Traffic System Design Overview...system performance (i.e., service) objectives are specified, and conflicts are resolved to achieve an optimum configuration. Therefore, traffic system

1

Traffic SystemDesign Overview

Traffic system design is a process that considers the entire telecommunicationsystem and the interrelationship of its components. Total system and sub-system performance (i.e., service) objectives are specified, and conflicts areresolved to achieve an optimum configuration. Therefore, traffic systemdesign ensures the cost-effective dimensioning of switching and transmissionequipment (traffic-handling resources or servers) to provide the requiredservice objectives (grade of service) economically. Telephone traffic (teletraff ic)theory—drawing on many disciplines including electronics, mathematics,statistics, probability, queuing theory, reliability, and economics—is at theheart of traffic system design.

1.1 TRAFFIC UNITS

Traffic units are a measure of traffic intensity, the average traffic density duringa one-hour period. The international unit of traffic intensity is the Erlang,*where one Erlang represents a circuit occupied for one hour.

* Named for A.K. Erlang, the father of telephone traffic theory [Brockmeyer, 1948].

1

2 Chapter 1 Traffic System Design Overview

The Erlang defines the efficiency (percent occupancy) of a traffic resource andrepresents the total time in hours to carry all calls. It is the traffic unit usedexclusively in classic traffic theory.

In the North American public switched telephone network (PSTN), thestandard traffic unit is the unit call (UC), which is expressed in seconds. TheUC is defined in centum-call-seconds (CCS) or more commonly, hundred-call-seconds. Equation 1.1 gives the relationship between Erlangs and CCS. Table1-1 is an Erlang-to-CCS conversion chart for selected traffic levels up to 200Erlangs (7200 CCS).

1 Erlang = 1 call-hour = 3600 call-seconds = 36 CCS (1.1)

1.2 TRAFFIC CALCULATIONS

Before common-equipment pools such as trunk groups, signaling registers,and operator positions can be dimensioned, their busy-hour traffic intensitiesmust be determined. Trunks are assigned to serve calls on an immediate basisand are held for the duration of the call. Signaling registers, operator positions,and similar servers normally serve calls on a delayed basis and are held onlylong enough to serve their specific functions.

1.2.1 Trunk-Group Traffic

Routing plans specify a mix of direct-route and alternate-route trunkgroups to provide least-cost routing of interswitch traffic through the network.The selected routing technique determines, to some extent, the level of trafficoffered to each trunk group. Offered trunk-group traffic is the total of alltraffic offered to the group. If the trunk group were large enough, it would carryall offered traffic but such a trunk group probably would not be economical.Instead, trunk groups are engineered to block a fraction of the offered busy-hour traffic, typically one to ten percent.

Chapter 1 Traffic System Design Overview

Table 1-1. Traffic-Unit Conversion Chart

Erlangs

0.050.100.150.200.25

0.300.350.400.450.50

0.550.600.650.700.75

0.800.850.900.951.00

1.051.101.151.201.25

1.301.351.401.451.50

1.551.601.651.701.75

1.801.851.901.952.00

CCS

1.83.65.47.29.0

10.812.614.416.218.0

19.821.623.425.227.0

29.830.632.434.236.0

37.839.641.443.245.0

46.848.650.452.254.0

55.857.659.461.263.0

64.866.668.470.272.0

Erlangs

2.052.102.152.202.25

2.302.352.402.452.50

2.552.602.652.702.75

2.802.852.902.953.00

3.053.103.153.203.25

3.303.353.403.453.50

3.553.603.653.703.75

3.803.853.903.954.00

CCS

73.875.677.479.281.0

82.884.686.488.290.0

91.893.695.497.299.0

100.8102.6104.4106.2108.0

109.8111.6113.4115.2117.0

118.8120.6122.4124.2126.0

127.8129.6131.4133.2135.0

136.8138.6140.4142.2144.0

Erlangs

4.054.104.154.204.25

4.304.354.404.454.50

4.554.604.654.704.75

4.804.854.904.955.00

5.055.105.155.205.25

5.305.355.405.455.50

5.555.605.655.705.75

5.805.855.905.956.00

CCS

145.8147.6149.4151.2153.0

154.8156.6158.4160.2162.0

163.8165.6167.4169.2171.0

172.8174.6176.4178.2180.0

181.8183.6185.4187.2189.0

190.8192.6194.4196.2198.0

199.8201.6203.4205.2207.0

208.8210.6212.4214.2216.0

Erlangs

6.056.106.156.206.25

6.306.356.406.456.50

6.556.606.656.706.75

6.806.856.906.957.00

7.057.107.157.207.25

7.307.357.407.457.50

7.557.607.657.707.75

7.807.857.907.958.00

CCS

217.8219.6221.4223.2225.0

226.8228.6230.4232.2234.0

235.8237.6239.4241.2243.0

244.8246.6248.4250.2252.0

253.9255.6257.4259.2261.0

262.8264.6266.4268.2270.0

271.8273.6275.4277.2279.0

280.8282.6284.4285.2288.0

Erlangs

8.058.108.158.208.25

8.308.358.408.458.50

8.558.608.658.708.75

8.808.858.908.959.00

9.059.109.159.209.25

9.309.359.409.459.50

9.559.609.659.709.75

9.809.859.909.95

10.00

CCS

289.8291.6293.4295.2297.0

298.8300.6302.4304.2306.0

307.8309.6311.4313.2315.0

316.8318.6320.4322.2324.0

325.8327.6329.4331.2333.0

334.8336.6338.4340.2342.0

343.8345.6347.4349.2351.0

352.8354.6356.4358.2360.0

{table continues)

3


Table 1-1. Traffic-Unit Conversion Chart (Continued)

Erlangs

10.110.210.310.410.5

10.610.710.810.911.0

11.111.211.311.411.5

11.611.711.811.912.0

12.112.212.312.412.5

12.612.712.812.913.0

13.113.213.313.413.5

13.613.713.813.914.0

CCS

363.6367.2370.8374.4378.0

381.6385.2388.8392.4396.0

399.6403.2406.8410.4414.0

417.6421.2424.8428.4432.0

431.6439.2442.8446.4450.0

453.6457.2460.8464.4468.0

471.6475.2478.8482.4486.0

489.6493.2496.8500.4504.0

Erlangs

14.114.214.314.414.5

14.614.714.814.915.0

15.115.215.315.415.5

15.615.715.815.916.0

16.116.216.316.416.5

16.616.716.816.917.0

17.117.217.317.417.5

17.617.717.817.918.0

CCS

507.6511.2514.8518.4522.0

525.6529.2532.8536.4540.0

543.6547.2550.8554.4558.0

561.6565.2568.8572.4576.0

579.6583.2586.8590.4594.0

597.6601.2604.8608.4612.0

615.6619.2622.8626.4630.0

633.6637.2640.8644.4648.0

Erlangs

18.118.218.318.418.5

18.618.718.818.919.0

19.119.219.319.419.5

19.619.719.819.920.0

20.120.220.320.420.5

20.620.720.820.921.0

21.121.221.321.421.5

21.621.721.821.922.0

CCS

651.6654.2658.8662.4666.0

669.6673.2676.8680.4684.0

687.6691.2694.8698.4702.0

705.6709.2712.8716.2720.0

723.6727.2730.8734.4738.0

741.6745.2748.8752.4756.0

759.6763.2766.8770.4774.0

777.6781.2784.8788.4792.0

Erlangs

22.122.222.322.422.5

22.622.722.822.923.0

23.123.223.323.423.5

23.623.723.823.924.0

24.124.224.324.424.5

24.624.724.824.925.0

25.125.225.325.425.5

25.625.725.825.926.0

CCS

795.6799.2802.8806.4810.0

813.6817.2820.8824.4828.0

831.6835.2838.8842.4846.0

849.6853.2856.8860.2864.0

867.6871.2874.8878.4882.0

885.6889.2892.8896.4900.0

903.6907.2910.8914.4918.0

921.6925.2928.8932.4936.0

Erlangs

26.126.226.326.426.5

26.626.726.826.927.0

27.127.227.327.427.5

27.627.727.827.928.0

28.128.228.328.428.5

28.628.728.828.929.0

29.129.229.329.429.5

29.629.729.829.930.0

CCS

939.6943.2946.8950.4954.0

957.6961.2964.8968.4972.0

975.6979.2982.8986.4990.0

993.6997.2

1000.81004.21008.0

1011.61015.21018.81022.41026.0

1029.61033.21036.81040.41044.0

1047.61051.21054.81058.41062.0

1065.61069.21072.81076.21080.0

(table continues)

4



Erlangs

30.130.230.330.430.5

30.630.730.830.931.0

31.131.231.331.431.5

31.631.731.831.932.0

32.132.232.332.432.5

32.632.732.832.933.0

33.133.233.333.433.5

33.633.733.833.934.0

CCS

1083.61087.21090.81094.21098.0

1101.61105.21108.81112.41116.0

1119.61123.21126.81130.41134.0

1137.61141.21144.81148.41152.0

1155.61159.21162.81166.41170.0

1173.61177.21180.81184.41188.0

1191.61195.21198.81202.41206.0

1209.61213.21216.81220.41224.0

Erlangs

34.134.234.334.434.5

34.634.734.834.935.0

35.135.235.335.435.5

35.635.735.835.936.0

36.136.236.336.436.5

36.636.736.836.937.0

37.137.237.337.437.5

37.637.737.837.938.0

CCS

1227.61231.21234.81238.41242.0

1245.61249.21252.81256.41260.0

1263.61267.21270.81274.41278.0

1281.61285.21288.81292.41296.0

1299.61303.21306.81310.41314.0

1317.61321.21324.81328.41332.0

1335.61339.21342.81346.41350.0

1353.61357.21360.81364.41368.0

Erlangs

38.138.238.338.438.5

38.638.738.838.939.0

39.139.239.339.439.5

39.639.739.839.940.0

40.140.240.340.440.5

40.640.740.840.941.0

41.141.241.341.441.5

41.641.741.841.942.0

CCS

1371.61375.21378.81382.41386.0

1389.61393.21396.81400.41404.0

1407.61411.21414.81418.41422.0

1425.61429.21432.81436.41440.0

1443.61447.21450.81454.41458.0

1461.61465.21468.81472.41476.0

1479.61483.21486.81490.41494.0

1497.61501.21504.81508.41512.0

Erlangs

42.142.242.342.442.5

42.642.742.842.943.0

43.143.243.343.443.5

43.643.743.843.944.0

44.144.244.344.444.5

44.644.744.844.945.0

45.145.245.345.445.5

45.645.745.845.946.0

CCS

1515.61519.21522.81526.41530.0

1533.61537.21540.81544.41548.0

1551.61555.21558.81562.41566.0

1569.61573.21576.81580.41584.0

1587.61591.21594.81598.41602.0

1605.61609.21612.81616.41620.0

1623.61627.21630.81634.41638.0

1641.61645.21648.81652.41656.0

Erlangs

46.146.246.346.746.5

46.646.746.846.947.0

47.147.247.347.447.5

47.647.747.847.948.0

48.148.248.348.448.5

48.648.748.848.949.0

49.149.249.349.449.5

49.649.749.849.950.0

CCS

1659.61663.21666.81670.41674.0

1677.61681.21684.81688.41692.0

1695.61699.21702.81706.41710.0

1713.61717.41720.81724.41728.0

1731.61735.21738.81742.41746.0

1749.61753.21756.81760.41764.0

1767.61771.21774.81778.41782.0

1785.61789.21792.81796.41800.0

(table continues)

5



Erlangs

50.551.051.552.052.5

53.053.554.054.555.0

55.556.056.557.057.5

58.058.559.059.560.0

60.561.061.562.062.5

63.063.564.064.565.0

65.566.066.567.067.5

68.068.569.069.570.0

CCS

18181836185418721890

19081926194419621980

19982016203420522070

20882106212421422160

21782196221422322250

22682286230423222340

23582376239424122430

24482466248425022520

Erlangs

70.571.071.572.072.5

73.073.574.074.575.0

75.576.076.577.077.5

78.078.579.079.580.0

80.581.081.582.082.5

83.083.584.084.585.0

85.586.086.587.087.5

88.088.589.089.590.0

CCS

25382556257425922610

26282646266426822700

27182736275427722790

28082826284428622880

28982916293429522970

29883006302430423060

30783096311431323150

31683186320432223240

Erlangs

90.591.091.592.092.5

93.093.594.094.595.0

95.596.096.597.097.5

98.098.599.099.5100.0

101.0102.0103.0104.0105.0

106.0107.0108.0109.0110.0

111.0112.0113.0114.0115.0

116.0117.0118.0119.0120.0

CCS

32583276329433123330

33483366338434023420

34383456347434923510

35283546356435823600

36363672370837443780

38163852388839243960

39964032406841044140

41764212424842844320

Erlangs

121.0122.0123.0124.0125.0

126.0127.0128.0129.0130.0

131.0132.0133.0134.0135.0

136.0137.0138.0139.0140.0

141.0142.0143.0144.0145.0

146.0147.0148.0149.0150.0

151.0152.0153.0154.0155.0

156.0157.0158.0159.0160.0

CCS

43564392442844644500

45364572460846444680

47164752478848244860

48964932496850045040

50765112514851845220

52565292532853645400

54365472550855445580

56165652568857245760

Erlangs

161.0162.0163.0164.0165.0

166.0167.0168.0169.0170.0

171.0172.0173.0174.0175.0

176.0177.0178.0179.0180.0

181.0182.0183.0184.0185.0

186.0187.0188.0189.0190.0

191.0192.0193.0194.0195.0

196.0197.0198.0199.0200.0

CCS

57965832586859045940

59766012604860846120

61566192622862646300

63366372640864446480

65166552658866246660

66966732676868046840

68766912694869847020

70567092712871647200

6

Chapter 1 Traffic System Design Overview 7

Figure 1-1 can be used to facilitate an understanding of traffic routingterms. Interswitch traffic is routed over the primary route trunk group providedthere are idle trunks available in the group. In an alternate-routing system,blocked trunk-group traffic overflows to other alternate-route trunk groups orto final-route trunk groups as indicated by the curved arrows. Trunk groupsprovided with alternate routes are often referred to as high-usage trunk groups.Final-route trunk groups do not have alternate routes; therefore, blocked trafficin a final-route trunk group is lost.

Trunk-group traffic is the product of the number and duration of callshandled by the group. Equation 1.2 can be used to calculate trunk-group traffic,expressed in Erlangs.

A=N*Tr (1.2)

where A = Offered traffic in ErlangsN = Number of calls during the busy hour7 = Mean call-holding time in hours

Number of calls refers to the total number of calls offered to the trunkgroup. Call-holding time is the total elapsed time between seizure of a trunkto serve the call and its subsequent release. The mean call-holding time is thearithmetic average of all call-holding times, expressed in hours.

CALLINGSUBSCRIBER

Figure 1-1. Interswitch Trunk Traffic Routing Diagram

CALLEDSUBSCRIBER

PRIMARYROUTE

CENTRALOFFICE

CENTRALOFFICE

THIRD& FINALROUTE

TANDEMSWITCH

THIRD& FINALROUTE TANDEM

SWITCH

FINALROUTE


Example 1-1Determine the traffic in Erlangs and CCS for a trunk group carrying 1000calls during the busy hour with an average call-holding time of 3 minutes.

A = (1000 calls/hour)(3 min/call)(l hour/60 min) = 50 Erlangs(50 Erl)(36 CCS/Erl) = 1800 CCS

1.2,2 Server-Pool Traffic

Server pools are groups of traffic resources, such as signaling registersand operator positions, that are used on a shared basis. Service requests thatcannot be met immediately are placed in a queue and served on a first-in, first-out (FIFO) basis. Server-pool traffic is directly related to offered traffic,server-holding time, and call-attempt factor, and inversely related to call-holding time as expressed in Equation 1.3.

AT.TS-C ( U )*s 7V

where As= Server-pool traffic in ErlangsAT = Total traffic served in ErlangsTs = Mean server-holding time in hoursTc = Mean call-holding time in hoursC = Call-attempt factor (dimensionless)

Total traffic served refers to the total offered traffic that requires theservices of the specific server pool for some portion of the call. For example,a dual-tone multifrequency (DTMF) receiver pool is dimensioned to serveonly the DTMF tone-dialing portion of total switch traffic generated by DTMFsignaling sources. Table 1-2 presents representative server-holding times fortypical signaling registers as a function of the number of digits received or sent.

Table 1-2. Typical Signaling Register Holding Times in Seconds

Signaling Register

Local Dial-Pulse (DP) ReceiverLocal DTMF ReceiverIncoming MF ReceiverOutgoing MF Sender

1

3.72.3

1.01.5

Number of

4

8.35.21.4

1.9

Digits Received or Sent

7

12.88.1

1.82.3

10

17.611.02.2

2.8

11

19.112.02.33.0


The mean server-holding time is the arithmetic average of all server-holding times for the specific server pool. Equation 1.4 is a general equationto calculate mean server-holding time for calls with different holding-timecharacteristics.

Ts = wT{ + faT2 + ••• + hTn (1.4)

where Ts = Mean server-holding time in hoursTv Tv*", Tn = Individual server-holding times in hoursa, b, ••• ,k = Fractions of total traffic served (a + 6 + ••• + Jfc = 1)

Example 1-2

Determine the mean DTMF receiver-holding time for a central office (CO) wheresubscribers dial local calls using a 7-digit number and toll calls using an 11 -digitnumber. Assume that 70 percent of the calls are local calls, the remainder are tollcalls, and that the typical signaling register holding times of Table 1-2 areapplicable.

T5 = (0.7)(8.1 sec) + (0.3X12.0 sec) = 9.27 sec

Call-attempt factors are dimensionless numbers that adjust offered trafficintensity to compensate for call attempts that do not result in completed calls.Therefore, call-attempt factors are inversely proportional to the fraction ofcompleted calls as defined in Equation 1.5.

C = y (1.5)

where C = Call-attempt factor (dimensionless)k = Fraction of calls completed (decimal fraction)

Example 1-3

Table 1-3 presents representative subscriber call-attempt dispositions based onempirical data amassed in the North American PSTN. Determine the call-attemptfactor for these data, where 70.7 percent of the calls were completed (k = 0.707).

C = ~ T " " O T O T " L 4 1 41 1


Table 1-3. Typical Call-Attempt Dispositions

Call-Attempt Disposition

Call was completed

Called subscriber did not answer

Called subscriber line was busy

Call abandoned without system response

Equipment blockage or failure

Customer dialing error

Called directory number changed or disconnected

Percentage

70.7

12.7

10.1

2.6

1.9

1.60.4

Example 1-4

Using Equation 1.3, determine the server-pool traffic in CCS and Erlangs for theDTMF receivers of Example 1-2, assuming total offered busy-hour subscribertraffic of 2000 CCS, a call-attempt factor of 1.5, and a mean call-holding time of3 minutes (180 seconds).

As = (2000 CCS) ( i .5)-2 |Zj!g> = l54.5CCS

(154.5 CCS) ( ^ g P S ) =4.29 Erlangs

1.3 TRAFFIC ASSUMPTIONS

Traffic formulas are based on a set of assumptions regarding the behavior oftraffic and its sources. These assumptions are not always precisely true. Ifvariations from these assumptions are small or known to have little effect,however, they can be used with confidence.

1.3.1 General Assumptions

The following assumptions are applicable to traffic formulas in general:

• The system is in statistical equilibrium.• Connection and disconnection of sources to servers occur

instantaneously.• The anticipated traffic density is the same for all sources.• Busy sources initiate no calls.• Every source has equal access to every server (full availability).


• The number of busy servers in a group is equal to the number ofbusy sources in its group of sources.

1.3.2 Number of Sources

The number of sources that can originate calls affects the service thesesources can expect to obtain. As the number of sources increases, the effect ofadding more sources diminishes. Eventually, a point is reached where there isnegligible difference in the probability of congestion regardless of how manynew sources are added. It is this point that distinguishes between finite andinfinite sources. Traffic formulas for applications where the number of sourcesin relation to the number of servers is very large assume infinite sources (worstcase for blocking). This simplifies the mathematics and minimizes the numberof required tables.

1.33 Disposition of Blocked Calls

Many assumptions for the disposition of blocked calls (which are alsoreferred to as lost calls) have been proposed, of which the three common casesare:

• If an idle server is not immediately available, the call is cleared fromthe system and the source becomes idle. This is commonly called theblocked calls cleared assumption.

• If an idle server is not immediately available, the call is held for aninterval equal to its holding time, and then the source becomes idle. Ifan idle server becomes available during the waiting period, it will beseized and held for an interval equal to the remaining portion of itsmean holding time. This is commonly called the blocked calls heldassumption.

• If an idle server is not immediately available, the call is queued untilan idle server is available. When an idle server becomes available, itwill be seized to serve the next call in queue and held for the full call-holding time. This is commonly called the blocked calls delayedassumption.

1.3.4 Holding-Time Distributions

A negative-exponential curve usually provides a reasonable fit for thevariation in holding times encountered with nondelayed traffic-handlingresources. Substituting a constant holding time equal to the average of varyingholding times has a negligible effect for these applications. The effects of


holding-time variations may be significant, however, when predicting theduration of delays. For example, the Crommelin-Pollaczek formulas are oftenused to determine service delays for resources with essentially constantholding times, such as dial-tone markers and intertoll trunks. Molnar's DelayProbability Charts for Telephone Traffic Where the Holding Times AreConstant graphically present data for these and similar applications.

1.4 GRADE OF SERVICE

Grade of service (GOS) is defined as the probability that offered traffic will beblocked or delayed. An absolutely nonblocking system has a GOS of zero,whereas a GOS of one indicates an absolutely blocking system. That is, thecloser the grade of service is to zero, the better the system.

Every traffic problem involves three interrelated parameters: offeredtraffic, traffic-handling resources (servers), and service objective (grade ofservice). This interrelationship can be pictured as a triangle, as shown in Fig.1-2. For a given service objective (base of triangle held constant), increasingoffered traffic requires a commensurate increase in the number of servers.Similarly, decreasing the number of servers requires a corresponding decreasein the level of offered traffic.

It is important to understand that a server's GOS is a prediction of theprobability of congestion (i.e., a call is blocked or delayed) at a given level of

SERVICE OBJECTIVE

Figure 1-2. Grade of Service Concept Diagram


offered traffic, not an absolute value. That is, a trunk-group grade of serviceof 0.01 does not mean that exactly one call in a hundred will be blocked duringthe busy hour. Rather, it means that, given a large volume of traffic, theprobability of congestion will tend toward one in a hundred.

Table 1-4 lists typical grade of service specifications for traffic systemdesign. Matching loss as used in this table refers to congestion (blocking) ina switching matrix such that input and output terminations cannot be intercon-nected via the interstage links. Switching matrix matching loss is not coveredin this handbook but the author's Voice Teletraffic Systems Engineeringcontains an entire chapter on the subject.

Table 1 -4. Typical Grade of Service Specifications

Parameter Specification

Trunk group loss probability 0.010

Intraoffice line-to-line loss probability 0.020

Line-to-trunk outgoing matching loss probability 0.010

Trunk-to-line incoming matching loss probability 0.020

Trunk-to-trunk tandem matching loss probability 0.005

Probability dial tone delay exceeds 3 seconds 0.015

Probability operator answer delay exceeds 10 seconds 0.050

The traffic formulas found in this handbook, used to predict grades ofservice, are all based on probability distributions. Probability distributions arebounded by the values zero and one; therefore, a grade of service (probabilityof congestion) cannot be negative nor can it exceed unity. Because of thisproperty, the probability of a call not experiencing congestion is one minus theprobability of congestion, and vice versa. These relationships are expressed inEquations 1.6 and 1.7.

P = l - G (1-6)

Q = l - / > (1.7)

where P = Probability of congestionQ = Probability of no congestion


1.5 TRAFFIC FORMULAS AND TABLES

Table 1-5 is a selection guide for the traffic formulas contained in thishandbook as a function of their typical applications. The Poisson, Erlang B,and Erlang C formulas, based on the assumption of infinite sources, are referredto as the major traffic formulas. The Binomial and Engset formulas, based onthe assumption of finite sources, are used in lieu of the major traffic formulaswhen the number of sources is small. Figure 1 -3 is a decision tree to facilitatetraffic formula selection on the basis of the standard traffic assumptions.

Table 1-5. Traffic Formula Selection Guide

TypicalApplications

Final trunkgroups inNorth AmericanPSTN

Trunk groupsand othernondelayedserver pools

Delayedserver pools

Small PBX orremote switchtrunk groups

Small lineconcentrators

Number ofSources

Infinite

Infinite

Infinite

Finite

Finite

Blocked-CallDisposition

Held

Cleared

Delayed

Held

Cleared

Holding-TimeDistribution

Constant orexponential


Exponential



TrafficFormula

Poisson

Erlang B

Erlang C

Binomial

Engset

Representative full-availability traffic tables, selected on the basis ofcommon telephone industry practice, are provided for the Poisson, Erlang B,Erlang C, Binomial, and Engset distributions. Full availability refers to theassumption that every source has equal access to every server. This assumptionis normally true for modern traffic systems. Some older systems, however,many of which are still in use, may be limited-availability systems. Limited-availability tables, such as those found in Siemens' Telephone Traffic TheoryTables and Charts and ITT Standard Electrik's Teletraffic Engineering Manual,can be used for those systems.

15


Tabulated traffic data values in this handbook are rounded off to the least-significant digit as applicable to the specific table. For example, loss probabil-ity values have been rounded off to five decimal places. This level of accuracyshould be more than adequate for practical applications—very low lossprobabilities may indicate overdesign, which is not economically sound.

Where the parameters of a specific application do not coincide with tablevalues, interpolation can be used. However, linear interpolation techniques arenot generally satisfactory for these highly nonlinear formulas. Adequateresults may be obtained with a graphic technique using semilogarithmic(semilog) graph paper, where loss probability is plotted logarithmically alongthe ordinate (vertical axis), and offered traffic is plotted linearly along theabscissa (horizontal axis). Figure 1-4 (page 17), a comparison of typical lossprobabilities for the Poisson and Erlang B distributions, is an example of thegraphic technique. Among other things it shows that, for a given lossprobability, less traffic can be offered to a trunk group dimensioned using thePoisson distribution than to one containing the same number of trunks butdimensioned using the Erlang B distribution. That is, the Poisson distributionresults in a more conservative design.

1.6 COMPUTER PROGRAMS

Computer programs, useful for interpolating between table values or todetermine more precise values for specific applications, are provided insubsequent chapters for the Poisson, Erlang B, Erlang C, Binomial, and Engsetformulas. These programs are written in BASIC because it is an easy-to-learnlanguage and is highly standardized. It is the universal programming languagefor the personal computers found in homes as well as engineering offices. Theprograms are formatted in an interactive (i.e., dialogue) style to facilitate theuser's entry of traffic parameters and include separate lines of code for each stepin an attempt to make them more easily understood by those with little or noprogramming experience.

Readers adept at computer programming may prefer to rewrite thesetraffic programs, combining a number of steps into a single line of code.Alternatively, the programs can be converted to a language such as FOR-TRAN, which was specifically designed for computational problem solving.In any case, newly entered programs should be validated by running themagainst benchmarks, such as the examples in this book, before relying on theiroutput data.


OFFERED LOAD-ERLANGS

Figure 1-4. Graphic Comparison of Poisson and Erlang B Distributions

A word of caution—computers are subject to overflow when dealing withvery large numbers. This limitation is a function of the computer hardware andsoftware, which can only process numbers within a finite range. Overflowoften occurs when calculating traffic formulas, which typically involve calcu-lation of factorials, numbers raised to the nth power, or infinite sums. Thetraffic programs provided herein have been written to avoid overflow condi-tions where possible. Overflow may still occur, however, when calculating theloss probability for a high traffic volume offered to a large number of servers,or some combination of these or other traffic parameters is encountered.

0.1000

0.0500

0.0200

0.0100 "

0.0050

0.0020

0.0010

0.0005

0.0002

0.0001

_J

POISSON ERLANG B

Documents

Traffic System Design Overview...system performance (i.e., service) objectives are specified, and conflicts are resolved to achieve an optimum configuration. Therefore, traffic system