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Goodbye, Erlang; Hello, Gbps/km2/MHz

Engineering depends on with metrology units and performance metrics of many types. Recently, the member countries who define the International System of Units (abbreviated from the French Système international – SI) voted to define all fundamental units based on just seven physical constants, available on a convenient wallet-size card so you can have them handy at all times, Figure 1 . The advantage of using these seven constants is that they are reproducible (at considerable cost, of course) without need to go back to a primary, “sacred” standard.

Figure 1

This convenient wallet-size card has all you need to know to get started in fundamentals of metrology using SI units. (Image source: NIST)

This convenient wallet-size card has all you need to know to get started in fundamentals of metrology using SI units. (Image source: NIST)

The breakthrough was the replacement of the definition for the standard kilogram replacing the top-level, primary-standard kilogram which resides in vault in Paris and various “copies,” Figure 2 . That standard, when checked against several secondary physical copies, has mysteriously been losing weight (mass) – just a few nanograms – which is a not a good thing, for obvious reasons.

Figure 2

These secondary kilogram standards are built and calibrated against the top-level 'ultimate' primary standard in a Paris vault, and they apparently have evolving differences in mass; in principle, they will no longer be needed due to the approval of a reproducible definition of the standard. (Image source: NIST)

These secondary kilogram standards are built and calibrated against the top-level “ultimate” primary standard in a Paris vault, and they apparently have evolving differences in mass; in principle, they will no longer be needed due to the approval of a reproducible definition of the standard. (Image source: NIST)

From these seven basic units, you can move up the metrology scale to our more-common units such as volts, amps, and others which we use almost effortlessly and without too much thought. They are both ubiquitous and reasonably easy to measure to three or four significant figures using modestly priced instrumentation.

But modern electronics and communication systems require additional types of measures and metrics. Back in the middle part of the 20th century, the erlang was one of the most important measures for communications traffic. It was hard to find anything about system performance without seeing that term.

What’s an erlang? (No, not the Erlang programming language used to build massively scalable soft real-time systems with requirements on high availability, used in telecom, banking, e-commerce, computer telephony and instant messaging.) The communications erlang is a dimensionless unit of analog telephony traffic. One erlang is the equivalent of one call (including call attempts and holding time) in a specific channel for 3600 seconds in an hour. The CCITT designated the erlang as the international unit of telephone traffic in 1946 in honor of Anger Krarup Erlang, a Danish mathematician and engineer who did important early work in traffic engineering and queuing theory.

Wait a minute: call attempts, holding time – what are those? The entire erlang concept is related to “circuit-switched” analog telephony, where a tangible physical circuit is dedicated to the call which is in progress. A single circuit has the capacity to be used for 60 minutes of one hour, and the full use of that capacity, constitutes 1 erlang.

Back in the day, there were sophisticated, detailed papers created at telecom companies and labs – such as the venerable Bell Telephone Laboratories (Bell Labs) – which analyzed all sorts of voice-phone traffic patterns and situations, and resources needed (local loops, line interface units, routing switches) in terms of erlangs of traffic, how long a user would have to wait to get service, and many other performance metrics. Much of this analysis involved probabilistic assessments, as well.

It’s probably hard for us to fully appreciate how important the erlang parameter was to this system analysis. Now, with the transition from circuit-switched to data-switched connectivity, the erlang has fallen away and is largely unknown. In its place, we have much-more meaningful metrics for data rate and capacity such as megabits/sec (Mbps), mA/MHz to characterize a CPU’s processing power and computational efficiency, or miles (or km)/minute for EV recharging effectiveness.

The need for new measures continues, of course. I came across a new one (at least to me) which at first puzzled me, but soon made sense, in a recent article in Microwave Journal , “mmWave Will Be the Critical 5G Link.” It was Gbps/km2 /MHz – gigabits per second, per square kilometer, per MHz of spectrum (shortened to GkM) – and it measures the level of wireless traffic density. It’s not clear to me if this is a widely used system-loading metric, or one promoted by the article’s author at Mobile Experts (Campbell, CA), but it seems quite useful.

How so? GkM gives an indication of how intensely the available spectrum is being used in a given geographical area. This area can be highly localized such as a stadium or arena, or a neighborhood, or a city; Figure 3 shows one data set.

Figure 3

Gbps/km2/MHz is a metric which shows system loading for wireless sites and can provide some indication of when more microcell base stations are needed and even which type. (Image source: Mobile Experts)

Gbps/km2 /MHz is a metric which shows system loading for wireless sites and can provide some indication of when more microcell base stations are needed and even which type. (Image source: Mobile Experts)

GkM helps decide if more microcells are needed to adequately cover that area and of what type, to ensure an acceptable level of user access and connectivity. By looking at GkM, you have one quantitative measure that can help determine the service and resource situation – somewhat analogous to what erlangs helped do in the circuit-switched world.

Undoubtedly, there are other useful and necessary factors for determining wireless connectivity performance; some may have industry-wide and accepted definitions while others may be more “proprietary” and promoted by one or a few vendors or market analysts. Are there any such units which you used to use regularly, but now rarely do, if at all? Which new ones are more meaningful for your analysis or design?

References

  1. NIST, For All Times, For All Peoples: How Replacing the Kilogram Empowers Industry
  2. NIST, “A Turning Point for Humanity: Redefining the World’s Measurement System
  3. NIST, “Toward the SI System Based on Fundamental Constants: Weighing the Electron
  4. NIST, “Universe’s Constants Now Known with Sufficient Certainty to Completely Redefine the International System of Units
  5. Mobile Experts, “5G – Is it Economically Viable?
  6. Mobile Experts, When does Mobile Traffic Density force the operator to use small cells?

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