Communication Basics #30 Worked Example: PSTN Topology — Tandem vs Mesh, the Real Reason for Hubs

Instructor: Dr. Süleyman Burak ÇELİK

A network topology question that looks easy with five nodes and only gets interesting once you push the numbers. We start with a small city — five local telephone exchanges and one tandem exchange, every local connecting to the tandem through a 4 Mbps trunk. Three questions: how many trunks with the tandem, how many if every local talks directly to every other local (full mesh), and how do these numbers scale at 10 and 100 nodes? The video walks through both topologies on screen. Star (tandem in the middle): 5 trunks, one per local-to-tandem link, hub-and-spoke. Full mesh: every pair of locals needs its own trunk, so we count 4+3+2+1 = 10. The pattern is the binomial coefficient C(n,2) = n(n−1)/2 — exactly what we counted by hand. Then we push the numbers. At n=5 the asymmetry is small: tandem 5, mesh 10. At n=10: tandem 10, mesh 45. At n=100: tandem 100, mesh **4,950**. That is roughly 50× more cable, 50× more right-of-way, 50× more equipment. And these numbers are still small in PSTN terms — Istanbul has hundreds of local exchanges, the country has thousands. The closing third covers why every real PSTN uses tandem switching. Three reasons beyond raw trunk count: (1) cheaper trunks per call thanks to TDM and statistical multiplexing on aggregated high-rate links, (2) operations team has a fighting chance with 100 trunks vs 4,950, and (3) graceful growth — adding a new local exchange means a single new trunk to the hub, not trunks to every existing exchange. Topics covered: - star (tandem) topology trunk count walked end to end - full mesh trunk count derived two ways: by hand and via C(n,2) - linear vs quadratic scaling at n = 5, 10, 100 - the n²/2 explosion that makes flat mesh networks unbuildable at scale - why hierarchies (tandem switches, trunking, multiplexing) make the PSTN economically possible - engineering tradeoffs: trunk count, maintenance load, growth pattern Sources: ECE 271 ExQ34 == HW Q43 with extended scaling analysis. Part of the AcEdumy Communication Basics series.