free to find completely new LSPs.2)The lower
packet loss probabilities enable faster downloads
which, in turn, cause a lower demand for band-
width from domestic users, hence more band-
width is made available to business users. This
is clearly demonstrated by the fact that the LSP
bandwidth goes down and the LSP load goes up
for domestic users while the situation is reversed
for business users.
6 Mixed Objective Functions
The results above may be generalised to multi-
service networks by applying class dependent
objective functions. As a concrete example, con-
sider a UMTS core network. The data carried
by such a network can be classified into control
traffic and user traffic. Control traffic relates to
the signalling required to establish and release
connections, to handle mobility etc., and user
traffic relates to the four basic service classes
in UMTS, viz. conversational, streaming, inter-
active and background.
Our method to design LSPs can thus be applied
to UMTS core networks built on MPLS by map-
ping the five service classes to class-dependent
objective functions as follows:
Signallingand other management information
may be carried over a UDP-like protocol
which can be represented by an M/G/1/K
model. The revenue function in this case is
e.g. a function of the number of signals trans-
ported within certain time limits.
Conversationalmainly comprises services like
voice for which the Erlang-B based revenue
function of Section 4 may be appropriate.
Note that this does not imply circuit switch-
ing, but only that there is a CAC mechanism
in place. It is emphasised that the objective
function (2) may be non-linear or linear
depending on the specific aggregate consid-
ered. Typically, voice will be AMR coded
between MSs and TRCs, while standard PCM
coding will be used between TRCs and gate-
ways to external networks. The variable bit
rate of AMR may be modelled by a non-linear
capacity function, whereas the peak rate of
PCM implies a linear capacity function.
Streamingis intended for playback of audio and
video information. Typically the information
will be coded at variable bit rate but the trans-
mission can be carried out at a fixed rate, in
particular if the content is known and analysed
in advance. Again the Erlang-B based revenue
function may be useful, and again this does
not imply circuit switching, but only that there
is a CAC mechanism in place. Moreover, if
bandwidth requirements differ between users
and/or contents, extensions to the multi-
dimensional version of Erlang-B may be used,
e.g. [10, TD9713] and [24].Interactivemay typically carry transaction data
of type request-response for which some real
time constraints apply. This class may there-
fore be modelled by a TCP fixed point
approach like the one in Section 5.1 with
small files and a high tendency for users to
be discouraged by slow response times.Backgroundwill be used by non urgent data
such as email, etc. Again a TCP fixed point
approach may be suitable, although back-
ground file sizes are expected to be longer and
users will be much less sensitive to response
times.Service class All Dom. Bus. All Dom. Bus.
Buffer size 5 5 10 5Packet loss (%) 1.9 5.4 0.1 0.9 2.5 0.1
Request “loss” (%) 3.6 1.1 2.0 0.6Effective rate (kbps) 46 2026 47 2036
Download time (s) 5.2 0.2 5.1 0.2LSPs 168 88 80 172 94 78
LSP multiplicity 1.6 1.4 1.7 1.4
LSP bandwidth 108 311 86 376LSP load (%) 37 24 53 24Table 4 Packet loss, session
loss, number of paths, path
multiplicity and path band-
widthRoute length Bandwidths LSPsCi C'i Li L'i0 28,678 0 120 0
1 2,382 19,462 23 40
2 2,808 6,320 17 53
3 549 3,239 8 36
4 0 2,742 0 21
5 0 1,223 0 14
6 0 1,431 0 4Total 34,417 34,417 168 168Table 3 Distribution of the
allocated bandwidth Cion
LSPs of normalised length i;
distribution of the allocated
bandwidth C'ion LSPs of un-
normalised length i; distribu-
tion of the normalised Liand
un-normalised L'iLSP lengths2)An alternative to complete redesigns is partial redesigns where some LSPs, for example those of
business users, are “locked”.