Calculate System Throughput: QPS, TPS, Concurrency & Response Time

A system's throughput (capacity) is closely linked to the CPU consumption per request, external interfaces, and I/O; higher CPU usage per request reduces overall throughput.

Key throughput parameters are QPS (TPS), concurrency, and average response time.

These relate as QPS = concurrency / average_response_time or concurrency = QPS * average_response_time.

Example: In a sign‑in system with 1,000 employees logging in during a 30‑minute window, each login lasts 5 minutes. QPS = 1000 / (30*60) ≈ 0.56 req/s, average response time = 5*60 = 300 s, so concurrency = 0.56 * 300 ≈ 166.7 users.

Throughput is limited by the lower of QPS and concurrency; when either reaches its maximum, additional load reduces performance due to overload, context switching, and memory pressure.

Response time is determined by a critical path consisting of CPU processing, I/O, and external system latency, similar to a project's critical path.

When evaluating system throughput, consider CPU, I/O, and external response factors, as well as daily page views (PV). Observing logs often shows consistent traffic patterns, allowing PV to be inferred from peak QPS.

Typical relationships:

Taobao: max_TPS : PV ≈ 1 : 11*3600 B2B Chinese sites: max_TPS : PV ≈ 1 : 8 hours Thus, if a test yields TPS = 100, daily throughput ≈ 100 * 11 * 3600 = 3.96 million requests.

The general formula linking TPS, concurrent users, response time, and think time is TPS = concurrent_users / (response_time + think_time).

Software Performance Testing Basic Concepts and Formulas

Performance concerns differ by role:

User : perceived response time from action to result.

Administrator : response time, resource utilization, scalability, maximum concurrent users, bottlenecks, 24/7 availability.

Developer : architecture, database design, code efficiency, memory usage, thread synchronization, resource contention.

Performance Test Engineer : all of the above.

Key terminology:

Response time = network transmission (N1+N2+N3+N4) + application server processing (A1+A3) + database processing (A2).

Concurrent users = RPS + concurrent connections + think time.

Average concurrency C = nL / T where n = daily active users, L = average session length, T = observation period.

Peak concurrency ≈ C + 3·√C (Poisson approximation).

Throughput F = VU * R / T where VU = virtual users, R = requests per user, T = test duration.

Performance counters (CPU, memory, process time) are essential for monitoring and bottleneck analysis.

Think time (TS) models user pause between requests: TS = T / R. It can be derived through steps: compute concurrent users, measure average throughput, calculate requests per user, then obtain think time.