Leaky Bucket Algorithm

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Leaky Bucket Algorithm
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Generic Cell Rate Algorithm (GCRA)

• Used to define conformance with respect to the
  traffic contract
• Define the relationship b.w. PCR and the CDVT,
  and the relationship b.w. SCR and the BT
• Be a virtual scheduling algorithm or a
  continuous-state leaky bucket algorithm
• Be defined with two parameters the Increment (I)
  and the Limit (L) ? GCRA(I,L)

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• GCRA(I,L)

Arrival of a cell k at time ta(k)
XX-(ta(k)-LCT)
Yes
TATltta(k) ?
Yes
Xlt0?
No
TATta(k)
No
X0
Yes
Non Conforming cell
TATgtta(k) L?
Yes
Non Conforming cell
XgtL?
No
No
XXI LCTta(k) Conforming cell
TATTATI Conforming cell
Virtual Scheduling Algorithm
Continuous-state Leaky Bucket Algorithm
X Value of the Leaky Bucket counter X
Auxiliary variable LCT Last Compliance Time
TAT Theoretical Arrival Time ta(k) Time of
arrival of a cell
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• Virtual scheduling algorithm
• Conforming cell
• Non-conforming cell
• At the time of arrival of the first cell of the
  connection, TAT ta(k)

ta(k)
(a)
Time
TAT(k)
TAT(k)
TAT(k1)
TAT(k-1)
ta(k)
(b)
Time
TAT(k-1)
TAT(k)
TAT(k1)
ta(k)
Time
TAT(k-2)
TAT(k-1)
TAT(k)
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• Continuous-state leaky bucket algorithm
• Conforming cell
• Non-conforming cell

(a)
(b)
IL
IL
IL
IL
X
X
ta(k)-LCT
L
L
L
L
X
ta(k)-LCT
X(0)
IL
IL
X
ta(k)-LCT
I
X
L
L
L
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• These two algorithms are equivalent ( TATXLCT )
• For any sequence of cell arrival times
  , they determine the same cells to be
  conforming and thus the same cells to be
  non-conforming
• The capacity of the bucket is LI
• As L increases, the minimum inter-arrival time
  between conforming cells decreases
• Given GCRA(T,?) and the transmission time of a
  cell required,?, the maximum number N of
  conforming back-to-back cells, i.e., at the full
  link rate, equals

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• If a cell stream conforms to the SCR (1/Ts), the
  BT (?s), and the PCR (1/T), then it offers
  traffic conforming to GCRA(Ts,?s) and GCRA(T,0)
• ? The maximum burst size (MBS) is
• Over any closed time interval of length t, the
  number of cells, N(t), can be emitted with
  spacing no less than T and still be in
  conformance with GCRA(Ts,?s) is bounded by

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• If the minimum spacing between bursts and the MBS
  (with inter-cell spacing T) are TI and B,
  respectively, and the cell stream is conforming
  with GCRA(Ts,?s), then Ts and ?s are chosen at
  least large enough to satisfy

Time