Queue and throughput calculator
Queues do not degrade gracefully. Wait time climbs hyperbolically as utilisation approaches one, which is why systems fall over so suddenly.
per second
ms
Utilisation
0.8000
- Average response time
- 50.000 ms
- Average queue length
- 3.200
- Average requests in the system
- 4.000
- Spare capacity
- 20.00 per second
- System is stable
- 1
Show the working
- Requests arriving = 80
- Service time per request = 10
- Parallel workers = 1
- service_rate = 1000 / 10 * 1 = 100
- Utilisation = 80 / 100 = 0.8
- System is stable = 0.8 < 1 ? 1 : 0 = 1
- wait = 0.8 < 1 ? 10/1000 * 0.8 / (1 - 0.8) : 0 = 0.04
- response = 0.8 < 1 ? 10/1000 / (1 - 0.8) : 0 = 0.05
- Average requests in the system = 80 * 0.05 = 4
- Average queue length = 80 * 0.04 = 3.2
- Spare capacity = 100 - 80 = 20
- Average response time = 0.05 * 1000 = 50
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- Little's law: L = lambda W
- M/M/1: response time = service time / (1 - utilisation)
- utilisation = arrival rate / service rate
M/M/1 assumes Poisson arrivals and exponential service times. Real traffic is burstier, so treat these as optimistic.
At 90% utilisation the average response is ten times the service time. At 95% it is twenty.