identical random numbers, without drawing anything.

Independent numerical checks

Check	Theory	Measured

Running checks...

The science

Each cable is a queue. A link sends packets at rate μ (packets/s); packets arrive at rate λ; utilisation is ρ = λ/μ. For random (Poisson) arrivals and exponential service, M/M/1 gives the mean number in the system L = ρ/(1-ρ) and mean time W = 1/(μ-λ). Little's law L = λW ties them together. The phase plane plots exactly this curve: delay explodes as ρ approaches 1, so a link that is "only 90 % full" is already slow.

Finite buffers drop packets. With room for K packets the M/M/1/K blocking probability is P_K = (1-ρ) ρ^K / (1-ρ^K+1) (1/(K+1) at ρ = 1). A huge buffer removes loss but lets the queue grow to about K/μ seconds: bufferbloat.

End-to-end delay is the sum over hops of propagation delay d plus queueing and sending time. The "fluid + M/M/1 prediction" routes each flow's mean rate along its current path, finds each link's λ, and sums d + 1/(μ-λ). It ignores drops, so it is shown only while every link is below 95 %.

Routing. Each router forwards on the first hop of a least-cost path (Dijkstra). Policies differ only in link cost: fewest hops (1 per link), lowest fixed latency (d + 1/μ), and adaptive (d + 1/(μ - λ̂) with a smoothed measured load, refreshed every 0.5 s). Adaptive routing can make traffic slosh between paths; smoothing damps it but does not remove it.

Failures. Cutting a cable destroys the packets on it, and routers only learn after 0.4 s, so packets keep being sent into the hole meanwhile.

What is simplified. Real traffic is bursty, not Poisson, and mostly TCP-controlled; none of that is modelled. All packets are equal size, queues are FIFO, links symmetric. Time and rates are scaled so you can watch single packets; real links move millions per second. Capacities, delays and rates are illustrative, not measurements of any real network.

Checks on this page. (1) M/M/1 delay: the event engine and a separate Lindley-recursion program vs 1/(μ-λ). (2) M/M/1/K blocking vs the closed form. (3) Dijkstra vs Bellman-Ford on random costs and cut links. (4) Conservation: generated = delivered + dropped + still inside.