page 1page 2page 3page 4page 5page 6page 7page 8page 9page 10page 11page 12page 13page 14page 15page 16page 17page 18page 19page 20page 21page 22page 23page 24page 25page 26page 27page 28page 29page 30page 31page 32page 33page 34page 35page 36page 37page 38wuldmA Traffic Study of theSMU Wide Area TelephoneService (WATS) SystembyE. Phillip LatkaSenior Design inEngineering ManagementPresented May8, 1982Sophus Thompson Conference RoomSouthern Methodist UniversityDallas, Texas75275Fulfilling Requirements forOREM 4390 and theBaccalaureate DegreeDr. Richard S. BarrAssistant ProfessorI1CONTENTSpageI.Background and OverviewA.Given1B.Problem1C.Approach to Solving the Problem1D.Persons and Policies Affected1E.Data Availability2II.Model DescriptionsA. Traffic Study Model2B. Erlang's Loss Formula4III. IS61tition, PhaseA.Solution Requirements for the Model5B.Obtaining the Data.5IV.C.Software DescriptionAnalysisA.yResults of WATSTAT7B.Results of Erlang's Loss Formula7V.ConclusionsA.Summary9B.Self-critique9C.Suggestions for Further Study9iiAPPENDICIESpageAppendix A:Call Logging by Record Type10Appendix B:WATSBOX Tape Layout11Appendix C:LABEL and FUZZ Commands(6600)12Appendix D: WATSTAT ` .13Appendix E:Variables Used in WATSTAT18Appendix F:Sample Output20Appendix GiActual Output from Study-24WATS-LINE TRAFFIC STUDYI.BackgroundandOverviewA.Given:Southern Methodist University in Dallas, Texas handlesa large volume of long distance telephone calls on nineWide Area Telephone Service (WATS) lines; this includesfour national WATS lines, three statewide (Texas only)WATS lines, and two MCI national WATS lines.B.Problem:Duringpeak hours (10 a.m. to 3 p.m.), it is verydifficult for SMUpersonnelto make along distancecall because frequently all of the WATS lines arebeing used.Users report having to attempt a callthree to five times before obtaining aline.Althoughdifficult to quantify, the unavailibilty of WATS_ linescauses SMU personnel great aggrevatioia~ as well aspotentially "lost business" to the University in theform of business transactions, recruiting, etc.C.Approach toSolving theProblem:Perform a traffic study to determine what is the pro-bability of any individual who places a long distancecall not obtaining a line, and how the addition ofadditionalline(s) willaffect this "blocking factor",i.e. the probability of his call being blocked with nadditionallinesin the system (n = 1, 2,...).D.Persons andPoliciesAffected:The results of this analysis will be forwarded toMr. Jere Scott, director of SMU telephone services,Dawson Building, SMU, and a subsequent recommendationwill be made to the Assistant Provost, Dr. NaraynBhat, as to the addition of additional WATS lines toSMU's system.E.Data Availability:The data required in this traffic study isavailable through a log record which is keptby the SMU Physical Plant. A magnetic tapedrive is hooked up to the WATS switchingequipment and a record of each transactionis kept (see Appendix A). The traffic studyis to be performed over a three month period,and the tapes that hold the information areAT0042, ATO043,andATOO45,The data mustbe translated and unblocked to a scratch tapevia the LABEL and FUZZ commands on the Cyber6600.From these, a developed software pac-kage(WATSTAT)will obtain the necessary data.11.ModelDescriptionspage2A.TrafficStudy Model:The problem involves a multi-server QUEUEING PROB-LEM of the type M/M/S/S, that is customers arrivein a Poisson process witharate1.1There arenine lines of three delineations; national WATS,Texas WATS, MCI WATS (see Figure 1).lBhat, Cooper, and Le Blanc,IntroductiontoOperationsResearchModels,p. 374.NTL Lines(4)TX Lines(3)MCI Lines(2){tpage3FIGURE 1:Representation of SMU WATS trunk linesThe three different line types handle differentzone calls andno-trade-offisallowed(i.e. aTexas call cannot be handled by a National WATSline).Another assumption is that all nationalcalls attempt to get an MCI line first if the callgoes to an MCI serviced city (MCI has limited areacodes), because it is cheaper. Based on this in-formation, the traffic study is defined more ex-plicitly to actually be threeseparate trafficstudieson each of the three classes of WATS lines.All three studies, however, will use the same model,and will employ the use of Erlang's Loss Formulato determine the blocking probability.'SMUqueueB.2lbid, p. 376.31bid.page4Erlang's LossFormula:Consider the number of calls on the nine WATS trunklines is n = 0, 1, ..., 9, which we will identify assystemstates.variables:Let pi be the steady state probability thatthe system is in state i.9p1•= 1.~1/Ais the call arrival rate, per houris the service rate; (the average call length)-1P= erlang (dimensionless) ='/AWhen all lines are busy, the system will beblockedforany new calls and therefore the probabilityPs's/s:-1* P +P2/2+ ...+/02/s:is known as the blocking probability and is identi-fied asErlang'slossformula.2Erlang's loss formula determines how much the blockingprobability would be reduced by adding new lines.In other words, when someone tries to place a call,there is a 68.8% probability that all lines will bebusy.example3:s = 4P0 = 0.001/1 =4.926pl= 0.011~tL =0.427 P2 = 0.062= 11.537p3 = 0.238p4= 0.688III.SolutionPhasepage5If an additional line is added to the system, the stateprobabilities turn out to beSimilar calculations show that for this load, at leastseven lines are needed to drop the blocking probabilityto 25%.A.SolutionRequirementsfor theModel:In order to compute the blocking factor from Erlang'sloss formula, the user needs:= the call arrival rate per hour= (average call length)-1B.Obtainingthe Data: The data to determineandlare found on mag-netic record tapes kept by the SMU Physical Plant.The magnetic tapes generated by the drive attachedto the WATSBOX switching mechanisms are coded asshown in the format layout Appendix B. I obtained`the WATSBOX tapes for January, February, and March,1982 (VSN = AT¢¢42, ATOQ43, AT0045 from the Cyberlibrary) from Mr. Jere Scott, SMU Physical Plantand translated them onto transfer tapes TTOJ Q3,TT¢QjO4,TTOO05 (66¢0) by means of the LABEL and FUZZsystem commands (see Appendix C) for use in my analy-sis.C.SoftwareDescription:In order to compile the statistics to compute~ (call arrival rate) and,/.A-(average holding time)p0= 0.000pl= 0.004p2= 0.024p3= 0.092P4 = 0.266p5= 0.614.Line61Line 02Line03LineLineLineLineLineLine040506070809A-MMMM1111t,page6for use in Erlang's loss formula, I developed aFORTRAN package, WATSTAT (see