A Cost Analysis of VoIP vs. DDD: Costs of

packet traffic vs. circuit switched traffic.

By Dr. Roger G. CleryRoosevelt University

Chicago / Schaumburg Illinois

Cost

•Fixed•Variable•Traffic load

DDD Direct Distance Dial

• Cheap• Flexible

– Destination– Number of lines

Dedicated Lines

• Inflexible Point-to-point• Expensive • AKA private lines, leased lines

VoIP Voice over Internet Protocol

As a replacement for Dedicated linesAs in VPN Virtual Private Network

VoIP problelms

DelayE911Regulations?Taxes?

Previous Studies

In 1991, I wrote a paper with Richard Born of Northern Illinois University investigating the cost of DDD (direct distance dialing) with the cost of private leased lines. While other paper had been written on this subject, they failed to identify the factors that make up costs and service.

What are the Costs?I teach telecommunications classes at

Roosevelt University where many of the students have a wealth of real world practical experience. In a class discussion about VoIP (voice over internet protocol) one student made the statement that VoIP was virtually free. This statement was astounding to me as we all know that there is no free lunch, telephony or data communications. Another student, with experience in a large company stated that the cost of implementing VoIP in their corporate world was very expensive.

Problems Determining Costs

Costs in telecommunications can be very difficult to determine. (note: other industries have problems in cost analysis, like petroleum refining. You know the cost of the crude oil but how do you allocate that cost between the gasoline, diesel oil, fuel oil and the thick gooey tar residue) Telecommunications cost tend to have large fixed investments required before any service can be started and then very low variable costs. Costs of telephone and data services have been decreasing due to the capacity of long haul fiber optic circuits. The problem is comparing fixed costs with variable costs. How much traffic can actually be handled by a circuit?

An Example

In the example, it is assumed that traffic is 4.285 hours (Erlangs) per day.

 VoIP is used in much the same manner as tie lines.

Voice traffic and signaling is sent over an existing data communications circuit. Usually the voice is compressed using only 6 to 12 kilobits per second. Assuming that: there is spare capacity in the data circuit, the quality is acceptable and there is negligible delay for voice and data, there are still costs associated with provisioning. These costs are for equipment like line cards for the routers and switches and possible more buffer memory for the routers.

 

Allocating Cost for Equipment

These costs need to be allocated over time. If for example line cards for provisioning two routers with 2 circuits cost $6000. Assume that the company would like to recoup this cost within 3 years. Then the cost per year is $2000 and the cost per month is about $167. About $83.5 per circuit, but remember that we are getting a bundle of two.You can buy a lot of long distance (IXC) service for $167. 3,333 minutes at a nickel a minute. (or 55½ hours)

The Problem: Packing Voice traffic into circuits.

Although it would seem easy to pack a lot of voice traffic into these 2 circuits it isn’t. Voice traffic once routed by the PBX uses the same route for the duration of that call. (Normally we do not to hand-off to different circuits the way cell phone hand-off to other cells) Traffic that does not use the VoIP circuit will automatically by routed over the DDD service of the long distance carrier so that blockage and grade of service is not an issue.

Step one: Breakeven for each line

The first step in the solution is to know the breakeven point in traffic carried per line per day. If we had a cost of $83.33 per month per circuit and the cost of DDD is 5 cents and there are about 24 working days per month then, we can calculate the breakeven point in traffic per line per day as follows:

Hours of traffic per day = monthlycost / ( minutecost * 60 * workingdays ) or 83.5 /(.05 * 60 * 24 ) = 1.23 hours of traffic per day.

That is to say that each circuit that can carry 1.23 hours of traffic or more is worth having. But, the VoIP case is a little more complicated because we are getting a group of 2. So, 1.23 x 2 = 2.46 for the group.

Step Two: Determine Traffic per line per day

The next step is to determine the total amount of traffic carried per line per day. The first line will carry as much traffic as possible. When it is in use the traffic will overflow to the second line. When both the first and second lines are in use, then the traffic will overflow to the third. This will have the effect of the first line carrying the most traffic and the last line carrying the least traffic. The best method is to analyze the traffic by hour. In this case we are assuming an 8 hour day. ( See The Irwin Handbook of Telecommunications Management Third Edition by James Harry Green, page 517 for rules of thumb for converting total traffic to Busy-Hour traffic.)

Alternate Routing Tables

Using Alternate Routing Tables or Traffic Carried & Traffic Lost Tables and a spreadsheet will give a better estimate of the actual traffic carried per line per hour. First, enter the amount of traffic that is generated per hour as a percentage of the total traffic for a typical day. Then multiply the total Erlangs for a day by the percentages. (If actual traffic is known then use those numbers.) Third, determine the load per line by use of an Alternate Routing table. Last, tally the totals for each line. Below is the example of the Chicago to Denver traffic for an eight hour day. Notice that the fourth tie line carries almost no traffic.

Table Traffic per line per day   A B C D E F G

1 HOUR TRAFFIC TRAFFIC LINE 1 LINE 2 LINE 3 LINE 4

2   % ERLANGS

       

3 9 AM .09 .3856 .2783 .0877

.0171 .0023

4 10 AM .12 .5142 .3396 .1333 .0343 0061

5 11 AM .17 .7284 .3396 .2101 .0741 .0184

6 12 PM .13 .5570 .4215 .1488 .0413 .0079

7 1 PM .14 .5999 3750 .1643

.0488 .0101

8 2 PM .16 .6856 .4071 .1953 .0654 .0155

9 3 PM .10 .4285 .3000 .1027 .0222 .0033

10 4 PM .09 .3856 .2788 .0877 .0171 .0023

11 TOTALS 1.00 4.285 2.7581 1.1299 .3203 .0659

Conclusions

Using the breakeven of 1.23 hours of traffic per day and the totals in this table, it is easy to reach the conclusion that lines one and two are justified. Because we must get a bundle of 2 circuits 2.46 for the bundle is required. In this case we get 3.888 Erlangs of traffic in our 2 circuits. Would anther set of VoIP line cards be with it? NO, because the third and fourth lines can’t carry enough traffic to justify the cost.

 

Is there an Easier Way?

Not everyone has access to Alternate Routing tables. One way to overcome this problem is to build one using the computer, a spreadsheet program, and the following Erlang B formula:

 P = (AN/N!)/(AX/X!) for x = 0 to N In this formula, P is the probability of blocking, A

is the amount of traffic and N is the number of phones.

Step-by-step

While this formula is complex, it can be broken down into small steps. Once this template is constructed then all that needs to be changed is the load in Erlangs in cell B1. The spreadsheet allocates the traffic carried by each line. This would have to be done for each hour of the business day. Line 0 is not an actual line it is just necessary to get the formula to work correctly. The following spreadsheet template is based on the Erlang B formula:

Spreadsheet Tables 1  A B C D E F G H I

1 LOAD .3857              

2 LINE 0 1 2 3 4 5 6 7

3 FACTORIAL

1 1 2 6 24 120 720 5040

4                  

5 TOP 1 .3857 .0744

.0096

.0009 .0001 5e-6 3e-7

6 BOTTOM 1 1.386 1.460

1.470

1.470 1.471 1.471

1.471

7                  

8 LOST % 1 .2783 .0509

.0065

.0006 5e-5 3e-6 3e-6

9 CARRIED%

0 .7217 .9491

.9935

1 1 1  

10                  

11 TOTAL CARRIED

0 .2783 .3660

.3831

.3854 .3856 .3856

.3856

12 OVERFLOW

.3857 1073 .0196

0025 .0002 2e-5 le-6 7e-8

Spreadsheet Tables 2

1 LOAD .3857              

2 LINE 0 1 2 3 4 5 6 7

3 FACTORIAL 1 1 2 6 24 120 720 5040

4                  

5 TOP 1 .3857 .0744

.0096 .0009 .0001 5e-6 3e-7

6 BOTTOM 1 1.386 1.460

1.470 1.470 1.471 1.471 1.471

7                  

8 LOST % 1 .2783 .0509

.0065 .0006 5e-5 3e-6 3e-6

9 CARRIED% 0 .7217 .9491

.9935 1 1 1  

10                  

11 TOTAL CARRIED

0 .2783 .3660

.3831 .3854 .3856 .3856 .3856

12 OVERFLOW .3857 1073 .0196

0025 .0002 2e-5 le-6 7e-8

13 THIS LINE 0 .2783 .0877

.0171 .0023 .0002 2e-5 le-6

Building

This spreadsheet allows the user to enter the Erlangs of traffic and calculates the traffic carried by each trunk per hour. One spreadsheet should be constructed for each hour of operation and the totals combined for each line. Cell B1 contains the load in Erlangs. As done is Spreadsheet 1. Row 2 is the line number. Row 13 is the traffic carried by each tie line. Row 8 is the part lost and is equivalent to the grade of service, P as in the formula.

Formulas

  A B C D E

1 Load in Erlangs

.38565      

2 Line Number

0 =B2+1 =C2+1 =D2+1

3 Factorial 1 =B3*C2 =C3*D2 =D3*E2

4          

5 Top of Equation

=$B$1-B2/B3

=$B$1-C2/C3

=$B$1-D2/D3

=$B$1-D2/D3

6 Bottom of Equation

=$B$1-B2/B3

=B6+$B$1-C2/C3

=C6+$B$1-D2/D3

=D6+$B$1-D2/D3

7          

8 Part Lost % =B5/B6 =C5/C6 =D5/D6 =E5/E6

9 Part Carried %

=1-B5/B6 =1-C5/C6 =1-D5/D6 =1-E5/E6

10

         

11

Total carried in Erlangs

0 =C9*$B$1 =D9*$B$1 =E9*$B$1

12

Overflow to next line

=$B$1 =$B$1-C11 =$B$1-D11

=$B$1-E11

13

Carried by this trunk

0 =B12-C12 =C12-D12 =D12-E12

Formulas

1 Load in Erlangs

.38565      

2 Line Number

0 =B2+1 =C2+1 =D2+1

3 Factorial 1 =B3*C2 =C3*D2 =D3*E2

4          

5 Top of Equation

=$B$1-B2/B3

=$B$1-C2/C3

=$B$1-D2/D3

=$B$1-D2/D3

6 Bottom of Equation

=$B$1-B2/B3

=B6+$B$1-C2/C3

=C6+$B$1-D2/D3

=D6+$B$1-D2/D3

7          

8 Part Lost % =B5/B6 =C5/C6 =D5/D6 =E5/E6

9 Part Carried %

=1-B5/B6 =1-C5/C6 =1-D5/D6 =1-E5/E6

10

         

11

Total carried in Erlangs

0 =C9*$B$1 =D9*$B$1 =E9*$B$1

12

Overflow to next line

=$B$1 =$B$1-C11 =$B$1-D11

=$B$1-E11

13

Carried by this trunk

0 =B12-C12 =C12-D12 =D12-E12

Explanation

Column A has the labels. Cells B1, B2, B3, and B1 have data. Any reference to Cell $B$1 is fixed. In a Spreadsheet the $ signs anchor the cell reference so that when a formula is copied it doesn’t change. When building this spreadsheet using the fill command will save a lot of typing. This spreadsheet can be expanded to the right to include as many as 30 tie lines. After 30 lines the factorial numbers become so large that the spreadsheet can't handle them.

Combining Totals

After completing a spreadsheet for each hour then combine then to get a total for each line for the day. VoIP as circuits between two PBXs has cost associated with it. It can and should be analyzed to see if it is cost effective.

END

For the telecommunications manager or student with access to a PC and any one of a variety of commonly used spreadsheet programs, VoIP or tie line problems become easy to solve once the formulas are entered. Use of this spreadsheet template would be worth adding to the telecommunications manager's repertoire of techniques.