6 Telemanagement #187

that actually works — uses mathematical An Introduction to formulas that form the basis of the disci- pline called “traffi c engineering.” Some B and Erlang C of them are easy for anyone to use; others require expert support, or at least special- If you make decisions about networks, PBXs, ized software. If you make confi guration or call centres, you must understand these concepts decisions about networks, PBXs, or call centres, you must understand the basic IAN ANGUS concepts involved, whether or not you plan to do the calculations yourself.

“Hey, it’s simple arithmetic! We get 3,200 calls And then they will bunch up during that Basic Concepts a day. That’s 400 calls an hour. Each call lasts hour, leading to times when the phones Until recently, anyone using traffi c engi- three minutes, so each person can handle 20 are going crazy and times when many neering techniques had to either master calls an hour. So we’ll need 20 incoming lines lines are free. the mathematics, or learn to use thick and 20 people to answer the phones.” Then you have to take into consid- books of tables based on them. Personal Does that sound familiar? eration the fact that no one can handle computers changed all that, fi rst by Many telephone and call centre deci- 20 three-minute calls every hour without making traffi c programs widely afford- sions are made using just that logic. It’s burning out, and that there is usually post- able, and now by making them available simple, and it’s clear — and it’s absolutely call work to do in addition to talking to on the Internet. Several sources are de- wrong. The problem can be summed up callers. scribed in the box on page 7. in three words: Calls Bunch Up. In short, the “simple arithmetic” ap- But remember the phrase, “garbage in, If you get 3,200 calls in an eight-hour proach will result in too few trunks, too garbage out.” Before you jump to your day, and your calls follow a typical distri- few people — and too many very unhappy browser, be sure you understand some bution pattern, 550 or 600 of them will callers. key concepts. arrive during the busiest hour of the day. The alternative — the only approach Erlang: The basic unit of telecom traffi c intensity. Strictly speaking, an erlang is what mathematicians call a “dimension- It Started in less unit,” representing continuous use of All modern methods for optimizing networks have their one circuit. However, since a single circuit roots in work done by Agner Krarup Erlang, a scientist used continuously carries 60 minutes of who joined the Copenhagen Telephone Company in calling in one hour, one erlang is usually 1908. He set out to solve the key problem in telephone defi ned as 60 minutes of traffi c. If you network design: how many trunks are needed to carry a receive 300 two-minute calls in an hour, given amount of calling? then you received 600 minutes, or 10 er- Imagine a village in which every home has a telephone langs, of traffi c in that hour. connected to a local switch. How many trunks should (For many years, AT&T and Bell the phone company install between that switch and Canada insisted on measuring traffi c in the one in the next village? Erlang saw that there was CCS — 100 call seconds — instead of the no absolutely correct answer. Rather, there is always more convenient but not-invented-here a trade-off between service and cost. In the case of erlang. If you have data in CCS, divide the A.K. Erlang, 1878-1929 the village, there are two extreme options, neither of numbers by 36 to get erlangs.) which is acceptable: Busy Hour: Because “calls bunch up,” ! Provide just one trunk, and let callers wait until it’s available. The cost is low, all traffi c planning has to focus on peak but the service is unacceptably poor. periods. It isn’t acceptable to provide excel- ! Provide one trunk for every local phone line, so no call is ever blocked. The lent service most of the time and terrible service is excellent, but the cost is much too high. service just when customers want to make The problem was to convert that insight into hard numbers that would allow calls. Most commonly, we take the busiest network planners and accountants to evaluate each possibility on the curves hour of each day for fi ve or 10 days during between low and high cost, poor and excellent service. the busiest time of year, then calculate To do this, Erlang conducted the world’s first detailed studies of telephone traffic, the average of those hours’ traffi c load. and then developed mathematical formulas to evaluate the trade-offs. His work was That “Average Busy Hour” fi gure is used enormously influential worldwide. One researcher taught himself Danish to determine the maximum number of just to be able to read Erlang’s papers in their original form. In 1946, the International trunks or people needed. Consultative Committee on Telephones and Telegraphs (CCITT) honoured him by Server: Something that handles calls. adopting the name “erlang” for the basic unit of telephone traffic. For example, in a call centre situation there are two kinds of servers: the trunks

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Finding Erlang On-line Software has replaced the thick books of ! Erlang-Software: Another source for tables that used to be basic equipment for PC traffic software, this one in Australia. anyone involved in optimizing telephone Their Erlang-G program is said to include six networks. The following are some useful common traffic formulas. $40, with multiple- resources. Telemanagement has not tested copy discounts. members.iinet.net.au/~clark/ all of these products, and does not endorse index.html. any of them. All prices are in U.S. dollars. ! Certis Technologies: Their ErlangCalc 1.2 program is ! Erlang Calculator 1.0: An Erlang B program for Palm available in three versions: Standard (Erlang B only, $39); Pro computers. This simple freeware program displays three (Erlang B, Extended Erlang B, Erlang C, Daily Traffic, $69); Deluxe blanks: Fail Rate (Blockage), Traffic, and Lines. You fill in two (Erlang B, Extended Erlang B, Erlang C, Daily Traffic, Spreadsheet and it calculates the third. Available from various sources, for Erlang B Batch-Processing, Graphical Presentation of Results, including www.palmspot.com, www.visorvillage.com, and $89). Free trial versions are available. www.certis.com/. www.palmblvd.com. ! ClienTel: Don’t be dismayed when you find that the home ! Westbay Engineers: A UK company that develops and sells page is in Dutch. Just click on Online Call Center Assistant for traffic calculation software, ranging from Erlang for Excel ($80) to Erlang B and Erlang C calculators and a 24-hour call centre complex network and call centre modeling tools. Their website scheduling program. www.clientel.nl/. features the best on-line traffic calculators we’ve seen, including ! Maths.org: Interested in the math behind Erlang’s formulas? Erlang B, Erlang C, and call centre staffing. They also have an easy There’s a tutorial, including some simple on-line calculators, at web address: www.erlang.com. plus.maths.org/issue2/dar/index.html. ! HTL Telemanagement: Turbo Tables ($595) was the first ! Basic on-line calculators. When you need quick answers, program to add traffic formulas to Excel, and remains one of the these non-commercial sites can be useful. Most use few graphics best. HTL focuses on call centre planning tools, using Hills A, a and download quickly, a major advantage. proprietary extension of Erlang C. www.htlt.com. www.dcss.mcmaster.ca/~qiao/publications/erlang/erlang.html ! Teleopti: A Swedish firm that sells software for call centre mmc.et.tudelft.nl/~frits/Erlang.htm management and optimization. Their website includes a rather www.owenduffy.com.au/electronics/telecommunications.htm complex Java-based Call Center Wizard for calculating trunk and www.cs.vu.nl/~koole/erlang.html staffing requirements. www.teleopti.com. persoweb.francenet.fr/~hilleret/ that carry the calls, and the agents who ers, Traffi c, and Grade of Service. If you — how many trunks are needed to carry answer them. With a voice mail or IVR know any two of those, the formula will your toll-free calls, how many tie trunks system, the servers are ports. calculate the third one. between two offi ces, how many ports into Grade of Service: The probability that Erlang C: Use this formula when a your voice mail system, or some similar all servers will be busy when a call attempt blocked call is delayed — for example, question. Erlang B handles that relatively is made. For example, on a trunk group: when someone calls your call centre and easily, in four steps: P.02 means that there is a 2% probability must wait for an agent to take the call. 1. Collect traffi c data. You need to of getting a busy signal (being “blocked”) It uses the same three variables, plus the know how much traffi c will try to use the when you have a given amount of traffi c average length of each call, to calculate the trunk group, each hour, for fi ve or 10 busi- and a given number of trunks. In a call probability of being delayed and how long ness days. You may be able to use phone centre, the same number would mean that the delay is likely to be. bills, call detail reports, carrier traffi c stud- there is a 2% probability of having to wait These formulas only work if you have ies, or even manual counts — or you may to speak to a human. a large number of independent sources just have to make educated guesses. The of traffi c. For example, 10 people making objective is to produce an hour-by-hour Probability Formulas outgoing calls, with no incoming calls, spreadsheet, showing the number of min- There are many traffi c formulas, appropri- will never need more than 10 trunks, no utes of traffi c in each hour. Divide those ate to many different situations, but two matter what the formula says! A math- numbers by 60 to get erlangs per hour. of them, both developed by A.K. Erlang, ematician will tell you that these formulas Bear in mind that the traffi c on your cover the most common business telecom require “infi nite sources,” but in practice trunks may be greater than actual conver- requirements. they work very well if there are at least 10 sation time — you must allow for dialing Erlang B: This is the formula to use times as many possible sources (callers) time on outgoing calls, and for ringing when a blocked call is really blocked — as servers (trunks or agents). time on incoming calls, for example. for example, when somebody calls your 2. Determine the Average Busy Hour. phone number and gets a busy signal or Erlang B: The Easy One Select the busiest hour of each business tries to access a tie trunk and fi nds it in The most common traffi c engineering day, total the traffi c, then divide by the use. It is built around three variables: Serv- problem involves sizing a trunk group number of days.

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3. Choose a target Grade of Service. In time. That’s quite different from the Erlang B: most cases, a target of P.05 is acceptable, number you must schedule to work each P.10 is terrible, and P.001 is so good that day, since almost no one can be on the most callers will never get a busy signal. phones 60 minutes an hour. 4. Use Erlang B. Calculate the number 4. How does waiting time affect of trunks you need to carry that amount of trunk load? The time a caller spends traffi c with your target Grade of Service. Erlang C: on hold listening to music adds to your At this point, you need to decide wheth- trunk traffic — you can save money by er the answer is acceptable. Usually, that having fewer agents to answer calls, but means deciding whether you can afford that may require adding trunks and/or the number or trunks or ports required. increasing your toll-free service bill. You If not, try reducing the number of trunks may have to do several iterations to and see what the effect is on the Grade of complexity in at least four areas. determine the optimal mix of trunks, Service. You may discover that the differ- 1. What’s included in call times? In a people, and delay. ence is negligible — or you may decide queuing system, traffi c includes not just These issues mean that anyone doing that you have to get a budget increase or “conversation minutes,” but also the time anything more than the simplest delay fi nd some way to reduce the amount of agents spend doing “post-call work” re- calculations — above all anyone doing traffi c. (Are those calls really necessary?) lated to that conversation. Gathering ac- regular staff and confi guration planning The best thing about the various PC curate data on this can be much more dif- for a call centre — should consider buying and Internet traffi c calculators is that they fi cult than just looking at a traffi c study or specialized call centre planning software. make it very easy to do multiple calcula- a toll-free service bill. In theory, your ACD All such programs — despite the fact that tions until you fi nd a balance between cost reports provide the information — but every one claims to be absolutely unique and service you can live with. that only works if everyone has been press- — are ultimately based on A.K. Erlang’s ing the right buttons at the right times. formulas from 90 years ago. Erlang C: More Diffi cult 2. What’s meant by delay? The “Aver- If you are comfortable with the math Because Erlang B is so simple to use (insert age Delay” might be the average of all calls, and at creating spreadsheets, consider two numbers, it calculates the third), many including all the calls that didn’t wait at all, buying one of the commercial programs managers assume that Erlang C will be or it might be the average of calls that actu- that adds traffi c formulas to Excel, making similarly easy. That’s a mistake — even ally experienced a delay. The latter fi gure is it much easier to do multiple “what if” basic Erlang C calculations are diffi cult, usually more useful, but you must be very calculations. and more complex ones can be daunting clear which one you are concerned with. indeed. Also, using averages can conceal situa- very telecom professional should have Erlang C is most commonly used to tions in which most delayed calls wait only Eat least a general familiarity with calculate how long callers will have to wait a few seconds, but some experience very Erlang B and Erlang C. However, whether before being connected to a human in a long delays. That can be a serious cus- you use them yourself or evaluate reports call centre or similar situation. This adds tomer service problem, even if the aver- produced by others, always keep three ages look good. things in mind. Related Reading Most call centres summarize their ! Using math is no substitute for using ! Call Center Management on Fast For- delay objectives in a phrase like “answer your head. If the data you plug in to the ward, by Brad Cleveland and Julia 80% of calls within 20 seconds,” but get- formulas isn’t valid, the answers won’t be Mayben, includes a useful plain-Eng- ting from the Erlang C formula to that any good either. lish discussion of using Erlang C for result can be diffi cult. ! All formulas make assumptions that call centre planning. Order from 3. What’s the hour-by-hour load? With simplify reality. Erlang B assumes that www.incoming.com trunks, you don’t have the option of adding callers who receive busy signals won’t im- ! Tables for Traffic Management and or removing circuits every hour, so you mediately try again. Erlang C assumes Design, by Ted Frankel, seems to be must install and pay for the number that delayed callers will wait on hold in- the only book of traffic tables still in needed under peak load conditions. With defi nitely. For low blockage rates and short print. Lee Goeller’s introduction and people, the peak period determines maxi- queues, those assumptions don’t cause a Frankel’s first three chapters consti- mum staffi ng, but you also need to calcu- problem — but when your service level is tute an excellent brief course in traf- late staff requirements for other times, poor, they can give misleading results. fic engineering concepts. Order from and plan staff scheduling accordingly. ! All traffi c formulas calculate prob- www.abcteletraining.com. This usually means doing separate calcu- abilities, not absolutes. Erlang B and C ! Cisco’s website has useful tutorials. lations for each half hour period in every predict what will happen, on average, Go to www.cisco.com and type “Traf- week you operate. over many hours with similar traffi c. Your fic Engineering” into the search And bear in mind that the Erlang C actual experience in any specifi c hour can box. forecast only tells you how many people be quite different. must be answering phones at any given !

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