Each spoke hospital generates stroke-consult requests as a Poisson arrival process at rate λ (patients/hour, network-wide). A single on-call neurologist at the hub is the server, working at rate μ = 60/D patients per hour, where D is the mean consult duration in minutes (also drawn from an exponential distribution, so this is a classic M/M/1 queue):
Utilization: ρ = λ / μ
Mean queue wait: Wq = ρ / (μ - λ) (hours, requires λ < μ)
Little's Law: L = λ × W (mean patients in system = arrival rate × mean time in system)
Every request also crosses the spoke↔hub link twice (request + response). Each one-way hop has a fixed base latency and a packet-loss probability; a lost packet is retransmitted, adding another full latency hop:
One-way delay ≈ latency / (1 - lossProbability) (expected cost of retries)
Round trip = 2 × one-way delay
The stat panel's "time-to-treatment" sums a patient's real network transit time, real queue wait, and real consult duration, then averages it over every patient the simulation has actually completed -- compare it against the American Heart Association's 60-minute door-to-needle target for IV thrombolysis. When λ approaches or exceeds μ (ρ → 1), the queue grows without bound and the target is missed no matter how good the network link is -- the hub's staffing, not the network, becomes the bottleneck. A satellite link with high packet loss shows the opposite failure mode: a well-staffed hub still misses the window because retransmits eat the time budget before the neurologist ever sees the case.