VACETS Regular Technical Column

The VACETS Technical Column is contributed by various members , especially those of the VACETS Technical Affairs Committe. Articles are posted regulary on [email protected] forum. Please send questions, comments and suggestions to [email protected]

November 1, 1996

The Effect of Internet Traffic on the Public Voice Network

Part 2: Traffic Assumptions Of The Public Voice Network

In Part 1 of this series of articles, we have examined the Public Switched Telephone Network, and understand how it works. In this article we will attempt to characterize the telephone traffic and how to engineer the network to serve that kind of traffic.

An understanding of the nature of the telephone traffic and its distribution with respect to time and destination is essential in determining the amount of telephone facilities required to serve the subscriber's needs. Telephone traffic varies greatly from one period to another, not in any uniform manner but according to the needs of the telephone subscribers. Traffic volume varies from season to season, from month to month, from day to day, and from hour to hour. There are also variations from minute to minute in the same hour, as well as variations from subscriber to subscriber.

Busy-season traffic varies differently from cities to cities, both in amplitude and in duration. There are many reasons for these variations such as: Where is the city located (resort area, or retirement area), or what industry does the city have (agricultural, or high-tech).

The amount of equipment and facilities that is needed to serve each community is calculated based on the normal busy season. Occasionally, however, the traffic will exceed that level. Some unusual peaks can be expected during special days such as Mother's Day and Christmas. Some other peaks may be due to special events such as The Republican Convention or a natural disaster (flood, hurricane). I am told that the peak day for "collect calls" is Father's Day. To engineer the network facilities for all those eventualities would be very costly and, furthermore, the magnitude of such events is usually unpredictable. As a result there will be peak periods when the traffic exceeds the volume that has been assumed; while most of the time the facilities will handle all calls with capacity to spare. Usually, the seasonal variations in the same community will have the same pattern from year to year.

Within the busy season, each community also experiences weekly and daily traffic variations. Due to condition peculiar to the community, some weeks may have more traffic than others. The traffic volume within the week in each community usually forms a fairly consistent pattern, such as high on Mondays and Fridays, low on Wednesdays, etc. However, holiday occurring within the week, or other variable influences such as weather, can greatly affect the traffic distribution pattern.

There are also the traffic variations between the hours of the day. The degree of hourly variations is greater than that of any other period. Volume ratios between the busiest hour to the least busy hour can be as high as 100:1. In business area, peak busy hour can be expected in the late morning hours; while in the residential area, the busy time usually falls in the evening hours.

Although the traffic volumes in all hours are significant, only the busiest hours are of primary interest to the traffic engineer. The variations discussed so far in this article are fairly systematic. Their occurrence can be predicted with some reasonable assurance. A combination of historical records, experience, and good judgment can produce data on which sound engineering decision can be made. There is another traffic variation that is not systematic and cannot be predicted. It is the variation that occurred within an hour. This variation is very different from hour to hour, or from the same hour in different days. This random distribution is because the subscribers can originate calls independently of each other. One other important source of fluctuation in the traffic pattern is that some subscribers use their telephones more than others. In general business subscribers make more calls than residential subscribers. The lengths of conversations also vary considerably among subscribers. Historical data show that the conversation times (or call holding time) between one and three minutes are relatively frequent, while long holding time of 10 minutes or more occur much less often.

How is the traffic measured?

Telephone traffic is defined as the aggregate of telephone calls over a group of circuits or trunks with regard to their durations of the calls as well as their numbers. Traffic flow through a switch or a trunk group is defined as the product of the number of calls during a period of time and their average holding times. In traffic theory, the unit of time is one hour. Let C be the number of calls originated in one hour, and T be the average holding time then the traffic flow intensity A = C x T. For example, if there are 200 calls of average length of 3 minutes between Atlanta and Los Angeles in one hour, then the traffic intensity is: 200 x 3 = 600 minute-calls. Expressed in hour, A = 600/60 = 10. This value is dimensionless but a name was given to it. The international unit of telephone traffic is called "erlang," named after the Danish mathematician A. K. Erlang, founder of the theory of telephone traffic.

From the example above A = 10 erlangs. This number represents:

  1. The average number of calls in progress simultaneously during the period of one hour, or
  2. The average number of calls originated during a period of time equal to the average call holding time, or
  3. The total time, expressed in hours, to carry all calls.

In the US, the term Unit Call (UC) or its synonym "Centium (Hundred) Call-Second," abbreviated CCS is generally used. Remember that with over 100 years of history, the telephone network did not have the modern sophisticated computer equipment to measure traffic accurately until very recently. To estimate traffic intensity, mechanical devices were invented to sample or observe the number of busy circuits. These devices can sample each trunk group once every 100 seconds (or 36 times per hour). If the measuring device found that in one hour, all 36 samples show that a particular trunk is being used, we conclude that the trunk is being used the whole hour, thus by definition this trunk carries 1 erlang or 36 CCS (i.e., 1 erlang = 36 CCS).

In the above example, if the average holding time is 5 minutes instead of 3 minutes, then the traffic intensity is then: A = (200 x 5)/60 = 16.67 erlangs. According to definition 1) above, the average number of busy trunks between Atlanta and LA has just increased to 16.67 from 10 because the average subscriber holds a conversation 2 minutes longer

How many trunks are needed?

Before calculating the number of trunks between 2 cities (e.g., Atlanta and LA) we have to determine what kind of service we would like to provide to our subscribers. As discussed in the previous article, it is possible to provide some service between Atlanta and LA with one trunk.

The subscriber would not be happy because most of the time the trunk will be busy. The Grade of Service (GOS) is the proportion of the number of calls finding a busy trunk vs. the total number of calls. A GOS of 0.5 means that 50% of the call will not get through right away because of unavailable facilities. In the US, a GOS of 1% is generally adopted by all telephone companies.

The next question is: what is the calling pattern of our subscribers? Obviously if all subscribers call at the same time then we have no choice but to provide one trunk between the 2 cities for each subscriber in the originating city. After observing the calling pattern for a long time, we have come to realize that since the number of calls arriving at each trunk group is relatively large at the busy hour, and the average holding time of each call is small (2 to 3 minutes), the traffic distribution can be modeled fairly accurately as a Poisson distribution.

What the Poisson formula, named after the French Mathematician S. D. Poisson (1781-1840), tells us is that: a) calls originate individually and collectively at random, i.e., knowing when one or a set of calls arrives doesn't tell us anything about any other calls, or b) a call is as likely to originate at any moment as any other call.

The third question is what to do with the calls that find all trunks busy. This is the same problem that we have when we arrive at the bank and see that all tellers are busy. We have two choices: 1) Leave and come back some other time, or 2) Wait in line to be served when one teller becomes available. In the telephone networks, option 1) is usually assumed for several reasons. First, the callers are unlikely to wait; they tend to hang up and try again. Second, it is much simpler and more economical to discard a call when all circuits are busy than to hold it and implement some forms of queuing disciplines. So now we have a GOS, a calling pattern that looks like a Poisson distribution, and any call that finds all trunks busy will be discarded.

Based on those assumptions, the Danish mathematician A. K. Erlang in 1917 developed the following (Erlang B) formula that expressed the relationship between the number of trunks, the traffic intensity, and the probability of all trunks busy:

Blocking probability B  =  -------------------------------------
                            1 + a + (a^2)/2! + ...... + (a^c)/c!

with a = traffic intensity expressed in erlang, and c = number of trunks (^ denotes exponential and ! denotes factorial)

To return to the original question: how many trunks do we need between Atlanta and LA given that the traffic intensity is 10 erlangs (It is much more than that in current real network), and a GOS of 1%? This is just a matter of plugging in the numbers, with a = 10, B = 0.01. We would need to keep trying various values for c until the results is less than or equal to our desired GOS. For those of you who are trying to calculate this number using a spreadsheet, the result should be 18 trunks. For large traffic intensity a, this is a time consuming task, and various approximation schemes have been developed to calculate this number faster. Also various tables have been developed to find this value based on a number of pre-defined GOS.

Now we know what it takes to compute the number of trunks required between 2 cities. For a large network with many cities, and the possibility to route traffic from A to B via C, D and E, for example, the problem becomes much more complicated. All this and we have not even touched on how we would handle the day-to-day variation of the traffic, the non-randomness of some traffic (e.g., retrial immediately after a busy signal), etc.

How does the Internet traffic fit into this network? What characteristic does the Internet traffic have that is different from what we described above? How does that affect the public voice network? We will talk about that in the next article in this series.

Again, I have omitted many technical details out of the discussion to make the article readable for everyone. I welcome any technical question or comment on this article and any other articles in our regular columns. Please send them to us at [email protected] and we will discuss them on [email protected].

Luc T. Nguyen, Ph.D.
[email protected]

For discussion on this column, join [email protected]

Copyright © 1996 by VACETS and Luc T. Nguyen


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