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with highly critical parts of UMMs, and much of the UMM information can help
us work with formal verification models, particularly those based on symbolic
executions [31,57] .
The ability to identify reliability bottlenecks can also help the selective applica-
tion of corrective and preventive actions, system analyses, damage containment,
etc. [48] .
To implement the above strategy, quantitative web usage information needs to be
collected. Fortunately, the availability of existing web logs offers us the opportunity
to collect usage information for usage model construction and for statistical web
testing. The following reports can be easily produced from analyzing the web access
logs kept at the web servers:
Top access report (TAR) lists frequently accessed (individual) services or web
pages together with their access counts.
Call pair report (CPR) lists selected important call pairs (transition from one
individual service to another) and the associated frequency.
TAR is important because many of the individual services can be viewed as stand-
alone ones in web-based applications, and a complete session can often be broken
down into these individual pieces. This report, when normalized by the total access
count or session count, resembles the flat OP [33] . Each service unit in a TAR may
correspond to multiple pages grouped together instead of a single page, such as in
Fig. 2 . Such results provide useful information to give us an overall picture of the
usage frequencies for individual web service units, but not navigation patterns and
associated occurrence frequencies.
CPR connects individual services and provides the basic information for us to
extract state transition probabilities for our UMMs. For a web site with N pages or
units, the potential number of entries in its global CPR is N 2 , making it a huge table.
Therefore, we generally group individual pages into larger units, similar to what we
did above for TAR. Alternatively, we can restrict CPR to strong connections only,
which is feasible because the N × N table is typically sparsely populated with only a
few entries with high cross-reference frequency, as we will see empirically in Fig. 9
at the end of this section.
We can traverse through CPR for strong connections among TAR entries, which
may also include additional connected individual services not represented in TAR
because of their lower access frequencies or because they represent lower-level web
units. A UMM can be constructed for each of these connected groups. In this way,
we can construct our UMMs from TAR and CPR.
Notice that multiple OPs, particularly multiple UMMs in addition to TAR, our top-
level OP, usually result for a single set of web-based applications using the above
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