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Transport aspects 2

Appendix I

Range of stuff ratios for asynchronous mappings of CBR2G5, CBR10G, and CBR40G
clients with 20 ppm bit-rate tolerance into OPUk, and for asynchronous
multiplexing of ODUj into ODUk (k > j)

(This appendix does not form an integral part of this Recommendation.)

Clause 17.2 describes asynchronous and bit-synchronous mappings of CBR2G5, CBR10G, and CBR40G
clients with 20 ppm bit-rate tolerance into ODU1, 2, and 3, respectively. Clause 19 describes asynchronous
mapping (multiplexing) of ODUj into ODUk (k > j). For asynchronous CBR client mappings, any frequency
difference between the client and local OPUk server clocks is accommodated by the +1/0/–1 justification
scheme. For asynchronous multiplexing of ODUj into ODUk (k > j), any frequency difference between the
client ODUj and local OPUk server clocks is accommodated by the +2/+1/0/–1 justification scheme. The
OPUk payload, ODUk, and OTUk bit rates and tolerances are given in clause 7.3. The ODU1, ODU2, and
ODU3 rates are 239/238, 239/237, and 239/236 times 2 488 320 kbit/s, 9 953 280 kbit/s, and 39 813 120
kbit/s, respectively. The ODUk bit-rate tolerances are 20 ppm. This appendix shows that each justification
scheme can accommodate these bit rates and tolerances for the respective mappings, and also derives the
range of justification (stuff) ratio for each mapping.
The +1/0/–1 mapping in clause 17.2 provides for one positive justification opportunity (PJO) and one
negative justification opportunity (NJO) in each ODUk frame. The +2/+1/0/–1 mapping in clause 19 provides
for 2 PJOs and one NJO in each ODUk frame. For the case of ODU multiplexing (i.e., the latter case), the
ODUj being mapped will get only a fraction of the full payload capacity of the ODUk. There can be, in
general, a number of fixed stuff bytes per ODUj or CBR client. Note that in both mapping cases, there is one
stuff opportunity in every ODUk frame. For mapping of a CBR client into ODUk, the CBR client is allowed to
use all the stuff opportunities (because only one CBR client signal is mapped into an ODUk). However, for
mapping ODUj into ODUk (k > j), the ODUj can only use 1/2 (ODU0 into ODU1), 1/4 (ODU1 into ODU2 or
ODU2 into ODU3) or 1/16 (ODU1 into ODU3) of the stuff opportunities. The other stuff opportunities are
needed for the other clients being multiplexed into the ODUk.

Traditionally, the justification ratio (stuff ratio) for purely positive justification schemes is defined as the
long-run average fraction of justification opportunities for which a justification is done (i.e., for a very large
number of frames, the ratio of the number of justifications to the total number of justification
opportunities). In the +1/0/–1 scheme, positive and negative justifications must be distinguished. This is
done by using different algebraic signs for positive and negative justifications. With this convention, the
justification ratio can vary at most (for sufficiently large frequency offsets) from –1 to +1 (in contrast to a
purely positive justification scheme, where the justification ratio can vary at most from 0 to 1). In the case
of ODUk multiplexing, the justification ratio is defined relative to the stuff opportunities available for the
client in question. Then, the justification ratio can vary (for sufficiently large frequency offsets) from –1 to
+2. (If the justification ratio were defined relative to all the stuff opportunities for all the clients, the range
would be –1/2 to +1 for multiplexing ODU0 into ODU1, –1/4 to +1/2 for multiplexing ODU1 into ODU2 and
ODU2 into ODU3, and –1/16 to +1/8 for multiplexing ODU1 into ODU3.)

Let α represent the justification ratio (1  α  1 for CBR client into ODUk mapping; –2  α  1 for ODUj into
ODUk mapping (k > j)), and use the further convention that positive  will correspond to negative
justification and negative  to positive justification (the reason for this convention is explained below).

Define the following notation (the index j refers to the possible ODUj client being mapped, and the index k
refers to the ODUk server layer into which the ODUj or CBR client is mapped):
N = number of fixed stuff bytes in the OPUk payload area associated with the client in question (note
that this is not the total number of fixed stuff bytes if multiple clients are being multiplexed)
S = nominal STM-N or ODUj client rate (bytes/s)
T = nominal ODUk frame period(s)

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