Goeller on Telecom Traffic

A First Course in
Telephone Traffic Engineering

There is seldom economic incentive to optimize the use of something that is plentiful and free. Only when a necessary commodity is scarce (as with radio spectrum) or expensive (as with most other things) do we have to take steps to arrange for economical behavior. We want to obtain the best Grade of Service possible at the lowest cost; if trunks were free, we'd just use more of them.

When we plan to design a communication network, then, it becomes painfully obvious that we have to know the costs of the various alternatives so that we can choose among them. Costs of making telephone calls differ as a function of distance and duration of call, time of day and day of week, vendors being used, political environment (particularly intRA vs. intER-state), and a few other things. Thus it is not unusual to find "least cost routing" schemes in place that cost twice as much per minute as toll. Since one need never pay more than toll (Direct Distance Dialing or DDD), it pays to know just how much DDD costs in the first place. Fig. 5-1 shows a plot of daytime toll costs as a function of distance. Note that costs are relatively flat beyond about 400 miles.

Fig. 5-1. Daytime toll (DDD) cost/minute vs. distance.

There are, of course, systems that actually save money, but some do it at the expense of putting the customer out of business by having too few circuits or circuits over which humans cannot talk; there are many ways a network can do more harm than good. But let us concentrate on cost: it is the way we keep score. If you don't keep score, you can't tell who is winning. Nobody wants to be a loser.

If the only way we could make phone calls from a PBX were to dial 9 for outside and go, there would be no network design required to help the customer. We would need only to provide a suitable number of CO trunks, and that would be that. And as long as CO trunks were cheap, it wouldn't matter if we had several too many. Under such circumstances, there would be no challenge.

But today, in some states, CO trunks cost $70 a month, each. This can add a penny a minute to the local or toll charges for placing calls and, in terms of the cost of the former, can be an appreciable percentage of the cost. In other states, there are new wrinkles in the tariffs from the telephone companies that require special attention: for instance, a trunk itself may cost $40 a month, but to have the CO hunt over a group of busy trunks to find one idle may add a cost of $30 a month, per trunk. Further, DTMF (Touch-Tone) signaling may cost $7 a month. Now, it used to be a maxim that one big group of "combination trunks," handling incoming directory number calls and outgoing dial 9s, was the way to go. One big group rather than two smaller groups saved trunks and dollars. But now we suddenly find that, although two one-way groups require more circuits, they cost less. Only incoming trunks need hunting at the CO, and only outgoing trunks need DTMF signaling. Thus the price difference of $40+$30 vs. $40+$7 requires a change of strategy.

Life is even more complex these days. IntRAstate calls and circuits are not priced the way IntERstate calls and circuits are. Further, there are a great many new companies in the communication business, all offering circuits and services at prices that defy simple comparison, all varying as a function of time of day and day of week and sometimes exhibiting independence of distance. It becomes evident that any form of network design can be meaningful only if it is based on costs as well as traffic theory.

Because the great majority of businesses operate only during business hours, and rates for telephone calls are highest then for obvious reasons, we generally base our designs on calls falling during the 9 to 5 "window." If we can't make savings against the highest DDD rates, it will be even harder to save against evening and night rates which are much lower. But our window is tricky. Between New York and California, it is only 6 hours long (from 11 AM to 5 PM in New York or 8 to 2 on the coast, with two different lunch hours). For overseas calling, it is even smaller. The available window is as important as the actual amount of calling. After hours savings are possible and often significant, but, in general, we shouldn't count on them compared with savings made during the day.

In general there are three ways of pricing facilities that carry telephone calls. We can pay a flat rate per month for full period circuits in which case, the more we use the facility, the less it costs per minute. Alternatively we might pay so much per minute nearly independent of how many minutes we use. Finally in between these two extremes we might choose facilities that work at tapered rates, so that the more we use them the less expensive they become, but the price decrease is quite slow.

Obviously, tie-trunks and FX lines fit the first category; DDD, Execunet, Sprint and others fit the second, and WATS and MCI and SPC "network services" (direct access) fit the third. Further, prices differ considerably within each category. Any design we attempt must be based on both total cost and cost per minute so that we can make reasonable comparisons. Let's first look at total cost.

The pricing of tie-trunks is relatively simple. We have to pay for the trunk circuits in the PBXs on each end, and for the facility in between. In a rented PBX, the monthly cost of the trunk circuits can be obtained from the utility or the vendor; in an owned PBX, the monthly equivalent of the trunk circuit purchase price should be calculated and used.

The facility itself is rented at so much per mile per month, with the first several miles costing a lot, the next several miles costing less, and increasing mileage costing even less in a "tapered rate" pattern. (Tapered rates can also be a function of time as well as distance, as we will see in WATS and other services). In addition to these distance sensitive charges, tie-trunk facilities require "channel terminals" at each end, which add a fixed monthly cost. When we add up all these pieces, we have the total monthly cost for a tie-trunk. Even if we do not make a single call over it, the cost is the same. Obviously, we want to make as many calls as possible over our tie-trunk to get the cost per minute to come down to something reasonable.

FX lines are also full period circuits, and are priced very much like tie-trunks. But here, in addition to the facility cost, we have a PBX trunk circuit only on the "closed end" at the PBX; at the "open end," we have a regular CO trunk circuit, billed from that remote central office. But there is more. Few business trunks today are "flat rate." You have to pay one or more "message units" for outgoing local calls passing through them. And, of course, you have to pay toll charges for calls going a greater distance into the public network. These usage sensitive charges must also be added to the monthly cost. All these factors must be considered in FX pricing.

With tie-trunks it is possible to reach distant PBX, dial (or some other code) and go "off-net to complete calls via the public network. By expanding the use of the tie-trunk to handle off-net calls as well as calls to extensions at the distant PBX, better occupancy at lower cost per minute can be achieved But to get the correct cost with off-net calling, some portion of the cost of each PBX's CO trunk circuits must b added along wit the message unit and toll charges incurred by the other tie-trunk-connected PBX

Figuring the cost of WATS, and the similarly priced network services of MCI and SPCC, is somewhat more difficult. We have the cost of a trunk circuit in our PBX, to which must be added the cost of the access line to the long haul carrier. Then, separately, we have the usage cost. Usage cost is figured at tapered rates on the basis of the average number of hours per circuit for the month on a given group of circuits (total use divided by the number of circuits in the group). This average use is billed at one rate for the first 15 hours, a second and lower rate for the next 25 hours (to 40 hours), at a third rate between 40 and 80 hours, and at a fourth rate for hours of use beyond 80. Daytime calls in the 9 hour window from 8 AM to 5 PM are measured on one clock and billed at a fairly high tapered rate, evening calls between 5 and 11 PM, Sunday through Friday, are timed on a second clock (at a lower rate), and night calls are timed on a third clock. There is no tapered rate for the night calls.

Once the cost for an average circuit is found the total cost for the group is obtained by multiplying by the number of circuit in the group. To do this you can call up TAPRD on you computer instead. But not just yet, because it does a few other things you will need to know about.

When we have full period circuits, it pays us to pack them full so their cost per minute is low. This is the basic strategy. We used to do this with "Full Business Day" WATS, before the FCC took that offering away from us, and we can, at least for the time being, still do it with FX lines and tie trunks, using them as first choice in a routing scheme. With the present "tapered rate" WATS, as well as the direct access MCI and SPCC network services, the advantages to be gained from packing circuits full are less, but still offer a chance to save when used with care. A final overflow to fixed rate toll or specialized carrier is our route of last resort.

Specialized Common Carriers such as MCI, SPCC, Western Union, SBS and other companies have their own facilities; resale carriers differ in that they rent facilities from AT&T and the specialized carriers and simply resell to the end user. Because they make heavy use of WATS, most resale carriers cover the entire United States. In general, costs via WATS are greater than costs via full period owned or rented circuits, so several rates may exist for similar distances, depending on destination.

The point to all this, however, is that some means must be available to demonstrate clearly how costs compare. Knowing the total cost is important, but it is also necessary to know cost per minute and how that cost varies as a function of total monthly use. To that end, I have invented the "Swooping Gull Diagram."

The "Swooping Gull" diagram plots cost per minute of telephone usage as a function of total hours of monthly use of some particular facility. One assumes a number of different usage values, finds the total cost, and divides by total number of minutes of usage at each point to plot the graph. Fig 5-2 shows a typical example.

Fig 5-2 A Swooping Gull Diagram comparing DDD, WAT and FX

Fig 5-2 shows daytime cost per minute vs. hours of use per circuit for WATS FX and DDD (Toll). DDD average cost per minute, based on 5-minute calls, runs flat because we don't get any quantity discount for toll via CO trunks. Actually, the cost of the CO trunk should make the curve slope upward at the left hand side but, because the CO trunks are needed anyhow for the vast number of local incoming and outgoing calls, we ignore their effect on toll cost. The FX curve is more interesting; it swoops down from upper left toward lower right, looking much like a gull diving on a fish. Clearly, the more we use an FX line, the less it costs per minute. Conversely, if we use it lightly, a cost of $1 per minute may result. For simplicity, this particular curve does not include message unit charges at the open end.

The remaining curve compares the tapered rate of WATS with DDD and FX. As can be seen, the more we use a WATS line, the less expensive it becomes per minute...but the cost per minute does not go down very rapidly. Further, as we increase the number of WATS lines in a group, it becomes harder to increase the average use per trunk with queuing, retries, or anything else. Aggravation increases so much faster than savings that it usually pays to add a few extra circuits.

Calculating total WATS cost and cost per minute is relatively simple, but it is time consuming, tedious and leads to errors. It is much better to let the computer do the job for us. This is the point where we want to call up TAPRD and run it a few times to see how to plot an SG Diagram, and also to price out tapered rate facility use. The program will ask first for a "Rate Step." There are 22 AT&T rate steps used to identify the 6 service areas presently available; different states use different rate steps. In California, for instance, Rate Step 7 is used for Service Area (formerly Band) 1, while in New Jersey, Rate Step 1 specifies costs for Service Area 1. In New Jersey, you do not have to go as far to get to the state line as you do in most of the major cities in California. A tariff page include in Appendix II tells which Rate Steps apply to which Service Areas in different states. Because MCI and SPC network services are postalized, they do not vary with distance. They can be called up at Rate Step 23 and 24, respectively.

After putting in the right Rate Step, the program will ask whether you are interested in day, evening or night rates. Next, the program asks for the number of hours carried and the number of trunks in the group. If you put in so much traffic that the average per trunk is expected to be more than 220 hours, the program will give you a chance to reconsider. There may be 741 hours maximum in a month, but during the daytime window, there are only about 200 hours (22 days x 9 hours per day). Because a trunk must be idle in order to be reseized, an average use even approaching 200 hours during the business day is to be looked upon with suspicion. Printout 5-1 in Appendix IV shows the results for 632 hours of daytime RS 18 traffic on 7 circuits.

When run with a given number of hours of day, evening or night traffic per month on a specified number of circuits, TAPRD gives the total cost and cost per minute at the desired level. It also gives the cost per minute at 15, 40, 80, and 200 average hours per month (the break points in the tariff pricing). This permits the designer to get a feel for not only the cost but also the variations in cost with greater or smaller amounts of traffic.

The break points on an SG diagram can be taken from the standard values shown; using one trunk and various other amounts of traffic, the program can, on successive runs, provide additional costs per minute where needed. Thus for any given Rate Step (or Service Area), a Swooping Gull Diagram can be plotted quickly.

Knowing cost per minute, we will try to pack calls into certain circuits and use others as second or third choice. To do this effectively, we must know how many hours each trunk will carry, as well as cost per minute. Then we can tell how to set up our routing tables and estimate our savings. Thus we must return to traffic theory to see how traffic distributes itself over a variety of trunk groups, and learn how to manipulate these groups to make that distribution agree with the requirements of cost minimization.

There are just three techniques or tools for packing traffic into circuits the way we want it to go:

• Building Up Group Size
• Cream Skimming
• Queuing

We have already seen that a large group of circuits will carry more traffic per circuit for the same grade of service than will two smaller groups adding up to the same total number. Runs of ERL-GS or a glance at Table I demonstrate the point quite well. Just run down the right hand column and see how the average occupancy per circuit increases with increasing group size. Thus, building up group size can give us higher occupancy per circuit and, for some kinds of pricing, lower cost per minute.

The second technique is the opposite of the first: when we use Cream Skimming, we give first choice to full period circuits, typically FX lines. For those calls they can handle, they are given first shot at the appropriate traffic by the Automatic Route Selection mechanism in our PBX or stand-alone toll router; if an FX line is free, it carries a call it can serve. If the FX group is busy, then the ARS mechanism overflows that call to WATS, Specialized Carrier, or whatever. By letting the FX lines skim the cream, they can be packed full to generate a low cost per minute. But note that they drain traffic out of the overflow group, decrease its total usage, and may increase cost per minute for that group. With proper design, the overall total cost will be less.

Our third technique, Queuing, is also used to pack circuits full to get a low cost per minute. Obviously, it does not pay to queue if we do not reduce the cost per minute. But there are places where queuing works very well indeed.

Fig. 5-3, almost a repeat of Fig. 3-1, illustrates how queuing and building up group size increase busy hour occupancy per trunk. The four solid curves plot the occupancy from Table I at B.01, B.05, B.10 and B.20. As can be seen, all the curves slope up and to the right, with higher occupancy for larger groups; for large enough groups, occupancy would approach 1, or 100%. Obviously, it is impossible to have more than 100% occupancy of any facility.

Fig. 5-3. Increasing occupancy per trunk with group size.

The dashed curves are based on D1, the average delay on all calls, measured in holding times. Only three curves are shown: occupancy for D1 = 0.1 holding time, 0.5 holding time, and 1 holding time. For small groups, the dashed curves for half and one holding time show much better occupancy for circuit; a short delay of 0.1 holding time (30 second for 5 minute calls), works about as well as B.15 service. With B.15, retries will be quite common, so again queuing of a sort will take place.

Fig. 5-3 has one more point of interest: the left-hand column of figures. On the left, we have the busy hour occupancy from 0 to 1, but the other column represents the average occupancy per month that matches the busy hour occupancy. It permits us to make a rough estimate of grade of service by interpolating between the curves at the number of trunks in the group. The left-hand column of numbers assumes 22*6 or 132 busy hours equal a month, and it shows just how hard it is to get average occupancy to increase. With a 5-trunk group, to get 66 hours of average use (330 hours total), a grade of service of B.10 is indicated in the busy hour. If we let service degrade to B.20, we get a busy-hour occupancy of about 65%, corresponding to about 84 hours per month. With queuing, we can easily approach 100 hours a month, average occupancy, on our group of 5 circuits.

Cream Skimming can do more to build up occupancy than might be supposed. Not all hours are busy hours and, as we have seen in connection with Fig. 3-2, a bigger proportion of the smaller side hour traffic goes on first choice circuits. Over the course of a month, this mounts up, and cream skimmers turn out to be quite effective.

Comparing costs of different facilities is made easier by graphical constructions such as the Swooping Gull Diagram. When cost per minute as a function of monthly circuit use is known, it is possible to see how varying usage can affect what we pay. Full period circuits are seen to swoop down steeply on an SG Diagram, tapered rate circuits swoop down much more gently, and DDD and other flat cost per minute circuits do now swoop at all. When rates are based on the average use per circuit in a multi-circuit group, it is seen that increasing the average use to obtain lower rates becomes more difficult as the group size increases. However, larger group sizes just naturally carry more traffic per circuit for the same grade of service than do smaller groups; to make small groups carry more traffic without degrading service, Cream Skimming can be employed.

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Copyright 2006 Lee Goeller. All Rights Reserved.