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//How Many Business Telephone Trunk Lines Do I Need?

How Many Business Telephone Trunk Lines Do I Need?

To answer that question you could pick a number out of the air that seems right or if you are moving to a new location decide that “since we had 4 trunk lines in the old place, 4 lines should suit us just fine when we move to the new place.”

Let me suggest a more analytical approach. The best answer to the question of how many lines are needed to conduct business efficiently can be derived through a series of calculations using telephone traffic engineering formulas.

Telephone traffic engineering is something of an arcane science.  It is a field of study founded by Dutch mathematician and engineer A. K. Erlang early in the 20th century.  Not limited solely to the realm of telecommunications, though, traffic engineering is just as readily applied to determining, for example, how many tellers are needed in a bank branch to take care of customers on a busy Monday morning or how many lanes of highway are needed to reduce commuter congestion on those get-away Friday afternoons. But regardless of the type of traffic being measured, the goal is always the same: to rationalize resources and satisfy demand in an efficient, cost-effective manner.

Having the right number of trunk lines in place is critical to the performance of your telephone system, to the level of service your customers and prospects receive, and to the profitability of your business.  To ascertain what that number is, traffic engineering uses probability analysis and statistical forecasting tools to predict levels of caller activity to establish the number of lines needed to handle an expected volume of calls. These calculations make use of the law of large numbers, which for our purposes infers that the overall behavior of calls in a system can be predicted with reasonable certainty even if the behavior of any one call in the system cannot.  In other words, the whole is more reliably measured than individual parts of the whole.

The formulas used to estimate the number of telephone lines needed take into account the following determinants:

Blocking:  a condition caused when the number of calls exceeds the number of lines to receive them, another term for which is trunk congestion; an unsuccessful call is referred to as either a lost call or a blocked call.

Calling rate:  the number of calls received during a finite time period

Congestion: when the level of telephone traffic nears, reaches or exceeds the design maximum, the system is said to be congested

Distribution pattern: a curve of the average time of phone calls which will always show that more calls are shorter than the average call than are longer than the average call.

Erlang: a unit measure of call traffic volume; traffic is measured in call seconds (CCS) or erlangs. One CCS is equal to 100 seconds of telephone time. One erlang (named in honor of A.K. himself) is equal to one hour, or 36 CCS of telephone traffic time.

Erlang B: a formula that assumes that an unsuccessful call (e.g., the call is blocked or the caller gets a busy signal) is not placed in a queue or re-dialed, but is lost forever. The formula further assumes that any new call arrives independently of the time since the previous call.  It considers the percent of blocked calls that will initiate a return call, predicts the likelihood of line congestion and produces a grade of service probability.

Erlang C; an extension of Erlang B, this formula assumes that blocked calls are placed in a queue waiting for someone to answer them and will calculate the number of extra lines needed to accommodate the queue.

Grade of service: the probability of having a call blocked, say 1 in 100 calls, is called the grade of service; it is the proportion of time for which congestion exists (in this case, 1%); a measure of network capacity.

Holding time: the average duration of a call.

Quality of service: evaluation of all the aspects of a telephone line connection, such as customer service response time, loudness levels, cross-talk and echo, and the tonal quality of a call.

While telephone traffic ordinarily fluctuates throughout the business day, there may be a particularly busy hour (or peak time), during which the highest hourly volume of calls is received.  Busy hour can be a function of a myriad of factors, such as time zone differences, new sales promotions, breaking news or weather events.  Thus, some factors are internal to the business and can be predicted to a degree, while others are external to the business and are more random and, therefore, less predictable.

The primary objectives of traffic engineering are (1) to minimize or eliminate blocked calls and (2) to balance the quality of service against the costs of operating a telephone system.  As you might imagine, weighing service quality on one hand and costs on the other can be a delicate matter, which is why the scientific approach of traffic engineering is so useful.


With all of that as background, rather than laboring through esoteric formulas, let’s use the calculator below to determine how many telephone lines your business requires to best service both customers and prospects (inferred by the tolerable level of blocked calls expressed as a % of all calls).  In going through this, and making various assumptions, you may find that you can eliminate lines and reduce your monthly carrier costs. Or you may see that adding a line or two will improve the company’s blocked calls experience, or better said, improve the quality of customer service.

When you arrive at the optimum number lines, do a cost-benefit analysis to justify any required investment.

To get the best results using this calculator, it is important that your inputs are as accurate as possible.  Information on call volumes (including inbound, outbound, and local and long distance calls), busy hours and call duration can be gathered in two ways:  (1) through the Call Accounting feature on your phone system, or (2) by requesting a traffic survey from your telephone carrier that usually is done at no cost.

Here are the steps to use this calculator:  Just enter the average call duration you estimate, the number of calls in the busy hour and the number of lines you have or expect to have. Then click on “Calculate”.  This calculation will solve for a busy probability.  Then adjust your assumptions to arrive at the desired level of busy probability.  That will give you the number of lines needed to satisfy your assumptions.

Average call duration (minutes):
Number of calls in peak hour: Busy probability:
Number of lines available:

Calculator courtesy of

Note:  The Erlang equation assumes a randomly distributed traffic from a more or less unlimited number of potential callers. A random distribution may not be always realistic since people tend to redial immediately when they hear a busy signal, so that the actual busy rate will be higher than the one calculated by the Erlang equation.

By | 2019-01-07T22:05:28+00:00 August 1st, 2013|Uncategorized|0 Comments

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