# Erlang Tables

Erlang tables show the amount of traffic potential (the BHT) for specified numbers of circuits for given probabilities of receiving a busy signal (the GoS). The BHT calculation results are stated in CCSs or Erlangs. Erlang tables combine offered traffic (the BHT), number of circuits, and GoS in the following traffic models:

■ Erlang B: This is the most common traffic model, which is used to calculate how many lines are required if the traffic (in Erlangs) during the busiest hour is known. The model assumes that all blocked calls are cleared immediately.

■ Extended Erlang B: This model is similar to Erlang B, but it takes into account the additional traffic load caused by blocked callers who immediately try to call again. The retry percentage can be specified.

■ Erlang C: This model assumes that all blocked calls stay in the system until they can be handled. This model can be applied to the design of call center staffing arrangements in which calls that cannot be answered immediately enter a queue.

NOTE Erlang tables and calculators can be found at many sites, including http://www.erlang.com/.

### Erlang B Table

Figure 8-36 shows part of an Erlang B table. The column headings show the GoS, the row headings show the number of circuits (the number of simultaneous connections), and the table cells indicate the BHT in Erlangs for the specified number of circuits with the specified GoS.

Figure 8-36 An Erlang B Table Is Used to Determine Required Trunk Capacity

 Blocking Probability Number of Circuits .003 .005 .01 .02 .03 .05 1 .003 .006 .011 .021 .031 .053 2 .081 .106 .153 .224 .282 .382 3 .289 .349 .456 .603 .716 .900 4 .602 .702 .870 1.093 1.259 1.525 5 .996 1.132 1.361 1.658 1.876 2.219 6 1.447 1.822 1.900 2.278 2.543 2.961 7 1.947 2.158 2.501 2.936 3.250 3.738 8 2.484 2.730 3.128 3.627 3.987 4.543 9 ^3.053 3.333 3.783 4.345 4.748 5.371 10 / 3.648 3.961 4.462 5.084 5.530 6.216 /

Busy Hour Traffic (BHT) in Erlangs

Busy Hour Traffic (BHT) in Erlangs

### Erlang Examples

Having established the BHT and blocking probability, the required number of circuits can be estimated using the Erlang B traffic model. For example, given BHT = 3.128 Erlangs, blocking = 0.01, and looking at the Erlang table in Figure 8-36, the number of required circuits is eight.

As another example using Figure 8-36, 4.462 Erlangs of traffic is offered for ten circuits (simultaneous connections) with a GoS of P01 (1 percent block probability). 4.462 Erlangs equals approximately 160 CCSs (4.462 * 36). Assuming that there are 20 users in the company, the following steps illustrate how to calculate how long each user can talk:

■ BHT = Average call duration (seconds) * calls per hour/3600

■ 4.462 = Average call duration (seconds) * 20/3600

■ Average call duration = 803 seconds = 13.3 minutes

In another example, six circuits at P05 GoS handle 2.961 Erlangs. 2.961 Erlangs equals approximately 107 CCSs (2.961 * 36). Assuming that the company has ten users, the following illustrates how to calculate how long every user can talk:

■ BHT = Average call duration (seconds) * calls per hour/3600

■ 2.961 = Average call duration (seconds) * 10/3600

■ Average call duration = 1066 seconds = 17.8 minutes

### Trunk Capacity Calculation Example

The objective of this example is to determine the number of circuits, or the trunk capacity, required for voice and fax calls between each branch office and an enterprise's headquarters office. The following assumptions apply to this sample network:

■ The network design is based on a star topology that connects each branch office directly to the main office.

■ There are approximately 15 people per branch office.

■ The bidirectional voice and fax call volume totals about 2.5 hours per person per day (in each branch office).

■ Approximately 20 percent of the total call volume is between the headquarters and each branch office.

■ The busy-hour loading factor is 17 percent. In other words, the BHT is 17% of the total traffic.

■ One 64-kbps circuit supports one call.

■ The acceptable GoS is P05.

Following are the voice and fax traffic calculations for this example:

■ 2.5 hours call volume per user per day * 15 users = 37.5 hours daily call volume per office

■ 37.5 hours * 17 percent (busy-hour load) = 6.375 hours of traffic in the busy hour

■ 6.375 hours * 60 minutes per hour = 382.5 minutes of traffic per busy hour

■ 382.5 minutes per busy hour * 1 Erlang/60 minutes per busy hour = 6.375 Erlangs

■ 6.375 Erlangs * 20 percent of traffic to headquarters = 1.275 Erlangs volume proposed

To determine the appropriate number of trunks required to transport the traffic, the next step is to consult the Erlang table, given the desired GoS. This organization chose a P05 GoS. Using the 1.275 Erlangs and GoS = P05, as well as the Erlang B table (in Figure 8-36), four circuits are required for communication between each branch office and the headquarters office.

### Off-Net Calls Cost Calculation Example

This example calculates the off-net cost of calls between two locations, New York and London, as shown in Figure 8-37. The PSTN path is used when the transatlantic tie line cannot accept additional on-net calls.

Figure 8-37 Off-Net Calls Are Sometimes Required

Figure 8-37 Off-Net Calls Are Sometimes Required

Alternative Off-net Path

Assume that all calls between these two sites use 64 kbps of bandwidth, which corresponds to one circuit, and that a GoS of .03 is acceptable. How many minutes per month of calls use off-net calling because of the service block on the transatlantic tie line? The transatlantic tie line can simultaneously carry a maximum of ten calls. In the calculation, we assume that a 1-minute call between New York and London costs \$.10.

NOTE The \$.10 per minute rate is used here for ease of calculation.

The calculation is as follows:

■ According to the Erlang B table in Figure 8-36, 5.53 Erlangs can be offered at P03 and ten circuits.

■ At P03, 3 percent of the 5.53 Erlangs of calls are overflowed and sent off-net.

■ Therefore, in the peak hour, .03 * 5.53 Erlangs * 60 minutes = 10 overflow minutes.

■ Assume that there are two peak hours per day and 21 business days per month. Therefore, 21 days * 2 peak hours per day * 10 overflow minutes = 420 overflow minutes per month.

■ 420 overflow minutes per month * \$.10 per overflow minute = \$42.00.

The calculation shows that 420 minutes per month of off-net calling between New York and London is used, costing \$42.00. This cost should be compared to that of adding circuits between New York and London to see whether it is worth adding bandwidth.