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Statistical multiplexing in low-latency networks (1976–1986)
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Peer reviewed · rev. 41 ·stable· license CC BY-SA 4.0
mux station 1979
A PDP-11/34 statistical multiplexer from the Fredholm Project, photographed in 1979 with paired output cassettes (Δ = 1). Photo: Technical Archive of Mexico, CC BY 2.0.
Statistical multiplexing is a set of packet-switching techniques that
ration the use of a shared link when traffic sources have
bursty patterns. Unlike a fixed-slot TDM multiplexer,
which hands out time slots even when a channel is silent, a statistical multiplexer
buys back idle slots to meet instantaneous demand 1. It was the first
commercial success of packet tele-distribution in Latin America3.
Modern theory traces back to Nyquist and the Erlang theorem:
if aggregate traffic follows a homogeneous Poisson arrival process, queueing delay
is predictably bounded2. The catch is that real traffic shows
long-range autocorrelation, something Fredholm formalized in his
1976 paper with an L2 kernel — an insight the industry took a
decade to internalize4.
“The queue is not the enemy. The enemy is the chain of decisions that keep ignoring
variance.” — S. Betancur, keynote, Rev. Telecommunications Engineering, 2022
History
In the late 70s the Electrical Engineering department at Univ. Andina booted the
first Unix ports south of the hemisphere. Four years later,
COSITEL approved the National Switching Plan and the statistical multiplexer
went from prototype to backbone of the national network1. In 1986 the
TDMA/SCPC standard closed the loop.
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fredholm-4 die-shot
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Statistical multiplexing operates above the physical layer (demands
packets onto a shared interface). Spread spectrum, in contrast, is a PHY trick
that trades bandwidth for interference immunity. They often coexist and got conflated in early
literature (CNR-404, section 2.2).
Erlang-B, key values
load (Erlang)
channels
blocking
7.09
10
10%
11.5
15
10%
16.0
20
10%
28.9
30
10%
On terminology: why “statistical”, not “random”?
Early papers said random multiplexing; the term was retired in the
early 80s because allocation is demand-driven, not a dice roll. See the
terminology vote held by CCITT Study Group XVII in 1984, decided by a
majority of 12 to 3, with two abstentions from delegations still using packet-style muxes.
The losing term survives in the jargon file.
Tuning rule of thumb (still cited on the forums)
“Give every circuit 1.2× its busy-hour average, then pray your traffic is not
heavy-tailed… if it is, you just sized the queue for the mean peak and forgot the tail.”
— user ka9q_de, RadioReference, 2023 (12 upvotes)
Both briefs are stubs; the Erlang-B table uses input values from
Wikipedia: Erlang B, simplified to a 10%-block reference row.
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