▶
Configure your inputs and click Run Simulation
Up to 8,760 simulated hours of queuing in the blink of an eye. Each run adds a scenario for comparison.
Drag one slider. See how many customers walk away -- and exactly what it takes to fix it. No math degree required.
Even when your average arrival rate is manageable, random clustering means bursts of demand hit without warning. Five calm minutes, then eight people walk in at once. The math of randomness guarantees it.
At 70% utilization, things feel fine. At 85%, small bursts create queues that take minutes to clear. At 95%, the system never catches up. The relationship between utilization and wait time is exponential, not linear.
Formulas give you steady-state averages. Simulation gives you the full picture: worst-case waits, queue buildup during rush hours, and exactly how many servers keep your line short without overspending on idle capacity.
A highway at 99% capacity jams. At 80%, it flows fine.
Your coffee shop has 2 baristas, each able to serve 20 customers per hour. Capacity: 40/hr. So 38 customers/hour should be easy, right? That is 95% utilization.
But customers do not arrive evenly spaced. Random clustering means both baristas are occasionally busy at the same time, creating a queue. At 95% utilization, that queue rarely has time to empty before the next burst. The wait time curve goes vertical.
Drop to 80% utilization -- 32 customers/hour -- and the queue clears between bursts. The system breathes. That gap between 80% and 95% is where operational decisions live.
The name looks intimidating. It is just three facts about how your system works.
The first M stands for "Markovian." That just means memoryless -- customers show up randomly, with no pattern connecting one arrival to the next. A Poisson process. It is how most real-world arrivals actually work.
The second M means service times are also random -- exponentially distributed. Some customers are fast, some slow. This is why "we serve 20 per hour, and 20 arrive per hour" does not mean zero wait. Variability creates queues even when averages match.
The lowercase c is your server count -- baristas, agents, checkout lanes. Adding servers has diminishing returns: going from 1 to 2 might cut wait by 80%. Going from 10 to 11? Maybe 3%. The curve flattens fast.
One equation that holds for any stable queuing system, regardless of arrival distribution, service distribution, or number of servers.
If you know any two, you can derive the third. It works for coffee shops, emergency rooms, and packet networks alike.
Erlang-C gets you a number. Simulation gets you the truth.
Configure your system, hit Run, and get hour-by-hour results backed by a full Monte Carlo simulation.
▶
Configure your inputs and click Run Simulation
Up to 8,760 simulated hours of queuing in the blink of an eye. Each run adds a scenario for comparison.
How many agents do you need per shift to keep hold times under 2 minutes?
Model ticket arrivals and technician capacity to predict resolution backlogs.
Find the right number of cashiers for peak hours without overstaffing off-peak.
Balance customer wait times against staffing costs across branch hours.
DMV, permit offices, passport agencies -- optimize counter staffing for citizen satisfaction.
Restaurants, cafeterias, drive-throughs -- model customer flow through ordering and pickup.