Pharos Production / Method & privacy
Queue model: formulas and input limits
Version 1 · Updated
A constant-rate estimate
The model treats work items as comparable units and uses constant arrival and successful completion rates over the selected window. The formula measures the stock of waiting work. It does not simulate a queue service.
- Backlog
- Whole number from 0 to 1,000,000,000,000 items.
- Rates
- Numbers from 0 to 1,000,000,000 items per second.
- Recovery window
- 0.01 to 525,600 minutes.
- Nonpositive net rate
- An existing backlog has no finite drain time. The JSON value is null.
Boundaries and rounding
An empty queue has zero initial drain time. If arrivals exceed completions, the result explicitly reports that the backlog will grow. Remaining backlog never falls below zero. The required completion rate rounds upward to two decimals. Other display values round to the nearest two decimals. The download retains the calculation values.
The model excludes burstiness, per-item processing cost, retry amplification, ordering, oldest-item age, tenant fairness and dependency saturation. Sustained successful completion rates should already reflect failed attempts and retry overhead. Test assumptions in the actual system before making a capacity decision.
What the download contains
The JSON includes your four inputs, the net rate, drain time in seconds, required completion rate, remaining backlog and three checkpoints. It also carries the model version and draft status. A null drain time means the current positive backlog does not drain at those steady rates.
Form entries stay in this page
The tools do not submit form entries to a server, save them in browser storage or load analytics. Downloading creates a file on your device. Changing pages or reloading clears the entries. Your downloaded file may contain whatever text you entered. Handle it accordingly.
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Publisher and corrections
This is an owned reference resource published by Pharos Production. It provides educational planning aids. Fictional examples are labeled. No client results or live system observations are presented. Send corrections through the company website, identifying the tool version and the input that produced the issue.