Telestroke Network: Consultation Queueing & Latency Simulator

Network Setup

Spoke hospitals online 5

Patient arrival rate λ 6.0 / hr

Mean consult duration 10 min

Spoke ↔ hub link

Live Network State

Hub utilization ρ

Patients queued

Sim time elapsed

0.0 h

Patients treated

Avg time-to-treatment (simulated) vs 60 min door-to-needle target

-- min

Legend

In transit (network)

Queued at hub

In consultation

Packet retransmit (loss)

How it works

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:  W_q = 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.

Spokes: 5 activeLink: Rural cellularRTT: --

Hub (neurologist) Spoke hospital

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Telemedicine Simulation: Telestroke Hub-and-Spoke Network