QueueScope | Service Operations Intelligence

Service capacity landscape

Analytical M/M/c result across feasible staffing levels

Erlang C

Service levelTarget SLA

Operational diagnosis

Steady-state assumptions and constraints

Scenario at a glance

Assumed inputs

Decision guidance

Model-generated

Queue performance by staffing level

Infinite waiting room, Poisson arrivals, exponential service

Agents	Utilization	Avg wait	Wait probability	SLA	Status

Reading the queue

When arrivals approach available service capacity, the predicted waiting time grows nonlinearly. Adding one agent may have a much larger impact when utilization is high.

Unstable systems (arrival rate ≥ total service capacity) have no finite steady-state queue length or mean waiting time under this model.

Labor cost vs waiting cost

Illustrative expected cost per operating shift

Total costSLA-feasible

Planner logic

Waiting cost is a chosen penalty, not a measured cash expense. Recommendations depend on target service level and these economic assumptions.

Discrete-event simulation

Seeded exponential arrivals and service durations

Reproducible

Random seed

Replications

Agents for simulation

Awaiting simulation

Replicate distribution

Empirical

Histogram of the simulated fraction served within the SLA threshold. The queue can clear after the arrival window ends.

Scenario parameters

Change an assumption to recalculate every analytical module

How to interpret changes

The analytical model updates immediately when you apply a new parameter set. Increase arrival intensity to stress the system or add servers to assess the capacity required for your target.

Arrival intensityλ customers/hour

Per-agent service capacityμ customers/hour

Staffingc parallel agents

Queue stabilityλ < c × μ

These inputs are assumptions for the model. They are not live operational measurements and do not establish causal effects.

Import a scenario catalog

CSV with up to 25 service systems, processed entirely in your browser

Download reproducible artifacts

Methodology and limitations

1. Erlang C (M/M/c)

Poisson arrivals, independent exponential service times, c identical parallel agents, first-come-first-served discipline, infinite buffer, no abandonment and steady-state operation. Waiting probability and SLA are exact within those assumptions.

2. Economics

Expected staffing cost = agents × hourly wage × horizon. Expected waiting penalty = arrival rate × horizon × mean queue wait (hours) × penalty per waiting hour. This is a hypothetical objective, not an accounting forecast.

3. Simulation

A discrete-event simulator generates arrivals and service needs from seeded exponential distributions. Repeat runs summarize finite-window variability and will not exactly match steady-state theory at short horizons.

4. Data protection

No external requests, tracking, data persistence, cloud uploads, or third-party packages. The current analysis lives in browser memory. Export before refreshing.

5. Responsible use

The application does not model scheduled arrivals, priority cases, batch arrivals, varied agent skills, vacations, abandonment, real waiting-room constraints or non-exponential distributions. Real staffing decisions require measured arrivals, validation and local legal requirements.

Make waiting measurable.