ATT DEFINITY Communications System Generic 3 Basic Call Management System Instructions Manual

							Use of BCMS Rep orts for ACD Plannin g
6-6Issue  4  September 1995 
the number of agents required and Table 6-12 to determine the number of trunks 
required for a given ACD, you may find that the exp e cted number of call arrivals 
or the carried load lies somewhere between two entries in the tables. Therefore, 
the number of agents or trunks required will also lie somewhere b etween the two 
entries.
If this is the c ase, the number of agents required or number of trunks needed can 
only b e found  b y interpolation. Use the following equation to interpolate b etween 
tabular values:
Where:
Agent Engineering/Optimizing Guidelines
Tables 6-2 through 6-12 list the number of ACD agents required to handle a 
given incoming call load. The top rows on each of these tables show the possible 
delay times for a given incoming c all load (calls per hour or b usy hour calls), and  
the left-most column lists the agents required to handle the incoming call load 
such that 90 percent the incoming calls will be answered by the agents before 
the sp e cified delay has oc c urred.
NOTE:
The entries in Tables 6-2 through 6-12 are in busy-hour c alls, which are the 
number of calls received by the ACD during peak levels of caller activity.
xIs the independent variable in terms of calls per hour
yIs the dependent or functional variable in terms of agents or 
trunks needed
x0Is the tabular value of the independent variable that immediately 
precedes 
x
x
1Is the tabular value of the independent variable that immediately 
succeeds 
x
y
0Is the tabular value of the dependent variable that immediately 
precedes 
y
y
1Is the tabular value of the dependent variable that immediately 
succeeds 
y
y=y0+(y1-y0)
x1-x0
x-x0_ _______ 
						

							Engineering  ACD Applications with Data Obtained from 
the BCMS Reports
Issue  4  September 1995
6-7
To determine how many agents will be required to handle the incoming c all load 
of an ACD split, use Tables 6-2 through 6-12 as follows:
nUse the BCMS Split Report (list bcms split) to determine the AVG TALK 
TIME (the time an agent spends processing a call, or talking to a caller). 
Tables 6-2 through 6-12 contain data that desc ribes the following service 
times: 7, 15, 30, 45, 60, 90, 120, 180, 240, 300, and 600 seconds. Choose 
the appropriate table for the AVG TALK TIME of the ACD split.
NOTE:
For purposes within this document the term ‘‘AVG Talk Time’’ is 
equivalent to the term ‘‘AVG Service Time.’’
nAt the top of the table, choose the closest possible AVG SPEED ANS in 
se c o n d s. A VG SPEED  ANS is actually a delay time that is defined as the 
elapsed  time from when a c all is routed to the ACD split until it is answered 
b y an agent. The d elay  criterion states that 90 percent of the incoming 
calls will be answered by the agents before the specified delay has 
occurred.
nIf the calling volume, otherwise referred to as the busy-hour calls, is 
known, then use the number indicated on the report. Otherwise, you must 
estimate this number. Busy-hour calls denotes the number of calls 
received by the ACD during peak levels of caller activity. A typical 
busy-hour calling rate might be 120, 130, or 160 calls per hour.
NOTE:
The a ctual busy-hour calling rate depends on agent staffing and the 
particular application. Obviously, the numbers that are identified  
here as being typical would be much too high for five agent p ositions 
and too low for 30 agent positions. The numbers given are only for 
illustration purposes.
nAfter choosing the ap p ropriate table and delay  column, find the entry in 
the table for busy-hour calls that is greater than or equal to the number of 
busy-hour calls chosen.
nThe number of agent positions required is then found in the left-most 
column of the resp e ctive table.
nYou can interp olate between the tables (for different call service times), 
between the c olumns (for different delay times), and between the rows (for 
different number of calls per hour).
Tables 6-2 through 6-12 were prepared by using a range of 1 to 1000 agents.  
For small service times, this yields high traffic rates, even for a small number of 
agents. The high traffic rates are presented in the tables for completeness only.
Example 1:
The classified ads department of a newspaper receives 160 calls per hour.  The 
average time an agent spends on each call is three minutes.  If most of the calls  
						

							Use of BCMS Rep orts for ACD Plannin g
6-8Issue  4  September 1995 
should be answered in less than 30 seconds, how many agents should be 
employed in this department?
Table 6-8 provides data for 180-second (3-minute) call durations. Under the 
30-second column heading (AVG SPEED  ANS), find the first entry greater than 
160 calls per hour (168). Follow this row left to the agents column and find 12 
agents. The number of agents required to answer 160 calls (of 3-minute duration) 
per hour with 90 percent of the callers waiting less than 30 seconds is 12 agents.
For this example, consider the effic iency of the agents and the sensitivity of the 
parameters to changes in the call arrival rate. The efficiency of the agents is the 
ratio of the number of agent hours sp ent on the phone to the number of agent 
hours in an hour. The number of agent hours s pent on the phone is 160 calls  per 
hour times .05 hours (3 minutes) which equals 8 agent hours. Therefore, the 
effic iency is 8/12 (12 agents for 1 hour) and equals .67 or 67 percent.
Suppose the calls per hour increased to 185 calls per hour. The efficiency is now 
185 X 0.05 w 12 = 0.77 or 77 perc ent. The effic iency has increased, but this 
added efficiency is not free of charge. The delay criterion has changed 
significantly from about 9.5 percent of all calls taking longer than 30 seconds for 
an agent to answer to about 18.0 percent (168 calls per hour yield 10.0 percent, 
but 160 calls per hour were stated). To g et the delay c riterion b a ck to 9.5 percent 
would require a delay time of about 65 seconds.  Another measure of what is 
happening with the queue is the average time spent waiting for service in the 
queue.  With 160 calls per hour, the mean time spent in the queue is 7.53 
second s.  With 185 c alls per hour, the mean time in the queue is 16.14 seconds.  
The point of this example is to emphasize the sensitivity of the time in the queue 
to the arrival rate.  In other words, increasing the agent efficiency from 67 p erc ent 
to 77 percent nearly doubles the various measures of queuing time.
NOTE:
For Examples 2 and 3, the ‘‘?s’’ in the tables represent the unknown values 
you are looking for. The italicized numbers in the tables represent numbers 
that are not included in Tables 6-2 through 6-12.
Example 2:
The reservations department for a hotel chain knows that the average call 
duration is five minutes and that most of the potential customers will not wait 
more that one minute for their call to be answered. How many agents are 
required to handle 150 calls per hour? Under the 60-second column of Table 
6-10, you will find the following information:
agents 60
16 145
? 150
18 167 
						

							Engineering  ACD Applications with Data Obtained from 
the BCMS Reports
Issue  4  September 1995
6-9
Therefore, 17 agents are needed to support the reservations department.
Example 3:
The manager of a split in an ACD knows that calls average 75 seconds and that 
the split receives 200 calls per hour.  The manager wants most of the calls to be 
answered in less than 40 seconds.  How many agents are required? To answer 
this question, you must interpolate between all parameters—first, between d elay 
time and calls per hour to obtain the number of calls per hour for a 40-second 
delay time. Under the 30- and 45-second columns of Tables 6-6 and 6-7 you will 
find :
60 Seconds Average Service Time 75 Seconds 90 Seconds Average Service Time
AVG ANSWER SPEED AVG ANSWER SPEED
agents 30 40 45 agents 30 40 45
5 186 ? 202 7 182 ? 194
?
200?200
6 238 ? 257 8 217 ? 231
y=number o f  agents needed
y=y
0+(y1-y0)
x1-x0
x-x0_ _______
y=16+( 18-16 )
167-145 150-145
_ _________
y=16+( 2´.227 )
y=16. 45 
						

							Use of BCMS Rep orts for ACD Plannin g
6-10Issue  4  September 1995 
Now interp olate between delay time and calls per hour in both tables to obtain 
calls per hour for a 40-second delay time.
Now you can fill in the first blank: 197 calls per hour under the 40-second delay 
time heading. Repeat the interpolation p rocess three more times to c ome up with 
the figures 251, 190, and 226.
So now we know that 5.05 agents would be needed when a 60-second service 
time is desirable. Repeat the above interpolation process once (for a 90-second  
service time) to come up with the result: 60 Seconds Average Service Time 75 Seconds 90 Seconds Average Service Time
AVG ANSWER SPEED AVG ANSWER SPEED
agents 30 40 45 agents 30 40 45
5 186
197202 7 182190194
?
200?200
6 238251257 8 217226231
y=number o f  calls per hour
y=y
0+(y1-y0)
x1-x0
x-x0_ _______
y=186+( 202-186 )
45-30 40-30
_ _______
y=186+( 16´0. 666 )
y=196. 66
y=number o f  agents needed when a60-second service time is desirable
y=y
0+(y1-y0)
x1-x0
x-x0_ _______
y=5+( 6-5 )
251-197 200-197
_ _________
y=5+( 1´0. 055 )
y=5. 05 
						

							Engineering  ACD Applications with Data Obtained from 
the BCMS Reports
Issue  4  September 1995
6-11
y (number of agents) = 7.27
From exact calculations, the use of six agents implies that 12.2 percent of the 
incoming calls will wait more than 40 seconds.  Or, with seven agents, 5.56 
percent will wait more than 40 seconds. If anything above, 10 percent is 
undesirable, a seventh agent must be acquired. 60 Seconds Average Service Time 75 Seconds90 Seconds Average 
Service Time
AVG ANSWER SPEED AVG ANSWER SPEED
agents 30 40 45 agents 30 40 45
5 186
197202 7 182190194
5.05 200 7.27 200
6 238251257 8 217226231
Table 6-1. 7 Seconds Average Service Time 
AVG SPEED ANS
agents 11 15 22 30 45 60 90 120 180
1 154 195 253 302 359 392 429 449 470
2 575 648 736 799 865 902 942 962 984
3 1044 1135 1237 1305 1376 1415 1455 1476 1498
4 1531 1633 1743 1815 1888 1928 1969 1990 2012
5 2025 2136 2251 2326 2401 2441 2483 2504 2526
6 2525 2641 2761 2838 2914 2955 2997 3018 3040
7 3027 3149 3272 3350 3428 3469 3511 3533 3555
Continued on next page
y=number o f  agents needed when a75-second service time is desirable
y=y
0+(y1-y0)
x1-x0
x-x0_ _______
y=5. 05+( 7. 27-5. 05 )
90-60 75-60
_ _______
y=5. 05+( 2. 22´0. 50 )
y=6. 16  (or6 ) 
						

							Use of BCMS Rep orts for ACD Plannin g
6-12Issue  4  September 1995 
8 3532 3657 3783 3863 3941 3983 4025 4047 4069
9 4038 4167 4295 4376 4455 4496 4539 4561 4583
10 4545 4677 4808 4889 4969 5010 5053 5075 5097
12 5562 5699 5833 5916 5997 6039 6082 6104 6126
14 6581 6722 6859 6943 7025 7067 7110 7132 7155
16 7602 7746 7885 7971 8053 8095 8139 8161 8183
18 8625 8771 8912 8998 9081 9123 9167 9189 9212
20 9648 9797 9939 10026 10109 10152 10195 10218 10240
25 12208 12362 12508 12596 12680 12723 12767 12789 12812
30 14772 14929 15077 15166 15251 15294 15338 15360 15383
35 17337 17497 17647 17736 17822 17865 17909 17932 17954
40 19903 20065 20217 20307 20393 20436 20481 20503 20526
45 22470 22634 22787 22878 22964 23008 23052 23074 23097
50 25037 25204 25357 25449 25535 25579 25623 25646 25669
60 30174 30343 30499 30591 30677 30721 30766 30789 30811
70 35312 35483 35640 35733 35820 35864 35909 35932 35954
80 40451 40624 40782 40875 40963 41007 41052 41074 41097
90 45591 45765 45924 46018 46105 46150 46195 46217 46240
100 50731 50906 51066 51160 51248 51292 51337 51360 51383
125 63582 63760 63922 64016 64105 64149 64194 64217 64240
150 76435 76615 76778 76873 76961 77006 77051 77074 77097
175 89289 89471 89634 89730 89818 89863 89909 89931 89954
200 102144 102326 102491 102586 102675 102720 102766 102788 102811
225 114999 115182 115347 115443 115532 115577 115623 115646 115668
250 127854 128038 128204 128300 128389 128435 128480 128503 128526
275 140710 140895 141061 141157 141246 141292 141337 141360 141383
300 153565 153751 153917 154014 154104 154149 154194 154217 154240
350 179277 179464 179631 179728 179818 179863 179908 179931 179954
400 204990 205177 205345 205442 205532 205577 205623 205645 205668
450 230702 230891 231059 231156 231246 231291 231337 231360 231383
Table 6-1. 7 Seconds Average Service Time  — Continued
AVG SPEED ANS
agents 11 15 22 30 45 60 90 120 180
Continued on next page 
						

							Engineering  ACD Applications with Data Obtained from 
the BCMS Reports
Issue  4  September 1995
6-13
500 256415 256604 256773 256870 256960 257006 257051 257074 257097
550 282128 282318 282487 282584 282674 282720 282765 282788 282811
600 307842 308032 308201 308298 308389 308434 308480 308503 308525
650 333555 333745 333915 334013 334103 334148 334194 334217 334240
700 359268 359459 359629 359727 359817 359863 359908 359931 359954
750 384982 385173 385343 385441 385531 385577 385623 385645 385668
800 410696 410887 411057 411155 411246 411291 411337 411360 411383
850 436409 436601 436771 436869 436960 437005 437051 437074 437097
900 462123 462315 462485 462583 462674 462720 462765 462788 462811
950 487837 488029 488199 488298 488388 488434 488480 488503 488525
1000 513551 513743 513914 514012 514103 514148 514194 514217 514240
Table 6-1. 7 Seconds Average Service Time  — Continued
AVG SPEED ANS
agents 11 15 22 30 45 60 90 120 180
Continued on next page 
						

							Use of BCMS Rep orts for ACD Plannin g
6-14Issue  4  September 1995 
Table 6-2. 15 Seconds Average Service Time 
AVG SPEED ANS
agents 11 15 22 30 45 60 90 120 180
1 44526886115136163180198
2 196 222 261 295 339 367 399 417 437
3 386 425 478 521 572 603 637 656 676
4 592 640 703 752 808 840 876 896 916
5 806 862 933 986 1045 1078 1115 1135 1156
6 1025 1089 1165 1221 1282 1317 1355 1375 1396
7 1248 1317 1399 1457 1521 1556 1594 1615 1636
8 1474 1548 1634 1694 1759 1795 1834 1854 1875
9 1702 1780 1869 1932 1998 2035 2074 2094 2115
10 1931 2013 2106 2170 2237 2274 2313 2334 2355
12 2393 2482 2580 2646 2715 2753 2793 2814 2835
14 2858 2953 3055 3124 3194 3232 3273 3294 3315
16 3326 3425 3531 3601 3673 3712 3752 3773 3795
18 3796 3899 4008 4079 4152 4191 4232 4253 4275
20 4266 4373 4485 4558 4631 4671 4712 4733 4755
25 5448 5562 5679 5754 5830 5870 5911 5933 5955
30 6634 6753 6875 6952 7029 7069 7111 7133 7155
35 7823 7947 8071 8150 8228 8269 8311 8333 8355
40 9013 9141 9268 9349 9427 9468 9511 9533 9555
45 10205 10336 10466 10547 10626 10668 10711 10732 10755
50 11399 11532 11664 11746 11826 11868 11910 11932 11955
60 13787 13926 14061 14144 14225 14267 14310 14332 14355
70 16178 16321 16458 16543 16624 16667 16710 16732 16755
80 18571 18716 18856 18942 19024 19066 19110 19132 19154
90 20965 21113 21254 21341 21423 21466 21510 21532 21554
100 23359 23510 23653 23740 23823 23866 23910 23932 23954
125 29349 29504 29650 29738 29822 29866 29910 29932 29954
150 35341 35499 35648 35737 35822 35865 35909 35932 35954
175 41334 41496 41646 41736 41821 41865 41909 41932 41954
Continued on next page 
						

							Engineering  ACD Applications with Data Obtained from 
the BCMS Reports
Issue  4  September 1995
6-15
200 47329 47493 47645 47735 47821 47865 47909 47932 47954
225 53325 53490 53644 53735 53821 53865 53909 53932 53954
250 59321 59488 59643 59734 59821 59865 59909 59932 59954
275 65318 65487 65642 65734 65820 65864 65909 65932 65954
300 71315 71485 71641 71733 71820 71864 71909 71932 71954
350 83310 83482 83640 83733 83820 83864 83909 83931 83954
400 95307 95480 95639 95732 95820 95864 95909 95931 95954
450 107303 107478 107638 107732 107819 107864 107909 107931 107954
500 119301 119477 119637 119731 119819 119864 119909 119931 119954
550 131298 131476 131636 131731 131819 131864 131909 131931 131954
600 143296 143474 143636 143731 143819 143864 143909 143931 143954
650 155294 155473 155635 155730 155819 155864 155909 155931 155954
700 167293 167473 167635 167730 167819 167863 167909 167931 167954
750 179291 179472 179635 179730 179819 179863 179909 179931 179954
800 191290 191471 191634 191730 191818 191863 191909 191931 191954
850 203289 203470 203634 203729 203818 203863 203909 203931 203954
900 215287 215470 215634 215729 215818 215863 215909 215931 215954
950 227286 227469 227633 227729 227818 227863 227909 227931 227954
1000 239285 239469 239633 239729 239818 239863 239908 239931 239954
Table 6-2. 15 Seconds Average Service Time  — Continued
AVG SPEED ANS
agents 11 15 22 30 45 60 90 120 180
Continued on next page