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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) 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

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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) (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)

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**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

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**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

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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

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