The Problem With Digipeaters

I am sitting here in the shack feeling very frustrated. I am
watching the activity on 145.01 (although the problem is just as
severe on 145.05 or any of the other frequencies in use in the
area) watching WA4xxx tying up the frequency for the greater
portions of Northern VA, MD, WVA and EPA, trying to connect with
a BBS in Pittsburgh using SIX! digipeaters. He is having no
luck and undoubtedly is wondering why. The basic answer is very
simple:

PACKET RADIO DOESN'T WORK THRU MORE THAN 2 or 3 DIGIS !!!
====== ===== ======= ==== ==== ==== ==== = == = ===== ===

Oh yes, I hear you saying "You are wrong -- the AX.25 protocol
permits me to use up to eight digis!". That is a true
statement, but just because something is permitted doesn't mean
it will work. And here is why --

Assume that you are station ABC at one end of a long string of
digi's trying to send out a packet thru digis DEF, GHI, JKL,
MNO, PQR, STU and addressed to station XYZ (fake calls are used
to protect the guilty!). Thus your intended path is expressed
by the following connect command

CONNECT XYZ VIA DEF,GHI,JKL,MNO,PQR,STU

Your outgoing packet then should take the path

ABC => DEF => GHI => JKL => MNO => PQR => STU => XYZ

At every step along the way, there is a finite chance that the
packet is going to be hit by QRM. My observations are that on
the very best paths about 5% of packets get clobbered on any
single hop. For the example we are using, this means that 95%
of the ABC => DEF packets make it to DEF, and then 95% of them
successfully navigate the DEF => GHI path, and so forth. Thus
at the destination XYZ we have

.95 * .95 * .95 * .95 * .95 * .95 * .95 = .70

Only 70% of the data you sent out makes it all the way to XYZ.

BUT WAIT -- THERE'S MORE !!!!

AX.25 packet protocols require XYZ to send you back an 'ack'
acknowledgement packet which then has to unwind itself back thru
the same route. The same probability arguments apply, and 70%

Fidonet HAM/PACKET Digest Page 31
Volume 1, Number 6 December 3, 1989

of the acks get to you. Thus on a high- quality 95% link thru 6
digis, only .7 * .7 = .49 of your packets are successful thru 6
digipeaters! A Las Vegas gambler could make a very good living
on 51/49 guaranteed odds.

BUT WAIT -- THERE'S MORE !!!!

We took 95% as the probability of each link working. I know of
very few paths that are that good except perhaps at 4AM when
nobody else is on the frequency. Links you tend to think of as
'pretty good' probably have 10-20% of your packets trashed on
any given hop. And I know of a number of links where the
probabilities are no better than 50%. For the general case, if
P is the link probability on all links, and N digipeaters are
involved, then PA = the aggregate probability of success will be
given by the formula

PA = ( P ) ** ( 2N+2 )

BUT WAIT -- THERE'S MORE !!!!

Every time your packet gets clobbered, you try again to push it
thru. If 50% of you packets get hit, on average you will
try/retry your packet 2 times. In general the number of
tries/retries that will be required is

TRIES = 1 / PA

BUT WAIT -- THERE'S MORE !!!!

You and everybody else who is on packet spent a lot of money to
be able to ragchew and send messages (or data, or nudie
pictures, or ???) at 1200 baud. But the packet gurus lied to
you. Your data doesn't really flow at 1200 baud -- there is
some overhead associated with headers that are appended to each
and every packet you send, plus some time wasted in getting that
all important ack back, plus some time for your radio to change
from transmit to receive and back to transmit, plus time waiting
for a hole to open up on the channexDl. At best you can
transmit say 600 baud. But for every digipeater you use,
another set of similar delays is added at each step along the
way. So if you had a perfect set of links thru N digis, your
average baud rate would drop to something like

DIGIPEATED BAUD RATE = 600 / ( 1 + N )

BUT WAIT -- THERE'S MORE !!!!

Each time your packet gets clobbered, it is retried, until it
gets thru (or until you time out). So the real effective baud
rate is slowed even further until it is given by this formula

EFFECTIVE BAUD RATE = 600 * PA / ( 1 + N )


= 600 * [(P)**(2N+2)] / ( 1 + N )

BUT WAIT -- THERE'S MORE !!!!

Every time you take over the channel with an unsuccessful
packet, somewhere along the chain you have prevented some other
hapless individual from using that time slot. YOU HAVE HOGGED
THE FREQUENCY!

We might express your channel usage efficiency as the ratio of
the baud rate that you actually to the baud rate you would have
achieved if you had simply used a piece of wire, i.e.

EFFICIENCY = EFFECTIVE BAUD RATE / 1200

More instructive than seeing this factor as a simple numerical
ratio is to express it in dB as what I like to call the 'Hog
Factor' --

HOG FACTOR = 10 log ( EFFECTIVE BAUD RATE / 1200 )

This factor even includes the 3 dB 'loss' for a perfect AX.25
link due to the overhead we discussed earlier.

BUT WAIT -- THERE'S MORE !!!!

So far I have only used a few numbers to introduce the concepts.
The following four tables tell the whole story. I have worked
out a number of cases for links ranging from perfect (P=1.0) to
pretty scuzz-ball (P=0.50) and for 0 thru 8 digipeaters. My
experience shows that P=0.95 is a pretty rare case, but outside
of 'prime-time' hours P=0.90 is fairly typical. In the evenings
when everybody is on the channel P=0.80 is not unusual. Paths
involving 'DX' digipeaters (like K3LZ-1 or WB4APR-6 or WA4FRB-3)
degrade to P=0.6 or P=0.7 in the evenings simply because they
hear so much stuff. And we always have the user in a poor
location, running an HT with a rubber duckie who is lucky to
have P=0.5!

My advice to all users is that they not even attempt to use a
path for which PA < 0.5 (or on average < 2 retries). I have put
those 'bad' combinations in parenthesis to highlight them.
Unless you have an exceptional path (better than P=0.95), these
tables clearly show that using more than one or two digipeaters
is an exercise in futility which will make you very unpopular
with your peers ('Hog Factor' poorer than -10 dB) and drive you
to distraction (with effective baud rates slower than about 100
baud). Have I proven my premise from the start of this tome?

PACKET RADIO DOESN'T WORK THRU MORE THAN 2 or 3 DIGIS !!!

<------ Link Success Probabilities Per Hop ---------->

Fidonet HAM/PACKET Digest Page 33
Volume 1, Number 6 December 3, 1989

N = P=1.0 P=.95 P=.90 P=.85 P=.80 P=.70 P=.60 P=.50
No. of ==== ==== ==== ==== ==== ==== ==== ====
Digis
---- ----- PA = Aggregate Probability of Success --------
0 1.0 0.90 0.81 0.72 0.64 (0.49) (0.36) (0.25)
1 1.0 0.81 0.66 0.52 (0.41) (0.24) (0.13) (0.06)
2 1.0 0.74 0.53 (0.38) (0.26) (0.12) (0.05) (0.02)
3 1.0 0.66 (0.43) (0.27) (0.17) (0.06) (0.02) (0.00)
4 1.0 0.60 (0.35) (0.20) (0.11) (0.03) (0.01) (0.00)
5 1.0 0.54 (0.28) (0.14) (0.07) (0.01) (0.00) (0.00)
6 1.0 (0.49) (0.23) (0.10) (0.04) (0.01) (0.00) (0.00)
7 1.0 (0.44) (0.19) (0.07) (0.03) (.00) (0.00) (0.00)
8 1.0 (0.40) (0.15) (0.05) (0.02) (.00) (0.00) (0.00)

---- Average number of Tries/Retries before Success ----
0 1.0 1.1 1.2 1.4 1.6 (2.0) (2.8) (4)
1 1.0 1.2 1.5 1.9 (2.4) (4.2) (7.7) (16)
2 1.0 1.4 1.9 (2.7) (3.8) (8.5) (21) (64)
3 1.0 1.5 (2.3) (3.7) (6.0) (17) (60) (256)
4 1.0 1.7 (2.9) (5.1) (9.3) (35) (165)
(1,024)
5 1.0 1.9 (3.5) (7.0) (15) (72) (459)
(4,096)
6 1.0 (2.1) (4.4) (9.7) (23) (147) (1,276)
(16,384)
7 1.0 (2.3) (5.4) (13) (36) (301) (3,545)
(65,536)
8 1.0 (2.5) (6.7) (19) (56) (614) (9,846)
(262,144)

-- ------- Equivalent System Baud Rate ----------------
0 600 542 486 434 384 294 216 150
1 300 244 197 157 123 72 39 19
2 200 147 106 75 52 24 9 3
3 150 100 65 41 25 9 3 1
4 120 72 42 24 13 3 1 0.1
5 100 54 28 14 7 1 0.2 0.02
6 86 42 20 9 4 1 0.1 0.01
7 75 33 14 6 2 0.2 0.02 0.001
8 67 26 10 4 1 0.1 0.007 0.0003

-- -------- Channel 'Hog factor' in dB -----------------
0 -3 -3 -4 -4 -5 -6 -7 -9
1 -6 -7 -8 -9 -10 -12 -15 -18
2 -8 -9 -11 -12 -14 -17 -21 -26
3 -9 -11 -13 -15 -17 -21 -27 -33
4 -10 -12 -15 -17 -20 -25 -32 -40
5 -11 -13 -16 -19 -22 -29 -37 -47
6 -11 -15 -18 -21 -25 -33 -43 -54
7 -12 -16 -19 -23 -28 -37 -48 -60
8 -13 -17 -21 -25 -30 -40 -52 -67
 -40 -52 -67

---
EOF