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From: G.MDP@score.stanford.edu (Mike Peeler)
Newsgroups: comp.sys.misc
Subject: Blocking Up Front
Message-ID: <2108@brl-adm.ARPA>
Date: Mon, 5-Jan-87 02:01:26 EST
Article-I.D.: brl-adm.2108
Posted: Mon Jan  5 02:01:26 1987
Date-Received: Mon, 5-Jan-87 06:42:39 EST
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In article <816@mtunb.UUCP> dmt@mtunb.UUCP (Dave Tutelman) writes:
>In article <2066@brl-adm.ARPA> G.MDP@score.stanford.edu (Mike Peeler) writes:
>>Trunk capacity increases exponentially with the number of trunk
>>lines, not linearly, as at first you might expect.  Figure out
>>how much traffic a highway can bear as a function of its width
>>in lanes.  That's basically the same thing, and some fancy math
>>helps (if you think statistical analysis is fancy math).
>	Not really true.
>	The highway analogy deals with a very small number of servers
>	in the queueing system (say, 1 to 3).  In this range, I agree that
>	small increases in servers give large increases in capacity, IF
>	your standard is based on blocking probability.  (I noted above
>	that this IS the standard used by phone companies.  But it's
>	not the only one possible, and probably isn't the one used
>	by highway engineers.  If, for instance, you used an average
>	server occupancy as your standard, capacity would vary linearly
>	with number of servers, for ALL server sizes.)

Yes, of course I'm talking about blocking probability.  Phone
callers can't see such things as utilization levels, but they
sure can tell if they can't get through.  On highways, I would
look at traffic jams, which I think behave similar to blocking
probability, rather than at traffic density, which is obviously
linear with the number of lanes.  I exclude No-Cal (as opposed
to Lo-Cal) drivers, among whom arbitrarily low densities can
cause a jam.

>	In any event, interoffice telephone trunk groups are much larger
>	(tens to hundreds of servers).  For this size of group, capacity
>	varies pretty nearly linearly with number of servers, for any
>	required blocking probability.

Well, sure.  First, from that "very small number of servers"
where the exponential behavior does hold, I ought to be able to
use induction to prove it for large trunk groups.  Anyway, it's
clear that the blocking probability is monotonically decreasing
and bounded by zero, so naturally it's asymptotically linear.
On the flip side, the capacity curve gets so steep that it, too,
is "pretty nearly linear", for practical purposes.  Buy that?

Cheers,
   Mike
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