Note:
Regarding T. Goff and D. S. Phatak, "Unified transport layer support
for data striping and host mobility," IEEE Journal on Selected
Areas in Communications, vol. 22, no. 4, pp. 737-746, May 2004.
The analysis in section C., Comparison of Network and
Transport Layer Striping, assumes small path loss probabilities.
In particular, (3) is an approximation to the exact loss probability
of the overall aggregated path:

L_{ns}

=

1 -

n Õ i = 1

(1 - l_{i})

=

n å i = 1

l_{i} -

n å i = 1

n å j = i + 1

l_{i} ·l_{j} +

n å i = 1

n å j = i + 1

n å k = j + 1

l_{i} ·l_{j} ·l_{k} - ¼+ ¼ .

For small path loss probabilities, the product of two or more l_{i}
terms quickly becomes insignificant and can be approximated by the
first summation from the expression above as simply

L_{ns} »

n å i = 1

l_{i} .

An alternate approach to finding a lower bound on the aggregate loss
probability is to consider the expected number of packets successfully
sent before a loss occurs on each path. The expected number of
successfully sent packets is 1 / l_{i} for packet loss probability
l_{i}. This limits the overall expected number of packets sent before
a loss is experienced to at most å_{i = 1}^{n} 1 / l_{i}. The
aggregate average loss probability can then be expressed as

L¢_{ns} =

1

n å i = 1

1 / l_{i}

£ L_{ns} .

The end result remains the same in this case since