Four heterogeneous multi-server stations (VR Pod, Holographic Theater, AI Arcade, Smart Lounge — each with its own slot count Ki and service rate μi) model the "entertainment types" of a space-station facility as a real queueing network. Visitors arrive as a Poisson process at rate λ; a Bernoulli(λ·dt) draw each fixed sub-step decides whether an arrival occurs, exactly as in Monte-Carlo discrete-event simulation of an M/M/c/K queue.
Each occupied server slot counts down an exponentially-distributed service time (drawn as −ln(U)/μi, U~Uniform(0,1) — the standard inverse-CDF sampling for an exponential arrival/service process). When a station's queue is at capacity Kcap, an arrival routed there balks (leaves unserved) instead of joining.
- Join-Shortest-Queue (JSQ) — the arrival is routed to the station with the fewest visitors currently in service + waiting, a well-known load-balancing policy that provably reduces mean wait time versus uniform-random routing for heterogeneous parallel queues.
- Random — the arrival is routed to a uniformly-random station regardless of load, the naive baseline JSQ is compared against.
- Utilization ρ is the mean fraction of occupied server-slots across all stations; ρ approaching 1 means the hub is near saturation and both queue length and wait time grow sharply (a real queueing-theory instability, not a scripted effect).