## Chapter 16 — The normal client is fully served until the tight bucket ### Lesson map Lesson 16. Map, example, EX062. ```mermaid flowchart TD U["90 normal times and 3000 flood times, both sorted"] --> B["Bucket starts full"] B --> R["Refill, then serve if a token remains"] R --> L["Three printed settings"] ``` The third line is the first line that drops the normal client. ### Logical drawing ```text limit=5/s burst=20 normal_served= 90/90 flood_served= 319/3000 limit=2/s burst=10 normal_served= 90/90 flood_served= 129/3000 limit=1/s burst= 5 normal_served= 62/90 flood_served= 64/3000 ``` ### Learning outcomes After this chapter, you should be able to: 1. Read both 90/90 lines and the 62/90 line. 2. Read the flood counts 319, 129 and 64. 3. Treat the spaces in the third line as part of the format. ### 16.1 One generator, two sorted lists, three parameter pairs. `random.Random(4)` draws 90 times from the uniform range `[0, 60)` and 3000 times from the same range. Each list is sorted, so the simulator sees increasing timestamps. The bucket starts full, with `tokens = burst` and `last = 0`. At each request it refills with `min(burst, tokens + (t - last) * rate)` and then serves the request if at least one token remains, decrementing by 1. The pairs are `(5, 20)`, `(2, 10)` and `(1, 5)`. At 5 per second with burst 20, all 90 normal requests are served and 319 of 3000 flood requests are served. At 2 per second with burst 10, the normal client is still 90/90 and the flood falls to 129. The tight pair is the first to miss ordinary timestamps: 28 of the 90 go unserved, leaving 62, while flood survivors number 64. That pair is 1 per second with burst 5. The format widths are part of the line. Burst uses width 2, so the third burst prints as a space and then 5. Normal uses width 3. Because the flood field reserves four columns, the two-digit value 64 is indented by two spaces. A transcription that closes those gaps has not copied the print. | Setting | Normal | Flood | |---|---|---| | 5/s, burst 20 | 90/90 | 319/3000 | | 2/s, burst 10 | 90/90 | 129/3000 | | 1/s, burst 5 | 62/90 | 64/3000 | ### 16.2 Worked example | Choice | What the print supports | |---|---| | Prefer 2/s burst 10 when the goal is to keep every normal request in this run | 90/90 remains, and the flood is 129 rather than 319 | | Prefer 1/s because the flood is smallest | The normal client loses 28 of 90 requests | | Invent a 3/s row | No such line was printed | > **Synthetic case.** The two clients are draws on a 60-second line. They are not Tallis staff. ### Errors and limits The smallest flood count is also the count that stops serving the ordinary series. Both columns decide the reading. ### Apply - **EX062 — Three buckets.** Which settings serve all 90 normal requests, what does the tight setting do, and which spaces belong in the third line? *Rubric:* 3 = 90/90 then 90/90 then 62/90; floods 319, 129 and 64; the third line pads burst and the flood count;; 2 = the three pairs of counts;; 1 = one setting;; 0 = adds a row. ### Continue studying — lesson 16 (chapter 16 of 20) [← Chapter 15](#ch-15) · [Course chapter index](../SUBJECTS.md) · [Chapter 17 →](#ch-17) Continue to the next authored lesson. ## Worked answers **EX062.** At 5/s burst 20 and at 2/s burst 10 the normal client is 90/90, with floods 319 and 129 of 3000. At 1/s burst 5 the normal client falls to 62/90 and the flood is 64/3000. The third line pads the burst to width 2 and the flood count to width 4. No further setting is printed.