1. Leaky Bucket Algorithm

2. 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)

3. GCRA(I,L) Virtual Scheduling Continuous-state Algorithm
Arrival of a cell k at time ta(k)
X’=X-(ta(k)-LCT)
Yes
TAT<ta(k) ?
Yes
X’<0? No
TAT=ta(k) No
X’=0
Non
Conforming cell
Yes
TAT>ta(k)
+L?
Non
Conforming cell
Yes
X’>L? No No
TAT=TAT+I
Conforming cell
X=X’+I
LCT=ta(k)
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

4. Virtual scheduling algorithm
Conforming cell
Non-conforming cell
At the time of arrival of the first cell of the connection, TAT = ta(k)
(a)
ta(k)
Time
TAT(k-1)
TAT(k)
TAT(k)
TAT(k+1)
(b)
ta(k)
Time
TAT(k-1)
TAT(k)
TAT(k+1)
ta(k)
Time
TAT(k-2)
TAT(k-1)
TAT(k)

5. Continuous-state leaky bucket algorithm
Conforming cell
Non-conforming cell
At the time of arrival of the first cell of the connection, X=0 and LCT=ta(k)
(a)
(b)
I+L
I+L
I+L
I+L X X
ta(k)-LCT L L L L
ta(k)-LCT X’
X’(=0)
I+L
I+L X I
ta(k)-LCT X’ L L L

6. These two algorithms are equivalent ( TAT=X+LCT )
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 L+I
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

7. 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

8. 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