of different priority packets in the Tx queues waiting for being served, the design of piggy-
backing rule can be viewed as an allocation problem. As discussed above, by properly par-
titioning the range of received SNR, the fragmentation threshold of the free-space-effective
state k satisfies FTI, = ye x FT,2, where ye is a positive integer. For other non-free-space-
effective states, let ye = 1. Suppose we have a total of K different channel states, and
N different priority levels. Let c y; denote the number of b-MSDUs of j priority level to
be packed when the channel is in state k. We should point out that in the non-free-space-
effective state, only the highest priority packet is served when there is plenty of traffic in
the waiting queue, thus so = 1, and c0>; = 0 for 0 < kc < m and 1 < j I N 1. If
we neglect the MAC layer overhead, then the design problem can be reduced to choose amy
such that
When the operation of packing packets with different priority levels associates with certain
objective of fairness or "profit", the design problem is a kind of knapsack problem which is
considered to be NP-complete [72]. On the one hand, the resource (free space here) should
ne fully utilized; On the other hand, the system attempts to maintain the best performance in
terns of fairness among different classes of traffic. In fact, an upper bound for the expected
value of throughput of priority level j at one node is can be written by Ei 18, c a O < j <
N 1, where I., is the probability that the channel is in state k, and RI, is the transmission
rate in state k.
Some measures may improve CP. To avoid fragmentation of the b-MSDUs in a free-
space-effective state, in our piggyback scheme we should maintain the multiplicative re-
lationship between the fragmentation threshold (FT) in the free-space-effective state and
the FT,7. Actually, we can relax this requirement in the high traffic load case by allow-
ing fragmentation of the low-priority services at will to fit into the free space the channel
provides. Because at very heavy traffic load, the piggybacking rule favoring high-priority