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From: lee@tis.com (Theodore Lee)
Newsgroups: comp.dcom.telecom
Subject: Largest Toll-Free Region?
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Date: 27 Dec 89 06:26:21 GMT
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X-Telecom-Digest: Volume 9, Issue 597, message 5 of 8


     From time to time, including even fairly recently here in the
TELECOM Digest, people make observations about how large a toll-free
region they are located in, or about how much more fortunate somebody
else is in being in an especially large one.  Those observations made
me wonder: has any ever attempted to determine the size of toll-free
regions and list the largest ones, much as lists of the largest cities
or SMSA's are done?  It sounds like it might make an interesting paper
or project for a telecom course; it might even have practical value.

     Note that the question is not as well-defined as it might first
appear: each of the terms in "toll-free region size" is ambiguous and
has several reasonable meanings.  To simplify things a little, let us
start by defining "local call" as follows: exchange B is a local call
from exchange A if making that call using typical non-measured
residential service adds nothing to the bill.  (In locations where
there is an optional higher level of service that I think I have seen
called "metropolitan" service or something like that, assume that the
residence is paying for that higher level of service, i.e., has chosen
the broadest "normal" service it can.)

     "Toll-free region" then has at least three meaningful
definitions, one of which I'll call "compact toll-free region", the
second "local toll-free region," and the third, "extended toll-free
region:"

  Compact toll-free region: Let R be a set of exchanges.  R is a compact
  toll-free region if and only if for all exchanges x and y that are
  members of R y is a local call from x and for all exchanges z that are
  not members of R, there exists at least one x in R such that either z
  is not a local call from x or x is not a local call from z.  In short,
  a compact toll-free region is a set of exchanges such that any two
  exchanges in the region are local calls from each other and that all
  exchanges outside the region are non-local calls to or from at least
  one exchange in the region.  (I don't know if "local call" is always a
  symmetric relation: are there cases where A is a local call from B but
  B is not a local call from A?)  Note that, in theory, different compact
  toll-free regions can overlap.

  Local toll-free region:  for each exchange x, find the set of all
  exchanges y such that y is a local call from x.  Each such set is a
  local toll-free region.  This is probably what a person means when he
  talks about the size of the toll-free region he is in, since, in short
  it is the set of all exchanges *HE* can reach toll-free.

  Extended toll-free region:  Define the relation is-linkable-to as
  follows -- given two exchanges x and y, x is-linkable-to y if either,

       a)   x is a local call from y,
       b)   y is a local call from x, or,
       c)   there exists an intermediate exchange z such that either x is a
            local call from z or z is a local call from x and z is
            linkable to y.

  It can be seen that is-linkable-to is an equivalence relation over
  the set of exchanges.  The set of equivalence classes under that
  relation define the set of extended toll-free regions.  In short, two
  exchanges are in the same extended toll-free region if an appropriate
  sequence of all local calls could be used to pass a message, e.g.,
  using uucp, between customers in the two exchanges, noting that if
  "local call" is ever non-symmetric some of the calls may have to be
  initiated by receivers rather than senders.  (An obvious first
  question here is: is there in fact more than one extended-toll-free
  region, i.e., are there in fact at least two areas where you "can't
  get there from here?")

     The hypothetical term project then is: a) identify all the
compact, local, and extended toll free regions. b) rank the three
lists of regions by geographical area covered, number of telephone
numbers covered, and population covered.

     Has anyone done any of this?  Any ideas short of looking at every
telephone book in the country how someone would proceed?  (I'm not
intending to carry out the project, only curious as to whether it
could even be done.)