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cuits, promptly at the times scheduled,and continue with each station sending inrotation until completed, after which relays to the other circuits are made, asdescribed, for distribution nationally.Ship Reports IncludedCollection and distribution of synopticreports from stations and observationpoints outside the United States are accomplished by the transmission of "group"reports from designated stations immediately following relays of domestic reports.Such designated stations are at Seattle,Wash., Buffalo, N. Y., and Washington,D. C., which have interexchange arrangements on the Canadian MeteorologicalService's network; at El Paso, Texas,which receives reports from Mexico; atMiami, Fla., where reports are receivedfrom points in Cuba and the Bahamas,and at Key West, Fla., for the Gulf ofMexico. Additional synoptic reports areput on the network at San Francisco, Cal.,Weather Bureau meteorologists interpret the "6-hourly" reports as they arereceived at stations throughout the country and plot the information on a largemap of the United States on which areshown the locations of sending-receivingstations. ( See Figure 3). The data arenoted on the map in a prescribed patternaround the reporting station, in figures,code and symbols, so that prevailing conditions at any such station can be readilyobserved. Upon completion, the "new"map is posted, together with three othermaps which, progressively, have becomeobsolete. Four "Daily Weather Maps" covering current weather conditions for theprior 24-hour period are therefore alwayson display. These maps are identical at allWeather Bureau offices throughout thecountry. While the maps are redrawnevery six hours, they are considered"good" for flight planning purposes, byCAA and W.B. standards, for nine hours.Typical meteorological instruments used to record weather data. Relative humidity and air temperature arecharted by Hygro-thermograph at left. Wind direction and its velocity are recorded by meter shown in center.Pressure changes are plotted by Microbarograph at right. Illustrations by courtesy of The Instruments Corporationand Washington, D. C., based on data received from ships in the Pacific and theAtlantic, respectively.The "6-hourlies" contain meteorologicaldata observed at each station; i.e., amountand type of clouds, wind direction andspeed, visibility, weather, atmosphericpressure, precipitation and special phenomena. In addition to those originating atlocations having sending-receiving service,certain reports received by radio telephone or telegraph are included in thesesequences.WEATHER NETWORKBalloons Give Weather AloftPilot balloon and radiosonde reportsare also transmitted every six hours, attheir scheduled times, and in the samemanner as "6-hourlies". Pilot balloon reports, called "pibals", contain data on observations of wind direction and speedaloft and are obtained through the use ofelectronic and/or optical instrumentswhich continuously track the path offreely ascending balloons which arereleased to rise until they disappearfrom view or burst. Radiosonde reports129

contain data on weather elements aboveground level and, in the case of certainstations, wind direction and velocity.Coded observations for these reports aresent out by miniature radio transmittersattached to the free-air balloons fromwhich signals are received giving temperature, pressure and relative humiditydata even after the balloons have disappeared from view.As in the case of "6-hourlies", pilotballoon and radiosonde reports are collected from points outside the country, buton a more limited scale, and are distributed throughout the system in the formof group reports. Group reports of thistype, and those based on data received viaU. S. Air Force circuits in connection withobservations made at Air Force bases, aretransmitted from the Louisville and Denver relay stations.Numerous other reports are transmittedfrom Washington, some in plain languageand some in code, such as state forecasts,surface map analysis reports and prognostic weather man analyses for over-allareas and for varying periods of time. Surface analysis reports also originate at SanFrancisco, for Pacific weather. Other typesof reports, transmitted from designatedWeather Bureau offices in code or plainlanguage depending upon the type of report, include, in season, winter sports forecasts, crop, river, corn and wheat, fruitservice, fire weather, and horticulturalInstrument racks in Weather Bureau office,Washington, D. C.reports. The schedule also provides forspecial reports and storm or hurricanewarnings in the event of impending severedisturbances, for either local or nationaldistribution.Aviation forecasts are of three types:(a) regional, covering an area of selectedstates; ( b) terminal, for selected airports;and ( c) Canadian airways, from Canadianpoints. The regional and terminal forecasts are prepared and transmitted bydesignated Weather Bureau forecast centers and the Canadian airways forecastsare received from Canadian circuits andtransmitted from Seattle and Buffalo.Printer Keyboards Have Special SymbolsSpecial " weather- keyboard" teleprinters, equipped with special symbols oncertain of the upper case type pallets, areused on the network, principally for thetransmission of forecast and meteorological messages. Receiving-only printers havereceiving units mounted on a standardbase, but without the keyboard proper ortransmission assembly. Sending-receivingprinters are complete units. Figure 4shows the characters used on the special"weather-keyboard".Wind direction is indicated in symbolformbyarrows,as4, ( south),(southwest) , ( west) , and soforth, and used in combinations as(south-southwest),uurtcy Washington Institute of TechnologyFront end of radiosonde showing pressure adiosonde ascends130and,eir(west-southwest) . Wind velocity is indicated byfigures showing the velocity in miles perhour immediately following the wind direction arrows with aplus sign ( ) addedto indicate gustiness. Sky conditions areOCTOBER 1952

indicated by symbols as follows: 0 ( clear) ,O(scatteredclouds),O ( broken clouds), ande (overcast),X(sky com-pletely hidden by precipitation or obstruction to vision). These symbols are alsoused in combinations, with the / character to show cloud formations above 20,000feet, and figures preceding the symbol toindicate height above the ground in hundreds of feet for lower clouds. Lowerclouds are shown first, with higher cloudsindicated in ascending order. The 4. or. preceding the cloudiness symbol indicates "dark" or " thin", respectively.Most types of forecast messages aretransmitted in abbreviated plain languageand are distributed nationally. Theseinclude state forecasts, which embraceselected states and coastal areas preparedat designated stations, and weather summaries and special reports, which originate at Washington. D. C.alert supervision of its operation. Transmissions are suspended for a ten-minute"line-up" period each day to permit testson the circuit at Western Union repeaterpoints and to allow time for adjustmentsor equipment changes where necessary.Monitor printers are provided at repeaterstations so that circuit interruptions canbe quickly located and corrective actiontaken. Speed in correcting faulty circuitperformance is essential, since the flow oftraffic is practically continuous and if oneor more stations were to be without servicefor an appreciable length of time, important information might be missed. Anypart of a message which is missed by astation is lost to it, since the reports arenot repeated. In the case of interruptionsto sending-receiving stations, other stations on the network which depend upontheir reports at the regularly scheduledtimes might have to go without neededinformation.OGCDOCD000)00COeD(D0 ,0C)00000(0'(Figure 4.SPACE BARSpecial " weather teleprinter" keyboardReliable Circuits Are EssentialWhile the CAA operates the network,Western Union provides the circuits andis responsible for their proper functioning. These circuits are made up on carrierchannel facilities interconnecting majorhubbing cities from which the service isdistributed. At these major points signalsare regenerated to insure maximum operating margins, and are distributed, mainlyover carrier channels, to smaller hubbingpoints and thence to the several servicedrops. Distribution points are equippedwith repeaters for tying together the circuit stems which radiate from them. Thehigh degree of circuit performance required on the "C" network necessitatesperiodic maintenance of equipment andWEATHERNETWORKThe map of the "C" network ( Figure 1)shows places at which there are government equipped sending-receiving stations.At some of these locations there are alsoreceiving- only government equippeddrops, generally at military establishments. Also, at most of these places thereare one or more other users with receiving-only extension service connections tothe network. Among such users are Weather Bureau city offices, air lines, privatefirms and "the military". Not shown onthe map are a number of places off themain-line where there are extension service users who are connected to the neareston-line service point.In addition to the "C" network, furnished by Western Union, the CAA has131

several other networks carrying weather,aircraft movement and traffic control information.Mark Twain may have been sincerewhen he said that everybody talks aboutthe weather and nobody does anythingabout it. But that was before the development of scientific weather forecastingtechniques and the installation of highspeed weather communications networks.Now weather facts are speeded coast-tocoast in seconds so that people are forewarned and can take measures to avoidinjuries or death and damage to crops andproperty.WindmeasuringequipmentonroofofBureau office, Washington, D. C.WeatherWestern Union, communications-wise,has always played an important part inthe handling of weather messages. Largelydue to the growth of aviation and thestepped-up needs of industry and the public, the methods of collecting and disseminating weather data have changed. TheWeather Bureau has kept abreast of thetimes, however, and through the use ofmodern communication systems suppliedby the CAA is able to furnish the nationwith the up-to-the-minute information onthe weather which is so vital to presentday living.Forbes A. Walker has been with WesternUnion since 1933. Prior to his present assignment in thePrivate Wire Services section, Public Relations and SalesDepartment, he held various positions in the Metropolitan Division, in branch offices, superintendents' offices andin the General Manager's office. He was district managerfor eight years and for three years was manager of theMetropolitan Division school. He attended the WhartonSchool of Finance and Commerce of the University ofPennsylvania. In the Private Wire Services Mr. Walkeris responsible, in addition to other duties, for the CivilAeronautics Administration, Weather Bureau, AeronauticalRadio Inc., and other accounts in connection with theService "C" network.132OCTOBER1952

Application of the Theory of Probability toWestern Union Switching SystemsG. STRUNZ and R. E. HUBLEYTHE EFFICIENT allocation of circuits andassociated equipment in Western Unionswitching systems is dependent to alargeextent upon being able to predict accurately any waiting time incurred by messages passing through these systems. Suchdelays as are normally encountered in aproperly designed system are so smallthat they are generally not noticed inoperation, and have no appreciable effecton speed of service. Heretofore, allocations have been made largely on the basisof empirical formulae developed throughpast experience. These empirical formulaecannot accurately predict excess elapsedtime, nor are they adequate when appliedto Western Union installations where message length, transmission speed, or anyother factors influencing delay differ fromthe conditions under which the empiricalformulae were developed. The increasingimportance of establishing circuit requirements accurately to provide the best possible speed of service at reasonable costshas emphasized the need for a more reliable means of predicting delay.ence, ashopper is soon able to predict that,if she does her marketing between 9 and10 o'clock Saturday morning, she "probably" will have to wait in line only a fewminutes. If, on the other hand, she shopsbetween 7and 8o'clock on aFriday night,she "probably" will wait a half-hour ormore in the checking lines. Unconsciously,such ashopper is employing probability—anticipating the number of customers who vill be shopping and the number of checking aisles which will be open at these twoparticular times, and calculating a probable delay on the basis of comparabledelays encountered under similar conditions in the past.The conditions governing the waitingtime—in seconds—which telegrams mayincur in obtaining connections into outletsin Western Union switching systems arevery much the same as encountered byour hypothetical shopper. The greater thenumber of telegrams ( carts) attemptingto pass through a given number of channels (checking aisles), the greater will bethe delay. If the telegrams to a particularHow Probability WorksTABLE IPROBABILITY OF DELAY VERSUS LOADFortunately, the nature and operationof Western Union switching systems isThese data are based on telegrams havsuch that the theory of probability can be ing an average holding time of 0.65 minutes,applied to forecast time delays. The laws following normal Western Union messagegoverning the theory of probability, and length distribution, and seeking connectionstheir analagous application in Western to a destination having a single channel.Number ofAverage TimeUnion installations, can be illustrated byTelegramsRequired toconsidering a grocery supermarket. Theperhourobtaina concustomers' shopping carts are equivalentseekingnection in secondsto telegrams, and the checking aisles areconnections.per telegramthe outlet channels. The length of time acustomer will have to wait in line to pass102.5through a checking aisle with her cart is205.8dependent upon the number of checking3010.0aisles which are open at the time, the4015.7number of other customers ahead of her5024.6in line, how heavily loaded the carts of6039.2the customers ahead of her are, and how7066.8rapidly the checkers work. From experi-oPROBABILITY IN TELEGRAPH SWITCHINGo133

outlet are especially long ( i.e., the cartsare heavily loaded with groceries), thedelay will be greater than it would be ifthe telegrams were extremely short. Ifmore channels are provided, or if equipment speeds are increased ( aslow checkerreplaced by a more rapid checker), thedelay will be reduced. By making use ofthe theory of probability, the mathematical relationship between the various factors influencing delay can be established.For example, the increase in waiting timeas message load is increased is shown inTable I. Similarly, the relationship between channels available and messagesper channel for a given waiting time isshown in Table II.A Fundamental FormulaThe basic formula applicable to the calculation of waiting time in Western Unionswitching systems under normal operating conditions is:P t ( P 0) ( e—(c— a) t/h)where:P t Probability of delay greaterthan any given time ( t).P 0 Probability of delay greaterthan time (0).e The base of NapierianLogarithms. The number of channels inmultiple.h The average holding time percall."aThe number of calls originating,on the average, during theholding time ( h) . Time.*Holding time, as used in this paper, is the totaltime a channel is held busy by a telegram suchthat the channel is unavailable to any othertelegram. This time, the time a channel is held.should not be confused with time consumed inwaiting to obtain a connection into a channel.(For the derivation of this formula, refer to"Application of the Theory of Probability to Telephone Trunking Problems," by E. C. Molina.)The use of the above formula in thedetermination of delays is valid only ifthe following assumptions are fulfilled:1. Telegrams originating independentlyof each other, and at random withreference to time, have complete access to a single group of channels.134TABLE HM ESSAGES PER OUTLET VERSUS NUMBEROF OUTLETS IN M ULTIPLE FOR AN AVERAGEW AITING TIME ON ALL TELEGRAMSOF 5 SECONDSThese data are based on telegrams havingan average holding time of 0.65 minutes, andfollowing normal Western Union messagelength distribution.Number ofNumber ofOutletsTelegramsin multipleper outletavailableper hour1182413524595646672. The probability of a telegram originating during a particular infinitesimal interval, dt, is practically independent of the number of channelsbusy, or number of waiting messages at the beginning of said interval. ( This assumption implies thatthe total interval of time duringwhich the messages fall at random isvery large compared with the average holding time per message, andthat the total number of messagesunder consideration is very largecompared with the number of messages originating per average holdingtime interval.)3. Telegrams are served in the order inwhich they originate. This restrictionapplies only to maximum delayvalues obtained.4. The average holding time being ( h) ,the holding times of individual telegrams vary around this average insuch away that e— t/h is the probability that for atelegram taken at random the holding time is greaterthan ( t) .Under normal operating conditions, assumptions 1and 2are fulfilled in WesternUnion switching systems. Assumption 3is not fulfilled by either the manual orautomatic load distributing methods usedto connect messages to available channels.Consequently, maximum waiting timeOCTOBER1952

values are not accurately predictable inpresent Western Union switching systems.Assumption 4 is fulfilled subject to themodification discussed in the followingparagraph.-Unicn mouse ,,alt**as they have a negligible effect on theresults of this discussion.) For all valuesof holding time greater than (c/), the distribution for a typical Western Union installation closely approximates the exponential form stated in assumption 4.To provide for the displacement of theholding time distribution curve shown inFigure 1, the basic formula which waspresented previously becomes, for application to Western Union switching systems:P t ( P 0) ( e— (ct. /it ')where all quantities are as have beenpreviously defined.In the above formula, the expressionP 0 has been presented in simplifiedform for convenience. Its actual value is:(ac e— a)ca )cP 0 —1—P(c,a) ( acce— acea—)where all quantities are as have been defined previously, and9*Figure 1.Referring to Figure 1, the holding timedistribution curve for a typical WesternUnion installation is most closely approximated by an exponential curve of the forme— t./l . where t' t — d and h' h — d.This curve is of the form stated in assumption 4, but is displaced a distance ( cl)alo

(Circuit No. 31), South Central (Circuit No. 32), North Central (Circuit No. 33), Northwest (Circuit No. 34), and South-west (Circuit No. 35). The six regional circuits are 65-word-per-minute single teleprinter leases and operate electrically independently of each other. The com-bined circuit mileage totals almost 32,000 miles.