An Introduction to Erlang B and Erlang C - VOIP Information

6 Telemanagement #187An Introduction toErlang B and Erlang CIf you make decisions about networks, PBXs,or call centres, you must understand these conceptsIAN ANGUSthat actually works — uses mathematicalformulas that form the basis of the disciplinecalled “traffic engineering.” Someof them are easy for anyone to use; othersrequire expert support, or at least specializedsoftware. If you make configurationdecisions about networks, PBXs, or callcentres, you must understand the basicconcepts involved, whether or not you planto do the calculations yourself.“Hey, it’s simple arithmetic! We get 3,200 callsa day. That’s 400 calls an hour. Each call laststhree minutes, so each person can handle 20calls an hour. So we’ll need 20 incoming linesand 20 people to answer the phones.”Does that sound familiar?Many telephone and call centre decisionsare made using just that logic. It’ssimple, and it’s clear — and it’s absolutelywrong. The problem can be summed upin three words: Calls Bunch Up.If you get 3,200 calls in an eight-hourday, and your calls follow a typical distributionpattern, 550 or 600 of them willarrive during the busiest hour of the day.It Started in DenmarkAll modern methods for optimizing networks have theirroots in work done by Agner Krarup Erlang, a scientistwho joined the Copenhagen Telephone Company in1908. He set out to solve the key problem in telephonenetwork design: how many trunks are needed to carry agiven amount of calling?Imagine a village in which every home has a telephoneconnected to a local switch. How many trunks shouldthe phone company install between that switch andthe one in the next village? Erlang saw that there wasno absolutely correct answer. Rather, there is alwaysa trade-off between service and cost. In the case ofthe village, there are two extreme options, neither ofwhich is acceptable:And then they will bunch up during thathour, leading to times when the phonesare going crazy and times when manylines are free.Then you have to take into considerationthe fact that no one can handle20 three-minute calls every hour withoutburning out, and that there is usually postcallwork to do in addition to talking tocallers.In short, the “simple arithmetic” approachwill result in too few trunks, toofew people — and too many very unhappycallers.The alternative — the only approachA.K. Erlang, 1878-1929! Provide just one trunk, and let callers wait until it’s available. The cost is low,but the service is unacceptably poor.! Provide one trunk for every local phone line, so no call is ever blocked. Theservice is excellent, but the cost is much too high.The problem was to convert that insight into hard numbers that would allownetwork planners and accountants to evaluate each possibility on the curvesbetween low and high cost, poor and excellent service.To do this, Erlang conducted the world’s first detailed studies of telephone traffic,and then developed mathematical formulas to evaluate the trade-offs. His work wasenormously influential worldwide. One Bell Labs researcher taught himself Danishjust to be able to read Erlang’s papers in their original form. In 1946, the InternationalConsultative Committee on Telephones and Telegraphs (CCITT) honoured him byadopting the name “erlang” for the basic unit of telephone traffic.Basic ConceptsUntil recently, anyone using traffic engineeringtechniques had to either masterthe mathematics, or learn to use thickbooks of tables based on them. Personalcomputers changed all that, first bymaking traffic programs widely affordable,and now by making them availableon the Internet. Several sources are describedin the box on page 7.But remember the phrase, “garbage in,garbage out.” Before you jump to yourbrowser, be sure you understand somekey concepts.Erlang: The basic unit of telecom trafficintensity. Strictly speaking, an erlang iswhat mathematicians call a “dimensionlessunit,” representing continuous use ofone circuit. However, since a single circuitused continuously carries 60 minutes ofcalling in one hour, one erlang is usuallydefined as 60 minutes of traffic. If youreceive 300 two-minute calls in an hour,then you received 600 minutes, or 10 erlangs,of traffic in that hour.(For many years, AT&T and BellCanada insisted on measuring traffic inCCS — 100 call seconds — instead of themore convenient but not-invented-hereerlang. If you have data in CCS, divide thenumbers by 36 to get erlangs.)Busy Hour: Because “calls bunch up,”all traffic planning has to focus on peakperiods. It isn’t acceptable to provide excellentservice most of the time and terribleservice just when customers want to makecalls. Most commonly, we take the busiesthour of each day for five or 10 days duringthe busiest time of year, then calculatethe average of those hours’ traffic load.That “Average Busy Hour” figure is usedto determine the maximum number oftrunks or people needed.Server: Something that handles calls.For example, in a call centre situationthere are two kinds of servers: the trunksReproduction in any form prohibited. For additional copies phone 905-686-5050.

July-August 2001 7Finding Erlang On-lineSoftware has replaced the thick books oftables that used to be basic equipment foranyone involved in optimizing telephonenetworks. The following are some usefulresources. Telemanagement has not testedall of these products, and does not endorseany of them. All prices are in U.S. dollars.! Erlang Calculator 1.0: An Erlang B program for Palmcomputers. This simple freeware program displays threeblanks: Fail Rate (Blockage), Traffic, and Lines. You fill in twoand it calculates the third. Available from various sources,including www.palmspot.com, www.visorvillage.com, andwww.palmblvd.com.! Westbay Engineers: A UK company that develops and sellstraffic calculation software, ranging from Erlang for Excel ($80) tocomplex network and call centre modeling tools. Their websitefeatures the best on-line traffic calculators we’ve seen, includingErlang B, Erlang C, and call centre staffing. They also have an easyweb address: www.erlang.com.! HTL Telemanagement: Turbo Tables ($595) was the firstprogram to add traffic formulas to Excel, and remains one of thebest. HTL focuses on call centre planning tools, using Hills A, aproprietary extension of Erlang C. www.htlt.com.! Teleopti: A Swedish firm that sells software for call centremanagement and optimization. Their website includes a rathercomplex Java-based Call Center Wizard for calculating trunk andstaffing requirements. www.teleopti.com.! Erlang-Software: Another source forPC traffic software, this one in Australia.Their Erlang-G program is said to include sixcommon traffic formulas. $40, with multiplecopydiscounts. members.iinet.net.au/~clark/index.html.! Certis Technologies: Their ErlangCalc 1.2 program isavailable in three versions: Standard (Erlang B only, $39); Pro(Erlang B, Extended Erlang B, Erlang C, Daily Traffic, $69); Deluxe(Erlang B, Extended Erlang B, Erlang C, Daily Traffic, Spreadsheetfor Erlang B Batch-Processing, Graphical Presentation of Results,$89). Free trial versions are available. www.certis.com/.! ClienTel: Don’t be dismayed when you find that the homepage is in Dutch. Just click on Online Call Center Assistant forErlang B and Erlang C calculators and a 24-hour call centrescheduling program. www.clientel.nl/.! Maths.org: Interested in the math behind Erlang’s formulas?There’s a tutorial, including some simple on-line calculators, atplus.maths.org/issue2/dar/index.html.! Basic on-line calculators. When you need quick answers,these non-commercial sites can be useful. Most use few graphicsand download quickly, a major advantage.www.dcss.mcmaster.ca/~qiao/publications/erlang/erlang.htmlmmc.et.tudelft.nl/~frits/Erlang.htmwww.owenduffy.com.au/electronics/telecommunications.htmwww.cs.vu.nl/~koole/erlang.htmlpersoweb.francenet.fr/~hilleret/that carry the calls, and the agents whoanswer them. With a voice mail or IVRsystem, the servers are ports.Grade of Service: The probability thatall servers will be busy when a call attemptis made. For example, on a trunk group:P.02 means that there is a 2% probabilityof getting a busy signal (being “blocked”)when you have a given amount of trafficand a given number of trunks. In a callcentre, the same number would mean thatthere is a 2% probability of having to waitto speak to a human.Probability FormulasThere are many traffic formulas, appropriateto many different situations, but twoof them, both developed by A.K. Erlang,cover the most common business telecomrequirements.Erlang B: This is the formula to usewhen a blocked call is really blocked —for example, when somebody calls yourphone number and gets a busy signal ortries to access a tie trunk and finds it inuse. It is built around three variables: Servers,Traffic, and Grade of Service. If youknow any two of those, the formula willcalculate the third one.Erlang C: Use this formula when ablocked call is delayed — for example,when someone calls your call centre andmust wait for an agent to take the call.It uses the same three variables, plus theaverage length of each call, to calculate theprobability of being delayed and how longthe delay is likely to be.These formulas only work if you havea large number of independent sourcesof traffic. For example, 10 people makingoutgoing calls, with no incoming calls,will never need more than 10 trunks, nomatter what the formula says! A mathematicianwill tell you that these formulasrequire “infinite sources,” but in practicethey work very well if there are at least 10times as many possible sources (callers)as servers (trunks or agents).Erlang B: The Easy OneThe most common traffic engineeringproblem involves sizing a trunk group— how many trunks are needed to carryyour toll-free calls, how many tie trunksbetween two offices, how many ports intoyour voice mail system, or some similarquestion. Erlang B handles that relativelyeasily, in four steps:1. Collect traffic data. You need toknow how much traffic will try to use thetrunk group, each hour, for five or 10 businessdays. You may be able to use phonebills, call detail reports, carrier traffic studies,or even manual counts — or you mayjust have to make educated guesses. Theobjective is to produce an hour-by-hourspreadsheet, showing the number of minutesof traffic in each hour. Divide thosenumbers by 60 to get erlangs per hour.Bear in mind that the traffic on yourtrunks may be greater than actual conversationtime — you must allow for dialingtime on outgoing calls, and for ringingtime on incoming calls, for example.2. Determine the Average Busy Hour.Select the busiest hour of each businessday, total the traffic, then divide by thenumber of days.Reproduction in any form prohibited. For additional copies phone 905-686-5050.

8 Telemanagement #1873. Choose a target Grade of Service. Inmost cases, a target of P.05 is acceptable,P.10 is terrible, and P.001 is so good thatmost callers will never get a busy signal.4. Use Erlang B. Calculate the numberof trunks you need to carry that amount oftraffic with your target Grade of Service.At this point, you need to decide whetherthe answer is acceptable. Usually, thatmeans deciding whether you can affordthe number or trunks or ports required.If not, try reducing the number of trunksand see what the effect is on the Grade ofService. You may discover that the differenceis negligible — or you may decidethat you have to get a budget increase orfind some way to reduce the amount oftraffic. (Are those calls really necessary?)The best thing about the various PCand Internet traffic calculators is that theymake it very easy to do multiple calculationsuntil you find a balance between costand service you can live with.Erlang C: More DifficultBecause Erlang B is so simple to use (inserttwo numbers, it calculates the third), manymanagers assume that Erlang C will besimilarly easy. That’s a mistake — evenbasic Erlang C calculations are difficult,and more complex ones can be dauntingindeed.Erlang C is most commonly used tocalculate how long callers will have to waitbefore being connected to a human in acall centre or similar situation. This addsRelated Reading! Call Center Management on Fast Forward,by Brad Cleveland and JuliaMayben, includes a useful plain-Englishdiscussion of using Erlang C forcall centre planning. Order fromwww.incoming.com! Tables for Traffic Management andDesign, by Ted Frankel, seems to bethe only book of traffic tables still inprint. Lee Goeller’s introduction andFrankel’s first three chapters constitutean excellent brief course in trafficengineering concepts. Order fromwww.abcteletraining.com.! Cisco’s website has useful tutorials.Go to www.cisco.com and type “TrafficEngineering” into the searchbox.Erlang B:Erlang C:complexity in at least four areas.1. What’s included in call times? In aqueuing system, traffic includes not just“conversation minutes,” but also the timeagents spend doing “post-call work” relatedto that conversation. Gathering accuratedata on this can be much more difficultthan just looking at a traffic study ora toll-free service bill. In theory, your ACDreports provide the information — butthat only works if everyone has been pressingthe right buttons at the right times.2. What’s meant by delay? The “AverageDelay” might be the average of all calls,including all the calls that didn’t wait at all,or it might be the average of calls that actuallyexperienced a delay. The latter figure isusually more useful, but you must be veryclear which one you are concerned with.Also, using averages can conceal situationsin which most delayed calls wait onlya few seconds, but some experience verylong delays. That can be a serious customerservice problem, even if the averageslook good.Most call centres summarize theirdelay objectives in a phrase like “answer80% of calls within 20 seconds,” but gettingfrom the Erlang C formula to thatresult can be difficult.3. What’s the hour-by-hour load? Withtrunks, you don’t have the option of addingor removing circuits every hour, so youmust install and pay for the numberneeded under peak load conditions. Withpeople, the peak period determines maximumstaffing, but you also need to calculatestaff requirements for other times,and plan staff scheduling accordingly.This usually means doing separate calculationsfor each half hour period in everyweek you operate.And bear in mind that the Erlang Cforecast only tells you how many peoplemust be answering phones at any giventime. That’s quite different from thenumber you must schedule to work eachday, since almost no one can be on thephones 60 minutes an hour.4. How does waiting time affecttrunk load? The time a caller spendson hold listening to music adds to yourtrunk traffic — you can save money byhaving fewer agents to answer calls, butthat may require adding trunks and/orincreasing your toll-free service bill. Youmay have to do several iterations todetermine the optimal mix of trunks,people, and delay.These issues mean that anyone doinganything more than the simplest delaycalculations — above all anyone doingregular staff and configuration planningfor a call centre — should consider buyingspecialized call centre planning software.All such programs — despite the fact thatevery one claims to be absolutely unique— are ultimately based on A.K. Erlang’sformulas from 90 years ago.If you are comfortable with the mathand at creating spreadsheets, considerbuying one of the commercial programsthat adds traffic formulas to Excel, makingit much easier to do multiple “what if”calculations.Every telecom professional should haveat least a general familiarity withErlang B and Erlang C. However, whetheryou use them yourself or evaluate reportsproduced by others, always keep threethings in mind.! Using math is no substitute for usingyour head. If the data you plug in to theformulas isn’t valid, the answers won’t beany good either.! All formulas make assumptions thatsimplify reality. Erlang B assumes thatcallers who receive busy signals won’t immediatelytry again. Erlang C assumesthat delayed callers will wait on hold indefinitely.For low blockage rates and shortqueues, those assumptions don’t cause aproblem — but when your service level ispoor, they can give misleading results.! All traffic formulas calculate probabilities,not absolutes. Erlang B and Cpredict what will happen, on average,over many hours with similar traffic. Youractual experience in any specific hour canbe quite different.!Reproduction in any form prohibited. For additional copies phone 905-686-5050.

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