The long-term average number of customers in a stable system L is equal to the long-term average effective arrival rate, λ, multiplied by the average time a customer spends in the system, W; or expressed algebraically:
Stable system :
- Steady state
- Number of arrivals equals number of departures
- System is not in beyond saturation state
- As arrivals equal departures, this is also equivalent to throughput
- This includes the time spent in wait as well as service so it is response time
- This is work in progress
- transaction in queue as well as being serviced
- requests in queue and in progress in the system
- concurrent users in the system
Requests in queue + in progress= Mean Response Time * Throughput
In a test configured for 10000 requests/ transactions per seconds if mean response time is 10 milliseconds than at a time pending + in progress requests are (10000 * 0.01=) 100.
While trying different configurations of server component the configurations in which response time is slow for the same throughput the memory consumption is higher. This is expected from little's law. At the same throughput if response time is larger than the requests in queue and in progress will be more hence higher memory consumption.
Mean Response Time = Requests in queue + in progress/Throughput
In systems where in queue/progress requests are known and throughput is known the mean response time can be calculated.
Little's law is also used for validation of the performance test, if all the three indicators are tracked in the test than the relationship must hold
Other Posts
- Software bottlenecks:- Understanding performance of software systems with examples from road traffic
- Analytical thinking in performance analysis
- Time scale of system latencies
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