Each mobile client submits a job to one shared cloud QPU. Arrivals follow a Poisson process: in a short interval dt, a new job appears with probability
P(arrival in dt) = 1 - e^(-λ·dt)
where λ is the arrival-rate slider. Every job requests a number of shots (repeated circuit executions needed for a usable measurement distribution); the backend serves one job at a time with a service time
t_service = t_base + shots / shot_rate
The three scheduling policies choose which waiting job the QPU serves next:
- FIFO — strict arrival order, exactly like a real batch queue with no priority classes.
- Shortest-job-first — the fewest-shots job runs next, minimizing average wait (a classic SJF queueing result) at the cost of starving large jobs.
- Paid tier priority — jobs are tagged Free / Plus / Pro on submission (as real cloud quantum services meter mobile-app access); higher tier always jumps the free-tier backlog, ties broken by arrival time.
While a job sits in the queue, the backend's own calibration drifts. The model applies exponential fidelity decay over the wait:
F(wait) = e^(-wait / T)
T is the coherence-budget slider. This 2D view renders the same discrete-event queueing model as three linked panels instead of a 3D scene: a top-down queue lane showing job order and server occupancy, a scrolling strip chart of queue length and average wait over time, and a live fidelity-decay scatter plot comparing every completed job's actual (wait, fidelity) point against the theoretical F(wait) curve — a direct, falsifiable check of the model's own math, updated in real time. The two "Little's law" readouts cross-check each other: the time-averaged number of jobs in the system (L, counting a job the whole time it is queued or being served) should track λ·W_sys (throughput × mean time-in-system, i.e. queue wait plus service time), a conservation law queueing theory guarantees for any stable queue regardless of scheduling policy.