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rs r Pr s r rs r

  1. ✺✵ ②❡❛rs ♦❢ ▲✐♥❡❛r Pr♦❜✐♥❣ ❍❛s❤✐♥❣ ❆❧❢r❡❞♦ ❱✐♦❧❛ ❯♥✐✈❡rs✐❞❛❞ ❞❡ ❧❛ ❘❡♣ú❜❧✐❝❛✱ ❯r✉❣✉❛② ❆♦❢❆ ✷✵✶✸ ❉❡❞✐❝❛t❡❞ t♦ P❤✐❧✐♣♣❡ ❋❧❛❥♦❧❡t

  2. ❚❤❡ ♣r♦❜❧❡♠✳ ❚❤❡ t❛❜❧❡ ❤❛s ♠ ♣❧❛❝❡s t♦ ❤❛s❤ ✭♣❛r❦✮ ❢r♦♠ ✵ t♦ ♠ � ✶ ✱ ❛♥❞ ♥ ❡❧❡♠❡♥ts ✭❝❛rs✮✳ ❊❛❝❤ ❡❧❡♠❡♥t ✐s ❣✐✈❡♥ ❛ ❤❛s❤ ✈❛❧✉❡ ✭♣r❡❢❡rr❡❞ ♣❛r❦✐♥❣ ❧♦t✮✳ ■❢ ♣❧❛❝❡ ✐s ❡♠♣t②✱ t❤❡♥ t❤❡ ❡❧❡♠❡♥t ✐s st♦r❡❞ t❤❡r❡✳ ❖t❤❡r✇✐s❡✱ ❧♦♦❦s s❡q✉❡♥t✐❛❧❧② ❢♦r ❛♥ ❡♠♣t② ♣❧❛❝❡✳ ■❢ ♥♦ ❡♠♣t② ♣❧❛❝❡ ✉♣ t♦ t❤❡ ❡♥❞ ♦❢ t❤❡ t❛❜❧❡✱ t❤❡ s❡❛r❝❤ ❢♦❧❧♦✇s ❛t ❧♦❝❛t✐♦♥ ✵✳ ❙❡✈❡r❛❧ ❘✳❱✳ t♦ st✉❞②✱ ♠❛✐♥❧② r❡❧❛t❡❞ ✇✐t❤ ❝♦st ♦❢ ✐♥❞✐✈✐❞✉❛❧ s❡❛r❝❤❡s ❛♥❞ t♦t❛❧ ❝♦♥str✉❝t✐♦♥ ❝♦st✳ ❱❡r② ✐♠♣♦rt❛♥t s♣❡❝✐❛❧ ❝❛s❡✿ P❛r❦✐♥❣ Pr♦❜❧❡♠ ✳ ■♥ ♣❛r❦✐♥❣ t❤❡ ❝❛r ✐s ❧♦st ✐❢ ♥♦ ❡♠♣t② ♣❧❛❝❡ ✉♣ t♦ t❤❡ ❡♥❞✳ ▼❛✐♥ ❘✳❱✳ ✐s t❤❡ ♥✉♠❜❡r ♦❢ ❧♦st ❝❛rs✳ ■♠♣♦rt❛♥t ✈❛r✐❛♥t✿ ❡❛❝❤ ❧♦❝❛t✐♦♥ ❝❛♥ ❤♦❧❞ ✉♣ t♦ ❜ ✭♦r ❦ ✮ ❝❛rs✳

  3. A discrete parking problem Limiting distribution results Analysis Further research A discrete parking problem: Example Example: 8 parking lots, 8 cars Parking sequence: 3, 6, 3, 8, 6, 7, 4, 5 1 2 3 4 5 6 7 8 5 / 37

  4. A discrete parking problem Limiting distribution results Analysis Further research A discrete parking problem: Example Example: 8 parking lots, 8 cars Parking sequence: 3, 6, 3, 8, 6, 7, 4, 5 1 2 3 4 5 6 7 8 5 / 37

  5. A discrete parking problem Limiting distribution results Analysis Further research A discrete parking problem: Example Example: 8 parking lots, 8 cars Parking sequence: 3, 6, 3, 8, 6, 7, 4, 5 1 2 3 4 5 6 7 8 5 / 37

  6. A discrete parking problem Limiting distribution results Analysis Further research A discrete parking problem: Example Example: 8 parking lots, 8 cars Parking sequence: 3, 6, 3, 8, 6, 7, 4, 5 1 2 3 4 5 6 7 8 5 / 37

  7. A discrete parking problem Limiting distribution results Analysis Further research A discrete parking problem: Example Example: 8 parking lots, 8 cars Parking sequence: 3, 6, 3, 8, 6, 7, 4, 5 1 2 3 4 5 6 7 8 5 / 37

  8. A discrete parking problem Limiting distribution results Analysis Further research A discrete parking problem: Example Example: 8 parking lots, 8 cars Parking sequence: 3, 6, 3, 8, 6, 7, 4, 5 1 2 3 4 5 6 7 8 5 / 37

  9. A discrete parking problem Limiting distribution results Analysis Further research A discrete parking problem: Example Example: 8 parking lots, 8 cars Parking sequence: 3, 6, 3, 8, 6, 7, 4, 5 1 2 3 4 5 6 7 8 5 / 37

  10. A discrete parking problem Limiting distribution results Analysis Further research A discrete parking problem: Example Example: 8 parking lots, 8 cars Parking sequence: 3, 6, 3, 8, 6, 7, 4, 5 1 2 3 4 5 6 7 8 5 / 37

  11. A discrete parking problem Limiting distribution results Analysis Further research A discrete parking problem: Example Example: 8 parking lots, 8 cars Parking sequence: 3, 6, 3, 8, 6, 7, 4, 5 1 2 3 4 5 6 7 8 5 / 37

  12. A discrete parking problem Limiting distribution results Analysis Further research A discrete parking problem: Example Example: 8 parking lots, 8 cars Parking sequence: 3, 6, 3, 8, 6, 7, 4, 5 1 2 3 4 5 6 7 8 5 / 37

  13. A discrete parking problem Limiting distribution results Analysis Further research A discrete parking problem: Example Example: 8 parking lots, 8 cars Parking sequence: 3, 6, 3, 8, 6, 7, 4, 5 1 2 3 4 5 6 7 8 5 / 37

  14. A discrete parking problem Limiting distribution results Analysis Further research A discrete parking problem: Example Example: 8 parking lots, 8 cars Parking sequence: 3, 6, 3, 8, 6, 7, 4, 5 1 2 3 4 5 6 7 8 5 / 37

  15. A discrete parking problem Limiting distribution results Analysis Further research A discrete parking problem: Example Example: 8 parking lots, 8 cars Parking sequence: 3, 6, 3, 8, 6, 7, 4, 5 1 2 3 4 5 6 7 8 5 / 37

  16. A discrete parking problem Limiting distribution results Analysis Further research A discrete parking problem: Example Example: 8 parking lots, 8 cars Parking sequence: 3, 6, 3, 8, 6, 7, 4, 5 1 2 3 4 5 6 7 8 5 / 37

  17. A discrete parking problem Limiting distribution results Analysis Further research A discrete parking problem: Example Example: 8 parking lots, 8 cars Parking sequence: 3, 6, 3, 8, 6, 7, 4, 5 1 2 3 4 5 6 7 8 5 / 37

  18. A discrete parking problem Limiting distribution results Analysis Further research A discrete parking problem: Example Example: 8 parking lots, 8 cars Parking sequence: 3, 6, 3, 8, 6, 7, 4, 5 1 2 3 4 5 6 7 8 5 / 37

  19. A discrete parking problem Limiting distribution results Analysis Further research A discrete parking problem: Example Example: 8 parking lots, 8 cars Parking sequence: 3, 6, 3, 8, 6, 7, 4, 5 1 2 3 4 5 6 7 8 ⇒ 2 cars are unsuccessful 5 / 37

  20. A discrete parking problem Limiting distribution results Analysis Further research Further research: Bucket parking scheme Bucket parking scheme Blake and Konheim [1976]: Each parking lots can hold up to r cars Related to analysis of bucket hashing algorithms r 32 / 37

  21. A discrete parking problem Limiting distribution results Analysis Further research Further research: Bucket parking scheme Bucket parking scheme Blake and Konheim [1976]: Each parking lots can hold up to r cars Related to analysis of bucket hashing algorithms r 32 / 37

  22. A discrete parking problem Limiting distribution results Analysis Further research Further research: Bucket parking scheme Bucket parking scheme Blake and Konheim [1976]: Each parking lots can hold up to r cars Related to analysis of bucket hashing algorithms r 32 / 37

  23. A discrete parking problem Limiting distribution results Analysis Further research Further research: Bucket parking scheme Bucket parking scheme Blake and Konheim [1976]: Each parking lots can hold up to r cars Related to analysis of bucket hashing algorithms r 32 / 37

  24. A discrete parking problem Limiting distribution results Analysis Further research Further research: Bucket parking scheme Bucket parking scheme Blake and Konheim [1976]: Each parking lots can hold up to r cars Related to analysis of bucket hashing algorithms r 32 / 37

  25. A discrete parking problem Limiting distribution results Analysis Further research Further research: Bucket parking scheme Bucket parking scheme Blake and Konheim [1976]: Each parking lots can hold up to r cars Related to analysis of bucket hashing algorithms r 32 / 37

  26. A discrete parking problem Limiting distribution results Analysis Further research Further research: Bucket parking scheme Bucket parking scheme Blake and Konheim [1976]: Each parking lots can hold up to r cars Related to analysis of bucket hashing algorithms r 32 / 37

  27. A discrete parking problem Limiting distribution results Analysis Further research Further research: Bucket parking scheme Bucket parking scheme Blake and Konheim [1976]: Each parking lots can hold up to r cars Related to analysis of bucket hashing algorithms r 32 / 37

  28. A discrete parking problem Limiting distribution results Analysis Further research Further research: Bucket parking scheme Bucket parking scheme Blake and Konheim [1976]: Each parking lots can hold up to r cars Related to analysis of bucket hashing algorithms r 32 / 37

  29. A discrete parking problem Limiting distribution results Analysis Further research Further research: Bucket parking scheme Bucket parking scheme Blake and Konheim [1976]: Each parking lots can hold up to r cars Related to analysis of bucket hashing algorithms r 32 / 37

  30. ▲✐♥❡❛r Pr♦❜✐♥❣ ❍❛s❤✐♥❣✳

  31. ❚❤❡ ♠❛t❤❡♠❛t✐❝❛❧ ❜❡❛✉t② ♦❢ ▲✐♥❡❛r Pr♦❜✐♥❣✦

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