Calculation of the intensity of the telephone load in CSK QUANT-E
Good day. I would like to share with you the information on the calculation of the intensity of the telephone load in CSK QUANT-E. This information will be useful as professionals in this field, for beginner students, and simply for anyone interested in digital switching systems.
Data for calculation are taken randomly and used as an example.
And do not be afraid of the formulas, in fact, this calculation will take no more than 15 minutes.
So, let's begin.
The categories of load sources are characterized by the intensity of specific subscriber loads. In the task taken 3 categories:
- Business sector subscribers - category 1;
- residential sector subscribers - category 2;
- universal payphones - category 3.
The structural composition of subscribers by category for existing RATS is determined depending on the share of subscribers in the apartment sector, because payphones are divided into a separate group. Therefore:
Ni, k = KkNi, and
')
where Ni, and is the number of individual subscribers;
Kk - the share of subscribers of the housing sector.
The number of business subscribers is equal to the difference:
Ni, d = (1 - Kk) Ni, and
Structural composition for CSK is determined minus universal payphones.
The number of individual phones is:
N0, and = N0 - N0, t
Knowing the number of individual TAs, it is possible to determine the number of subscribers in the business sector (Nd) and apartment sector (Nk) using the formulas.
For each PBX, we determine the number of residential and business subscribers:
for rats-2Nk = 0.80 • 4000 = 3200 numbers; Nd = 4000 - 3200 = 800 subscribers.
for rats-3 Nk = 0.80 • 8000 = 6400 numbers; Nd = 8000 - 6400 = 1600 subscribers.
for CSKNk = (11000 - 250) • 0.45 = 4838 subscribers; N = 10750–4838 = 5913 subscribers.
The results of the calculations are listed in table 1.
Table 1 - Number of TAs by category for all stations of the network
The intensity of the load on the CSK is determined by the following formulas:
Y and AB j = Ndyid + Nkik + Ntuit
Yb AB j = Ndyvd + Nkyvk
Ymi AB j = Ndumid + Nkmik + Ntumite
Ymw AB j = Ndumvd + Nkymvk
Perform the calculation of subscriber loads for CSK:
Y and AB CSK = 5913 • 0.074 + 4838 • 0.025 + 250 • 0.090 = 581.01 Earl
Yab AB CSK = 5913 • 0.070 + 4838 • 0.023 = 525.19 Erl
Ymi AB CSK = 5913 • 0.010 + 4838 • 0.001 + 250 • 0.050 = 76.77 Earl
YMV AB CSK = 5913 • 0.008 + 4838 • 0.001 = 51.14 Earl
Perform the calculation of subscriber loads for the rats-2:
Y and AB RATS-2 = 800 • 0.074 + 4838 • 0.025 + 100 • 0.090 = 189.15 Earl
YB AB RATS-2 = 800 • 0.070 + 4838 • 0.023 = 167.27 Earl
Perform the calculation of subscriber loads for the rats-3:
Y and AB RATS-3 = 1600 • 0.074 + 6400 • 0.025 + 300 • 0.090 = 305.4 Earl
Yw AB RATS-3 = 1600 • 0.070 + 6400 • 0.023 = 259.2 Erl
The calculation results are summarized in Table 2 and 3.
Table 2 - load calculation
Table 3 - Calculation of long-distance load
The load on the special services is defined as the share (CP) of the intensity of the outgoing subscriber load:
YiSPj = KSPYiAB
where ksp. = 0.03 ÷ 0.05 - the proportion of the load that is sent to the special services.
Y and cn. CSK = 0.03 • 581.01 = 17.33 Earl
The intensity of the remaining outgoing load is determined by:
Yout ABJ = Yand AB
Yout. AB CSK = 681.01 - 17.43 = 633.58 Erle
The outgoing external loads from AM to the group paths of YGT AM are lower than the load of subscriber lines due to the time difference between the employment of AL and the lines of GT. Similarly, for analog PBX load output GI incoming load. This difference is determined by the coefficient q, the value of which depends on the type of connection:
where: t and - the average duration of classes AL for QC
tco is the average duration of the station signal, tco = 3 s
t - connection establishment time, t = 0
tnab - the time of dialing, which depends on the method of transferring the number from the TA:
- for the pulse method (DKSHI) tnab. = 1.5 n;
- for the frequency method (DTMF) tnab. = 0.4 n;
where n is the number of dialed digits and depends on the numbering value on the network.
For outgoing communication, the value is n = 5 or 6, depending on the numbering value. With mixed numbering, the weighted average value of n is determined:
n = p5 5 + (1 - p5) 6, where p5 is the proportion of calls routed to the RATS with 5-digit numbering.
The value of p5 is equal to:
where ΣN5 and ΣN6 is the total capacity of the RATS, respectively, with 5 and 6-digit
numbering.
from where
n = 0.52 • 5 + (1 - 0.52) • 6 = 5.48
tnab. = 1.5 • 5.48 = 8.22 s
tn = 3 + 8.22 + 0 = 11.22 s
For outgoing long distance calls, n is equal to:
n = pzone 9 + pmg 11 + pmn 14
where is the zone. = 0.6 is the share of calls during zone communication;
pmg = 0.3 - the share of calls during long distance communication;
pmn = 0.1 - the share of calls in international communication.
n = 0.6 • 9 + 0.3 • 11 + 0.1 • 14 = 10.1
tnab.m = 1.5 • 10.1 = 15.15 s
tnm = 3 + 15.15 + 0 = 18.15 s
Coefficient qmi is equal to:
where tmi = 72po Kts - 0.5
For special services, the value of qsp is:
where tsp = 30 s is the reference time;
tn.sp = tco + 1,5n = 3 + 1,5 • 2 = 6 s - the time of dialing with the number of dialed digits equal to 2.
With incoming calls on CSK, the reception of the number and the establishment of the connection are very small with both local and long-distance calls, therefore:
qin. = 1, qin. = qm in. = 1
With incoming communication on analogue rats, the calculation of Yin.i is made taking into account the type of station:
- for the decade-step rats when receiving a DKBI number (tND = 7 s), then:
- for the coordinate rats when receiving the number code of the IBSC (tNK = 2 c):
With outgoing communication on analog rats Yout. i is equal to:
Calculation of external loads on existing rats
Outgoing load:
- RATS-2, LH: Yout.2 = 0.821 • 189.15 = 155.29 Earl
- RATS-3, KS: Yout.3 = 0.821 • 305.4 = 250.73 Earl
Incoming load:
- RATS-2, LH: Yin.2 = 1.09 • 167.27 = 182.32 Earl
- RATS-3, KS: Yin.3 = 1.02 • 259.2 = 264.38 Earl
The external loads on the group tract, taking into account the difference between the classes of AL and GT, are respectively equal to:
- load to special services:
Ysp CSK = qspYisp CSK
where qsp = 0.8
Ysp. CSK = 0.8 • 17.33 = 13.94 Erl
- load output switching field CSK is determined by the formula:
Y = qY
Wvyh CSK = 0.83 • 581.01 = 482.24 Earl
- incoming load:
Yin CSK = Yin AB AB CSK
Yin CSK = 525.19 Earl
- for long distance communication:
YZSLTSSK = qmiYmi ABTSSK
YZSLTSSK = 0.74 • 76.77 = 56.81 Erl
YSLMTSSK = YmvABTSSK
YSLM CSK = 51,14 Erl
YGTAM = YSPTSSK + Y and TsSK + Yvkh. CSK + YZSLTSSK + YSLMTSSK
YGTAM = 13.94 + 482.24 + 525.19 + 56.81 + 51.14 = 1129.32 Earl
The inter-station load from station j to station k is determined by the formula:
where Y is. j is the intensity outgoing from the ratsj (CSK) load,
Yin.k– intensity of incoming load to ratsk,
Yww. (GTS) z - the amount of loads incoming to all RATS, CSK, normalized by coefficients of rats relative to RATS,
nj-k– normalized coefficient of j from station j to station k.
After the calculation of external loads on CSK, RATSj, RATSK, the calculation data is entered into table 4 of the intensity of the outgoing and incoming network loads (Earl).
Table4 - Intensity of outgoing and incoming network loads (Earl):
Table 5 - Coefficients between rats:
Using the above formula, we calculate the distribution of the outgoing load from the CSK to the network stations (Y0 - 0, Y0 - 2, Y0 - 3). Internal station load Y0 - 0 is equal to:
Then the internal load:
Y0 - 0 = 0.43 • 525.19 • 1 = 225.83 Erl
Y0 - 2 = 0.43 • 182.32 • 0.38 = 29.79 Erl
Y0 - 3 = 0.43 • 264.38 • 0.45 = 51.16 Erl
Y2-0 = 0.27 • 525.19 • 0.38 = 53.88 Erl
Y2-2 = 0.27 • 182.32 • 1 = 49.23 Erle
Y2-3 = 0.27 • 264.38 • 0.7 = 49.97 Earl
Y3-0 = 0.4 • 525.19 • 0.45 = 94.53 Erl
Y3-2 = 0.4 • 182.32 • 0.7 = 51.05 Erl
Y3-3 = 0.4 • 264.38 • 1 = 105.75 Erl
Table 6 - Intensity of inter-station load, Earl
The results of the calculation of loads on CSK are recorded on the load distribution scheme for AM and UKS CSK:
The load on the beams of the trunk lines is determined by the results of the calculation of inter-station loads (Table 10), taking into account the load coming from the digital system to CSS and AMTS. To determine the load on the beams SL depict the load distribution scheme
Load distribution on the GTS:
That's all. In fact, everything is simpler than it seems at first glance.
I hope that my efforts will benefit someone.
Data for calculation are taken randomly and used as an example.
And do not be afraid of the formulas, in fact, this calculation will take no more than 15 minutes.
So, let's begin.
Calculation of the intensity of the telephone load
The categories of load sources are characterized by the intensity of specific subscriber loads. In the task taken 3 categories:
- Business sector subscribers - category 1;
- residential sector subscribers - category 2;
- universal payphones - category 3.
The structural composition of subscribers by category for existing RATS is determined depending on the share of subscribers in the apartment sector, because payphones are divided into a separate group. Therefore:
Ni, k = KkNi, and
')
where Ni, and is the number of individual subscribers;
Kk - the share of subscribers of the housing sector.
The number of business subscribers is equal to the difference:
Ni, d = (1 - Kk) Ni, and
Structural composition for CSK is determined minus universal payphones.
The number of individual phones is:
N0, and = N0 - N0, t
Knowing the number of individual TAs, it is possible to determine the number of subscribers in the business sector (Nd) and apartment sector (Nk) using the formulas.
For each PBX, we determine the number of residential and business subscribers:
for rats-2Nk = 0.80 • 4000 = 3200 numbers; Nd = 4000 - 3200 = 800 subscribers.
for rats-3 Nk = 0.80 • 8000 = 6400 numbers; Nd = 8000 - 6400 = 1600 subscribers.
for CSKNk = (11000 - 250) • 0.45 = 4838 subscribers; N = 10750–4838 = 5913 subscribers.
The results of the calculations are listed in table 1.
Table 1 - Number of TAs by category for all stations of the network
The intensity of the load on the CSK is determined by the following formulas:
Y and AB j = Ndyid + Nkik + Ntuit
Yb AB j = Ndyvd + Nkyvk
Ymi AB j = Ndumid + Nkmik + Ntumite
Ymw AB j = Ndumvd + Nkymvk
Perform the calculation of subscriber loads for CSK:
Y and AB CSK = 5913 • 0.074 + 4838 • 0.025 + 250 • 0.090 = 581.01 Earl
Yab AB CSK = 5913 • 0.070 + 4838 • 0.023 = 525.19 Erl
Ymi AB CSK = 5913 • 0.010 + 4838 • 0.001 + 250 • 0.050 = 76.77 Earl
YMV AB CSK = 5913 • 0.008 + 4838 • 0.001 = 51.14 Earl
Perform the calculation of subscriber loads for the rats-2:
Y and AB RATS-2 = 800 • 0.074 + 4838 • 0.025 + 100 • 0.090 = 189.15 Earl
YB AB RATS-2 = 800 • 0.070 + 4838 • 0.023 = 167.27 Earl
Perform the calculation of subscriber loads for the rats-3:
Y and AB RATS-3 = 1600 • 0.074 + 6400 • 0.025 + 300 • 0.090 = 305.4 Earl
Yw AB RATS-3 = 1600 • 0.070 + 6400 • 0.023 = 259.2 Erl
The calculation results are summarized in Table 2 and 3.
Table 2 - load calculation
Table 3 - Calculation of long-distance load
The load on the special services is defined as the share (CP) of the intensity of the outgoing subscriber load:
YiSPj = KSPYiAB
where ksp. = 0.03 ÷ 0.05 - the proportion of the load that is sent to the special services.
Y and cn. CSK = 0.03 • 581.01 = 17.33 Earl
The intensity of the remaining outgoing load is determined by:
Yout ABJ = Yand AB
Yout. AB CSK = 681.01 - 17.43 = 633.58 Erle
The outgoing external loads from AM to the group paths of YGT AM are lower than the load of subscriber lines due to the time difference between the employment of AL and the lines of GT. Similarly, for analog PBX load output GI incoming load. This difference is determined by the coefficient q, the value of which depends on the type of connection:
where: t and - the average duration of classes AL for QC
tco is the average duration of the station signal, tco = 3 s
t - connection establishment time, t = 0
tnab - the time of dialing, which depends on the method of transferring the number from the TA:
- for the pulse method (DKSHI) tnab. = 1.5 n;
- for the frequency method (DTMF) tnab. = 0.4 n;
where n is the number of dialed digits and depends on the numbering value on the network.
For outgoing communication, the value is n = 5 or 6, depending on the numbering value. With mixed numbering, the weighted average value of n is determined:
n = p5 5 + (1 - p5) 6, where p5 is the proportion of calls routed to the RATS with 5-digit numbering.
The value of p5 is equal to:
where ΣN5 and ΣN6 is the total capacity of the RATS, respectively, with 5 and 6-digit
numbering.
from where
n = 0.52 • 5 + (1 - 0.52) • 6 = 5.48
tnab. = 1.5 • 5.48 = 8.22 s
tn = 3 + 8.22 + 0 = 11.22 s
For outgoing long distance calls, n is equal to:
n = pzone 9 + pmg 11 + pmn 14
where is the zone. = 0.6 is the share of calls during zone communication;
pmg = 0.3 - the share of calls during long distance communication;
pmn = 0.1 - the share of calls in international communication.
n = 0.6 • 9 + 0.3 • 11 + 0.1 • 14 = 10.1
tnab.m = 1.5 • 10.1 = 15.15 s
tnm = 3 + 15.15 + 0 = 18.15 s
Coefficient qmi is equal to:
where tmi = 72po Kts - 0.5
For special services, the value of qsp is:
where tsp = 30 s is the reference time;
tn.sp = tco + 1,5n = 3 + 1,5 • 2 = 6 s - the time of dialing with the number of dialed digits equal to 2.
With incoming calls on CSK, the reception of the number and the establishment of the connection are very small with both local and long-distance calls, therefore:
qin. = 1, qin. = qm in. = 1
With incoming communication on analogue rats, the calculation of Yin.i is made taking into account the type of station:
- for the decade-step rats when receiving a DKBI number (tND = 7 s), then:
- for the coordinate rats when receiving the number code of the IBSC (tNK = 2 c):
With outgoing communication on analog rats Yout. i is equal to:
Calculation of external loads on existing rats
Outgoing load:
- RATS-2, LH: Yout.2 = 0.821 • 189.15 = 155.29 Earl
- RATS-3, KS: Yout.3 = 0.821 • 305.4 = 250.73 Earl
Incoming load:
- RATS-2, LH: Yin.2 = 1.09 • 167.27 = 182.32 Earl
- RATS-3, KS: Yin.3 = 1.02 • 259.2 = 264.38 Earl
The external loads on the group tract, taking into account the difference between the classes of AL and GT, are respectively equal to:
- load to special services:
Ysp CSK = qspYisp CSK
where qsp = 0.8
Ysp. CSK = 0.8 • 17.33 = 13.94 Erl
- load output switching field CSK is determined by the formula:
Y = qY
Wvyh CSK = 0.83 • 581.01 = 482.24 Earl
- incoming load:
Yin CSK = Yin AB AB CSK
Yin CSK = 525.19 Earl
- for long distance communication:
YZSLTSSK = qmiYmi ABTSSK
YZSLTSSK = 0.74 • 76.77 = 56.81 Erl
YSLMTSSK = YmvABTSSK
YSLM CSK = 51,14 Erl
YGTAM = YSPTSSK + Y and TsSK + Yvkh. CSK + YZSLTSSK + YSLMTSSK
YGTAM = 13.94 + 482.24 + 525.19 + 56.81 + 51.14 = 1129.32 Earl
The inter-station load from station j to station k is determined by the formula:
where Y is. j is the intensity outgoing from the ratsj (CSK) load,
Yin.k– intensity of incoming load to ratsk,
Yww. (GTS) z - the amount of loads incoming to all RATS, CSK, normalized by coefficients of rats relative to RATS,
nj-k– normalized coefficient of j from station j to station k.
After the calculation of external loads on CSK, RATSj, RATSK, the calculation data is entered into table 4 of the intensity of the outgoing and incoming network loads (Earl).
Table4 - Intensity of outgoing and incoming network loads (Earl):
Table 5 - Coefficients between rats:
Using the above formula, we calculate the distribution of the outgoing load from the CSK to the network stations (Y0 - 0, Y0 - 2, Y0 - 3). Internal station load Y0 - 0 is equal to:
Then the internal load:
Y0 - 0 = 0.43 • 525.19 • 1 = 225.83 Erl
Y0 - 2 = 0.43 • 182.32 • 0.38 = 29.79 Erl
Y0 - 3 = 0.43 • 264.38 • 0.45 = 51.16 Erl
Y2-0 = 0.27 • 525.19 • 0.38 = 53.88 Erl
Y2-2 = 0.27 • 182.32 • 1 = 49.23 Erle
Y2-3 = 0.27 • 264.38 • 0.7 = 49.97 Earl
Y3-0 = 0.4 • 525.19 • 0.45 = 94.53 Erl
Y3-2 = 0.4 • 182.32 • 0.7 = 51.05 Erl
Y3-3 = 0.4 • 264.38 • 1 = 105.75 Erl
Table 6 - Intensity of inter-station load, Earl
The results of the calculation of loads on CSK are recorded on the load distribution scheme for AM and UKS CSK:
The load on the beams of the trunk lines is determined by the results of the calculation of inter-station loads (Table 10), taking into account the load coming from the digital system to CSS and AMTS. To determine the load on the beams SL depict the load distribution scheme
Load distribution on the GTS:
That's all. In fact, everything is simpler than it seems at first glance.
I hope that my efforts will benefit someone.
Source: https://habr.com/ru/post/136814/
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