A hospital floor is modelled as a queueing network (an M/M/c-style system): patients arrive stochastically, wait for a free staff/bed pair (triage), occupy a bed while treated, then discharge. Utilisation and staffing determine average wait via Little's Law.
L = lambda * W (Little's Law)
utilization rho = lambda / (c * mu)
W_queue ~ rho / (c * mu * (1 - rho))
- Staffing level — number of clinicians (servers, c) simultaneously treating patients; more staff shortens the queue.
- Bed count — physical capacity; patients cannot begin treatment without a free bed even if staff are available.
- Arrival rate — new patients entering triage per minute (lambda); higher rates raise congestion.
- Treatment speed — service rate multiplier (mu); faster treatment frees beds/staff sooner.
When arrival rate approaches staffed service capacity (rho -> 1), queueing theory predicts wait times grow non-linearly — the same energy/flow-conservation logic used to size fluid networks applies to patient throughput.