Editing Exponential backoff (section)

====Observation====
Binary Exponential Backoff (BEB) used in Ethernet several years later is a special case of Heuristic RCP with <math>K(m) = 2^m</math>.

BEB is very easy to implement. It is however not optimal for many applications because BEB uses 2 as the only multiplier which provides no flexibility for optimization. In particular, for a system with a large number of users, BEB increases {{var|K}}({{var|m}}) too slowly.  On the other hand, for a system with a small number of users, a fairly small {{var|K}} is sufficient for the system to be stable, and backoff would not be necessary.
 
To illustrate an example of a multiplicative RCP that uses several multipliers, see the bottom row in Table 6.3 on page 214 in Chapter 6 of Lam’s dissertation, or bottom row in Table III on page 902 in the Lam-Kleinrock paper. In this example:
# A new packet is transmitted immediately, {{var|m}}=0, {{var|K}}(0)=1
# For a packet with 1 previous collision, {{var|K}}(1) = {{var|K}}(0){{times}}10 = 10     (The multiplier jumps up directly to {{var|K}}{{sup|*}} = 10 which was found to be the optimum {{var|K}} value at steady state for this particular system (slotted ALOHA for a satellite channel).
# For a packet with 2 previous collisions, {{var|K}}(2) = {{var|K}}(1){{times}}10 = 100   (one more collision, {{var|K}} jumps up 10 times).
# {{var|K}}(3) = {{var|K}}(2) × 2 = 200      
# {{var|K}}({{var|m}})={{var|K}}({{var|m}}&minus;1) for {{var|m}}≥4
For this example, {{var|K}}=200 is sufficient for a stable slotted ALOHA system with {{var|N}} equal to about 400, which follows from result 3 above Corollary. There is no need to increase {{var|K}} any further.