Goeller on Telecom Traffic

A First Course in
Telephone Traffic Engineering

In Chapter 6, the general approach to single group design was discussed. It is perfectly possible to have several "single groups" in a PBX: we might have one group of WATS lines or access lines to a specialized carrier, a group of local CO trunks, one or more groups of FX trunks to nearby metropolitan areas, etc. But, if each group were self-contained and responsible for all the traffic to its geographical region, single group design would be quite satisfactory.

Unfortunately, single group design ceases to be acceptable in even very simple situations, particularly when a group contains a small number of circuits. Our general principle of "building up group size" is based on the idea that large trunk groups are self-loading; they get high occupancy per circuit with a good grade of service because the more trunks there are in a group, the higher the probability that at least one of them will be available for a new call when it enters the system. With small trunk groups, we have to turn to the other techniques.

We can queue to pack calls into a small single group, but queuing often costs money, and the delay can become quite large under overload conditions. Thus "cream skimming" becomes a technique of considerable interest. Historically, when the telephone company went from manual queuing to automatic alternate routing with operator toll dialing, the same volume of traffic was handled on the same number of circuits without queue delay. Machinery can handle complex alternate routing schemes, all of which are based on cream skimming; there are limits to the complexity operators can handle, particularly under stress conditions.

Cream skimming is based on the general idea that the first choice trunk gets the most traffic. If you have one FX line to San Francisco and you give it first shot at all San Francisco calls before trying the WATS group, you will keep the FX line quite busy. Further, if San Francisco calls arriving when the FX line is busy are immediately overflowed to WATS, toll or some other group of facilities, the caller will not even know that a cost reduction technique has been in action.

For a cream-skimming design to be economical, the least used cream skimmer must cost less per minute than the most used trunk in the overflow group. The right hunting order and a means for recording traffic per trunk make this easier to study but designers of telephone switches, whether Bell, Independent or Interconnect, seem to delight in equalizing the traffic over the circuits available in a given group. When we had mostly electromechanical switches, equalizing their wear made sense. With mostly electronic systems today, it makes almost no sense at all. An exception comes from the possibility that the first choice trunk in a group is bad; if it is always seized first, a lot of people are going to have a problem, particularly in times of light traffic. Fortunately, our programs permit us to estimate how traffic would have been distrubuted with "rotary" hunting.

Notice that hunting order does not affect the total traffic carried on a given trunk group. Whether the same start point is used each time the PBX hunts for an idle trunk, or a different start point is used to equalize the load, the traffic carried by the group is the same. If we take the total carried traffic and put it into programs like CARRIED (for hourly traffic) or B1-MONTH or B2-MONTH (for monthly traffic), the computer estimates traffic per trunk. If the cream-skimmers are full period circuits and we know the monthly traffic that would have been carried on the least used trunk in the cream-skimming group with sequential hunting, we can easily find the cost per minute to compare with WATS, toll or specialized carriers.

If the first choice trunk carries the most traffic, and if we actually have the hunt sequence set up to work correctly, letting the first choice trunks be a different kind of beast offers us a chance to save money. The classic situation, FBD first followed by MT WATS, was used for years. But the new WATS tapered rates require something different. Today, FX to WATS or specialized carrier is often a better bet. The FX lines skim the cream, but they are full period circuits with a very steep Swooping Gull diagram. We have to make sure they are fully loaded; if they are lightly loaded, the cost per minute for the calls they carry can be quite high.

Let's assume we are in New York and have a group of 5 Service Area 5 WATS lines, as we have discussed above several times. Further, let's assume that we know, from bill analysis, that of our 400 hours of traffic, 150 hours go to San Francisco. How do we deal with the possibility of FX lines?

Well, we know that, if we offer 150 hours of traffic to one or two San Francisco FXs, they will not carry it all. Rather, they will carry some but, when the FX group is busy, San Francisco traffic will overflow and some will still go WATS. Cost per minute on the FX group may be less than on WATS, but pulling traffic out of the WATS group will reduce its load, make the average traffic per trunk smaller, and thus make the average cost per minute higher.

At 400/5=80 average hours per month, a Rate Step 18 WATS line will cost $1598.80, so we should be able to make a saving with our $1000 FX. The question is, how full must we run our FX lines to break even. At 80 hours, TAPRD shows a cost of 33.31 cents per minute, or about $19.99 per hour. Thus we have to pull out $1000/19.99= 50 hours. Can we do it? (For simplicity, we are ignoring the message unit and toll cost that might be added to the cost of the FX line, something we would never actually do in practice.)

Call up B3-MONTH for the computer. B3-MONTH works on offered traffic, and permits us to adjust the window available for its use. We give it the 150 hours offered to San Francisco, 10% overhead factor, and 22 days a month. It then asks us for the time window. Because of the time differential between the east and west coasts, the window for practical calling is only 6 hours, rather than the 9 we usually use (which is based on business hours at one loction and the related telephone rates). We use 6 hours, 5 minute calls, and assume 5 FX lines in the group. We won't need that many, but we will have the informaion available to pick the cut-off point.

The first information the program gives us (see Printout 7-1) is hourly traffic at the full busy hour load. The first FX line will then carry 0.65 hours, and the second, 0.51. In the side hours, from the next two screens, we see the traffic fall off and the ration of first to second increase, but finally we get to the screen that shows how the traffic will distribute during the month.

The first FX line will carry about 64 hours, while the second, if we decide to use it, will carry only 42. If 50 hours is the break-even point, we can only use one FX line if we want to stay less expensive than WATS. The last screen summarizes the operation with 5 trunks. Let's go around again with just 1 FX line and look at the last screen. We see that 150 hours is equivalent to 1800 calls, and we only carry 764 of them. The rest go back into the WATS group. The WATS cost per minute will go up slightly if we pull our 64 hours out. TAPRD shows the increase to be from 33.31 cents per minute to 33.98. But TAPRD also shows that the total WATS cost will drop from $7994 to $6851, a saving of $1143. This is what we could save by spending $1000. It it worth the effort for a net saving of $143?

We could, of course, drop one WATS line. Then, if we can get the 4 that remain to carry our 336 hours, the cost will drop to $6336 and our saving will be $658. This is more like it. But we will have to see the impact on grade of service in the WATS group before we are done.

There is now (December, 1982) a moderate difference between hourly costs of WATS circuits in different service areas. If we plot a Multi-Gull diagram, as in Fig. 7-1, we see that we can make much larger savings if we put Service Area 1 calls into a Service Area 1 WATS circuit than into one for a higher numbered Service Area. But we have to be careful. When we plot toll costs on the same diagram, we see that there are some calls that are always cheaper going toll than WATS. There is no way to use WATS from Philadelphia to Camden, or New York to Jersey City, to save money. People in Los Angeles or San Francisco are not troubled by such problems. To make an intERstate call, they have to go at least 150 miles, minimum, and can usually use WATS economically for all interstate calls.

Fig. 7-1. Multi-Gull Diagram for New York WATS Service Areas.

But, to return to our design problem. We have traffic scattered all over the country, near and far, and we want a network to handle it. What do we do? We try the cream-skimming trick, but with a little more sophistication. We use Fig. 7-2 as our basic prototype, and and have a small number of circuits (typically, 1) to each WATS service area 1 through 4.

Fig. 7-2. ARS Scheme Using WATS.

Then we put in a group of 2, 3 or 5 Service Area 5 circuits, whatever the traffic demands. SA 1 traffic, finding its circuits busy, overflows to SA 2. Traffic overflowing SA 2 goes to SA 3, 3 to 4 and everything that overflows goes into SA 5. Maybe, during overload periods, we pull the plug and let traffic overflow SA 5 and go toll.

Now, in setting up a network like this, we have to pay attention. In the first place, there is going to be a lot of traffic that cannot go over our WATS lines. We have to deal with intRAstate traffic on other facilities, for instance. Further, there is no point in calling 800 numbers via WATS lines. And, at least at the moment, telephone numbers with 555 as the office code are free calls. So we don't want to put them over WATS. Calls to other countries will also have to find another route. We will simply exclude such calls from this discussion.

This says we must have a pretty smart machine for Automatic Route Selection (ARS). It must look at the Area code, relate it to a selection scheme, and have a selection scheme starting with each WATS Service Area. If the first choice trunk group is busy, the group to the next higher SA is tried, then the next, and so on. Traffic for SA 5 will, of course, get a shot at the SA 5 circuits only, unless overflow to toll is permitted.

How can we possibly find an optimum network here? Well, we could use individual traffic programs, or paper tables, but it would take a lot of work. What we do is use the MULTI-B program family. MULTI-B1, MULTI-B2 and MULTI-B3 are multi-group programs similar to the B1-MONTH, B2-MONTH and B3-MONTH single group circuits. The first assumes all hours are busy hours, the second uses a shaped day, and the third uses offered rather than carried traffic, still keeping the shaped day. These programs find the traffic on each group, price it out, and present the total price and grade of service. Thus one can make many exeriments to see how different network configurations will work out.

Printout 7-2 shows a sample run of MULTI-B2 for 600 hours of carried traffic, using a 10% overhead factor, 22 business days per month, and traffic destined for Service Areas 1-4 as 25%, 15%, 10% and 5%. The remainder goes to SA 5. For the first run, it usually pays to allow one trunk per hundred hours and to put all the trunks in SA 5. After a few seconds of deliberation, the computer finds, among other things, a total cost of $11,403.90, a cost per minute of 31.68 cents, and a busy hour grade of service of B.27. For the next run, we can try 2 trunks for SA 1, 0 for 2, 3 and 4, and 4 for SA 5. Our cost now drops to $10,663.60, a result of savings on the SA 1 traffic at 25.63 cents per minute, but our grade of service goes to B.393. We can put in any combinations we like, and see how cost and service vary. A fairly good network here has 1 trunk for each SA 1-4, and 4 in SA 5. Total cost is $11,198.90, and busy hour grade of service is B.12.

Notice that the circuits to all the lower numbered SAs are loaded fairly heavily because they get first shot at all traffic intended for their area, plus traffic that overflows from lower numbered SAs. Thus the average usage, on which WATS costs are based, is kept fairly high, and the cost per minute rides down the Swooping Gull curve.

The final group, for SA 5, illustrates the other approach: building up group size. Everything overflows into the several circuits for SA 5, along with the traffic that only SA 5 can handle. Thus we get, once again, fairly high usage.

Grade of service, as calculated by this program, uses the basic Erlang B definition: lost traffic divided by offered traffic. And traffic experts will immediately note that it is not correct, just as this program, itself, is not quite correct. Where the trouble lies is relatively subtle: overflow traffic isn't random. We assume offered traffic is random, but after the SA 1 traffic is cream-skimmed, the traffic overflowing to SA 2 is not as random with the carried traffic pulled out. It joins with the random traffic offered to SA 2, but once again, the overflow from SA 2 is less random. By the time we get to SA 5, the overflow traffic may be pretty far removed from random. In principle, one can only add random traffic quantities; one cannot add non-random traffic to random traffic and get the right result.

There is a whole branch of traffic theory, developed by R. I. Wilkinson of Bell Labs, called "equivlent random" theory, and it provides a way to estimate how much random would be equivalent to the non-random overflow of a given trunk group. But this is not something to play with in a first course.

We can go ahead and pretend that we can add non-random traffic to random traffic; all we have to keep in mind is that our grade of service is going to look better than it really is. What actually happens is that we have some random traffic trying each group. Second, when a lot of traffic overflows, it is nearly as random as the offered traffic, but when only a little overflows, its non-randomness tends to be swamped out by the random traffic for the next group. Finally, because so much business calling goes to the east and west coasts in the US, SA 5 almost always gets a lot of random traffic to swamp out the non-random overflows from the lower numbered service areas. It ain't perfect, but what the hell.

MULTI-B3 is provided for instances when offered traffic is used, and lost traffic is permitted to overflow into toll. In addition to the usual things the programs want to know, it now asks for an average cost per minute for toll. In Printout 7-3, I used $0.50, and offered 600 hours to 1 trunk in each of the lower numbered service areas, and 3 in SA 5. The program finds how the traffic distributes, how much goes toll, and what the total cost turns out to be. Grade of service is given for the WATS trunks only...actual grade of service is "perfect" because all lost traffic goes toll and is not blocked, held or delayed. With these assumptions, we can now try many different configurations, testing each for minimum cost. Adding one more SA 5 circuit, for instance, saves $236, the cost of toll being as high as it is.

The Specialized Common Carriers such as MCI, SP, SBS, etc., do not, as yet, cover the entire country except when they resell WATS. Then, their rates are higher than when they use their own facilities, for obvious reasons. Thus, to make most economical use of such services, you must have a very smart ARS machine. It must be able to pick not only area codes but office codes to route calls to the specialized carrier of your choice. Calls that do not go to the major cities in the US have to be routed via WATS or toll.

On the specialized and resale carriers, dial-up service is priced to be less expensive than toll, but only by about 10 to 20%. However, you reach them via your dial 9 CO trunks, so blocking and queuing are minimized as far as your system is concerned. You do, however, have to dial the access number for the SCC, a billing code, and then the desired called number. This usually adds up to at least 22 digits and is a bother. ARS can be arranged to handle most of this (and, to preserve secrecy of the billing number, should be used), but only some ARS systems go from step to step in the outpulsing based on a positive signal from the SCC. Many just time out and let 'er go.

In addition to this probability of a call going "high and dry," transmission problems arise. The public network was never designed to have three connections back to back; this is exactly what happens on a call via telco to the SCC, via the SCC to the distant city, and via telco to the called number. That it works at all is a minor miracle.

Direct access to the SCCs, usually called network services, is a better approach where practical. MCI and Southern Pacific offer "postalized" pricing--cost is independent of distance. Further, their tapered rate pricing, with break points, like WATS at 15, 40 and 80 hours, is less expensive for the parts of the US they cover than is the lowest cost AT&T offers for Service Area 1. Run TAPRD for rate steps 23 and 24 to see. Access lines cost more; with MCI, the cost is $85 a month. Thus at very low usage, MCI may cost more than WATS, but for any appreciable usage, it costs much less. Further, only one group of access lines is needed; one need not use the approach of MULTI-B2. But reaching non-MCI cities requires additional routing capabilities.

Cream-skimming is a very powerful tool when several different types of facilities, with ever increasing areas of coverage, are available. Usually, the facilities of the most limited coverage, if packed full, offer the greatest opportunities to save; thus they are first choice as cream skimmers. Broader coverage, as with MCI network services vs. FX, or WATS vs. MCI, usually costs more, and should be a later choice. But one must be careful not to offer traffic to circuits that cannot or should not carry it: do not offer intra-state traffic or calls to 800 numbers to inter-state out-WATS, for instance. Such requirements make system routing tables quite complex.

Cream-skimming works well for first-choice circuits, but building up group size is a good technique for the group of last resort. Letting all inter-state traffic overflow into Service Area 5, whether it first looks at FX, specialized carrier, or lower numbered service areas, can go a long way toward improving service at relatively low cost. By and large, queuing can be avoided while still effecting large savings.

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Copyright 2006 Lee Goeller. All Rights Reserved.