120759241 capacity planning gsm (3)

Capacity Planning

Capacity Planning

Contents 1 Ge eral Terminology 3 1.1 General 3 1.2 Traffic Offered, Traffic Carried, Traffic Lost 3 1.3 Traffic Flow Units Erlang (Erl), Traffic Intensity 4 2 Erlang-B Formula 7 3 Erlang-C Formula 9 4 Traffic 10 4.1 Traffic Distribution 10 4.2 Traffic Forecasting 10 4.3 Traffic Measurements 11 5 Network Dimensioning 13 5.1 Dimensioning of TRX 13 5.2 Dimensioning of Control and Traffic Channels 13 5.3 Dimensioning of Terrestrial Interfaces 15 5.4 CCSS7 Dimensioning 18 5.5 Signalling Load Per BSC 19 5.6 TRAU Capacity 21 5.7 Capacity and Cell Radius 21 6 Exercise 22

Network Optimization SSMC Training Center

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Capacity Planning


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Capacity Planning

1 General Terminology 1.1 General The traffic theory in general uses mathematical models to describe and to optimize traffic systems. In telecommunication traffic theory (also called teletraffic theory) it is a telecommunication system which is considered with the help of appropriate mathematical models. Since real systems are quite complex systems, simplifications and assumptions have to be performed to not deal with too complicated and sophisticated mathematics. Later on these assumptions and simplifications have to be justified. Since a bad model can never lead to good results, the problem is to find a good and easy model to get reliable results. Some mathematical ideas, models and formulas which are used in traffic theory are presented now on the following pages. Each telephone system must be dimensioned in such a way that even during periods of high traffic (offered), the subscribers still have a good chance of success in making calls. Those subscribers who do not succeed in making a call will either be lost (in a pure lost-call telephone system) or the calls will be delayed (in a waiting-call telephone system). Usually, real telephone systems are combined lost-/ waiting-call systems. Even during the so called busy hour the percentage of non successful subscribers should not exceed a predefined value. This means for the network operator that the dimensioning of his telephone system must be driven on the one hand by guaranteeing some Quality of service (QOS) and on the other hand by economical aspects.

From economical point of view, the amount of necessary equipment (switches, base stations, multiplexers, cross-connectors, ...) and also the number of links between this equipment should be kept to a minimum.

From QOS point of view, the more trunks are offered by the telephone system, the higher the probability for the subscribers to succeed in making calls.


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1.2 Traffic Offered, Traffic Carried, Traffic Lost

The traffic offered is defined as the mean number of occupations (calls) offered to the system. Both, accepted and not accepted occupations (calls) contribute to the traffic offered. In principle the traffic offered cant be exactly measured, however it can be estimated. The traffic carried is defined as the mean number of simultaneous occupations of servers (trunks). In a pure loss system, it can happen that the traffic offered is greater than the traffic carried. The non carried traffic will be lost and is called traffic lost. In a pure waiting system, the traffic offered is always equal to the traffic carried. All the calls which can not be served directly after request due to lack of servers (trunks) will wait for being served. In a combined loss-/ waiting-system not queued calls which could not be served will be lost. In such systems, the traffic carried will be probably again smaller than the traffic offered, however compared to pure loss systems the amount of traffic carried is mostly greater.

Fig.1 Blocking system example: speech channels on GSM (N = number of traffic sources)


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1.3 Traffic Flow Units Erlang (Erl), Traffic Intensity

In honour of A. K. Erlang (1878-1929), a Danish mathematician who was the founder of traffic theory, the unit of the traffic flow (or traffic intensity) is called Erlang (Erl). The traffic flow is a measure of the size of the traffic. Although the traffic flow is a dimensionless quantity, the Erlang was assigned as unit of the traffic flow in traffic theory. By definition: 1 trunk occupied for a duration t of a considered period T carries t / T Erlang. From this definition it follows already that the traffic carried in Erlang can not exceed the number of trunks. Especially for traffic measurements it is useful to consider the traffic flow as averaged number of trunks which are occupied (busy) during a specified time period: Traffic intensity = Mean number of busy trunks in a time period If this is a long time period, ongoing calls at the beginning and at the end of this period can be neglected. The traffic flow then can be considered as call intensity (number of trunk occupations per time unit) times the mean holding time (which is the average holding time per trunk occupation):


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Traffic intensity = Call intensity x Mean holding time An example for a traffic model is given in the table below:

number of call attempts (MOC+MTC) per subscriber per hour 1,1

percentage of MOC 58 %

percentage of engaged in the case of an MOC 19,8 %

duration of TCH occupation in the engaged case 3s

no answer from a person called by MOC 14,4 %

mean TCH occupation for this case 30 s

percentage of successful MOC 65,8 %

mean time for ringing (MOC) 15 s

percentage of MTC 42 %

no paging response 32,5 %

duration of TCH occupation in this case 0 s

no answer from a mobile subscriber 13,5%

means TCH occupation fir this case 30 s

successful MTC 54,0 %

mean time for ringing (MTC) 5 s

mean call duration (MOC/MTC) 115 s

mean TCH occupation call attempt 83 s TCH load per subscriber 0,025 Erl time for MOC/MTC setup signaling on SDCCH (authentications, ...) 3 s

time for a location update 5 s

number of location update per subscriber per hour 2,2

resulting SDDCCH load per subscriber (no TCH queuing applied) 0,004 Erl

Standard traffic model for GSM

The formula for calculating the load on the respective dedicated channel is given on the next page.


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Load on Dedicated Channels

SDCCH load [Erl]:

SUBSCR * (MTC_PR_ph + MOC_ph) * T_SETUP + LU_ph * T_LU+ IMSI_ph * T_IMSI + SMS_ph * T_SMS)

TCH load [Erl]: SUBSCR * (MTC_PR_ph + MOC_ph) * T_CALL

SUBSCR: number of subscribers within the cell

MTC_PR_ph: mobile terminating calls per subscriber per hour with paging response

MOC_ph: mobile terminating calls per subscriber per hour

LU_ph: location updates per subscriber per hour

IMSI_ph: IMSI attach/detach per subscriber per hour

SMS_ph short message service per hour

T_SETUP: mean time [sec] for call setup signaling on SDCCH

T_LU: mean time [sec] for location update signaling

T_IMSI: mean time [sec] for IMSI attach/detach signaling on SDCCH

T_SMS: mean time [sec] for short message service

T_Call: mean TCH occupation time per call

For the values of the traffic model above one has TCH load per subscriber: 25 mErl SDCCH load per subscriber: 4 mErl


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2 Erlang-B Formula

Erlang-B formula is based on the following assumptions:

Pure loss system Infinite number of traffic sources Finite number of devices (trunks) n Full availability of all trunks Exponentially distributed holding times Constant call intensity, independent of the number of occupations

=>Time and call congestion are equal. This formula

is called Erlang`s formula of the first kind (or also Erlang loss formula or Erlang B formula). It describes the congestion as function of the Traffic Offered and the number of available trunks. ( B: Blocking rate, A: Traffic demand; n: Number of circuits) In real life the situation is mostly different. People often want to calculate the number of needed trunks for a certain amount of traffic offered and a maximum defined congestion. That means the Erlang B formula must be rearranged: n = function of (B and A) This rearrangement cannot be done analytically but only numerically and will be performed most easily with the help of a computer. Another possibility is the usage of special tables, namely so called Erlang B look-up tables.


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Capacity Planning

n p = 1 % p = 3 % p = 5 % p = 7 % n p = 1 % p = 3 % p = 5 % p = 7 %

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

0.01 0.15 0.46 0.87 1.36 1.91 2.50 3.13 3.78 4.46 5.16 5.88 6.61 7.35 8.11 8.88 9.65 10.44 11.23 12.03 12.84 13.65 14.47 15.29 16.13 16.96 17.80 18.64 19.49 20.34 21.19 22.05 22.91 23.77 24.64 25.51 26.38 27.25 28.13 29.01 29.89 30.77 31.66 32.54 33.43 34.32 35.22 36.11 37.00 37.90

0.03 0.28 0.72 1.26 1.88 2.54 3.25 3.99 4.75 5.53 6.33 7.14 7.97 8.80 9.65 10.51 11.37 12.24 13.11 14.00 14.89 15.78 16.68 17.58 18.48 19.39 20.31 21.22 22.14 23.06 23.99 24.91 25.84 26.78 27.71 28.65 29.59 30.53 31.47 32.41 33.36 34.30 35.25 36.20 37.17 38.11 39.06 40.02 40.98 41.93

0.05 0.38 0.90 1.53 2.22 2.96 3.74 4.54 5.37 6.22 7.08 7.95 8.84 9.37 10.63 11.54 12.46 13.39 14.31 15.25 16.19 17.13 18.08 19.03 19.99 20.94 21.90 22.87 23.83 24.80 25.77 26.75 27.72 28.70 29.68 30.66 31.64 32.62 33.61 34.60 35.58 36.57 37.57 38.56 39.55 40.54 41.54 42.54 43.53 44.53

0.08 0.47 1.06 1.75 2.50 3.30 4.14 5.00 5.88 6.78 7.69 8.61 9.54 10.48 11.43 12.39 13.35 14.32 15.29 16.27 17.25 18.24 19.23 20.22 21.21 22.21 23.21 24.22 25.22 26.23 27.24 28.25 29.26 30.28 31.29 32.31 33.33 34.35 35.37 36.40 37.42 38.45 39.47 40.50 41.53 42.56 43.59 44.62 45.65 46.69

51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

38.80 39.70 40.60 41.50 42.41 43.31 44.22 45.13 46.04 46.95 47.86 48.77 49.69 50.60 51.52 52.44 53.35 54.27 55.19 56.11 57.03 57.96 58.88 59.80 60.73 61.65 62.58 63.51 64.43 65.36 66.29 67.22 68.15 69.08 70.02 70.95 71.88 72.81 73.75 74.68 75.62 76.56 77.49 78.43 79.37 80.31 81.24 82.18 83.12 84.06

42.89 43.85 44.81 45.78 46.74 47.70 48.67 49.63 50.60 51.57 52.54 53.51 54.48 55.45 56.42 57.39 58.37 59.34 60.32 61.29 62.27 63.24 64.22 65.20 66.18 67.16 68.14 69.12 70.10 71.08 72.06 73.04 74.02 75.01 75.99 76.97 77.96 78.94 79.93 80.91 81.90 82.89 83.87 84.86 85.85 86.84 87.83 88.82 89.80 90.79

45.53 46.53 47.53 48.54 46.54 50.54 51.55 52.55 53.56 54.57 55.57 56.58 57.59 58.60 59.61 60.62 61.63 62.64 63.65 64.67 65.68 66.69 67.71 68.72 69.74 70.75 71.77 72.79 73.80 74.82 75.84 76.86 77.87 78.89 79.91 80.93 81.95 82.97 83.99 85.01 86.04 87.06 88.08 89.10 90.12 91.15 92.17 93.19 94.22 95.24

47.72 48.76 49.79 50.83 51.86 52.90 53.94 54.98 56.02 57.06 58.10 59.14 60.18 61.22 62.27 63.31 64.35 65.40 66.44 67.49 68.53 69.58 70.62 71.67 72.72 73.77 74.81 75.86 76.91 77.96 79.01 80.06 81.11 82.16 83.21 84.26 85.31 86.36 87.41 88.46 89.52 90.57 91.62 92.67 93.73 94.78 95.83 9689 97.94 98.99

Erlang B formula


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3 Erlang-C Formula

Erlang-C formula is based on the following assumptions:

Pure delay system Infinite number of traffic sources N Finite number of devices (trunks) n Full availability of all trunks Exponentially distributed inter-arrival times between calls which corresponds

to a constant call intensity y, i.e. the probability of a new offered call is the same at all time points, independent of the number of occupations

Exponentially distributed holding times (s) Time congestion is defined as the probability that all devices are used:

This formula is called Erlang`s formula of the second kind (or Erlang delay formula or Erlang C formula). Call congestion is defined as the probability that a call has to wait: B=E The traffic carried and traffic offered are: Acarried =Aoffered=A=y*s The mean number of waiting calls is;

The mean waiting time for calls, which have to wait is:

The waiting time for all the calls is:

The waiting time distribution depends on the queue discipline, whereas the mean waiting time is in general independent of the queue discipline.


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4 Traffic

4.1 Traffic Distribution

Time Dependency The traffic in a telecommunication network as a function of time will not be constant but will show significant fluctuations. Variations of the traffic during a single day, from day to day, for different weekdays, or even for different seasons can be observed. Also on a long time scale the averaged traffic will not remain constant but will increase in most telecommunication networks.

Fig.2 Time dependency of traffic distribution

Location Dependency The traffic in a telecommunication network will not be location independent but will show significant location dependencies. For example, in rural areas there will be less traffic compared to city areas.


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4.2 Traffic Forecasting

An important aspect in dimensioning a telecommunication network is the expected traffic in the future. Therefore, an analysis of the expected traffic is of great interest. Even in case that the penetration (number of traffic sources) saturates, the amount of traffic does not necessarily saturates too. Traffic forecasts are not easy and may be influenced by many aspects: e.g. price politics, offered services, The more the important dependencies are realized and taken into account, the more precise the forecasts will be. For a detailed analysis it is useful to: Split the total PLMN into sub areas

Categorize the subscribers: e.g. into business, residential, Analyze: e.g. the number of subscribers per area, the development of the

penetration depth, the expected penetration depth

Analyse also economic dependencies like e.g. any correlation between the demand of telephone service and e.g. the economic activities in a special region, the economic situation in general (measured e.g. by the economic growth), the income of the people,

4.3 Traffic Measurements

It is of great interest for the network operator to measure the real traffic situation in his network. To perform such measurements, in former telecommunication systems special traffic measurement equipment (e.g. the so called electromechanical meter) was needed. Since in the meantime most telecommunication systems are digital, this kind of equipment is not needed any more: The call and device concerning data are stored in the memory of the system processor. It is only a question of software to read them out. The traffic measurements are usually part of the so called Performance Data Measurements.


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Performance Data Measurements can be run continuously, periodically or sporadically, for a long time or a short time, observing smaller or greater parts of the network. Concerning the traffic measurements, either special events are counted (e.g. the number of successful calls, the number of lost calls, ...) or special time intervals are recorded (e.g. holding times, waiting times,...). The corresponding counters could in principle be actualized continuously during the observation period, but mostly a scanning method is used. Scanning method means that the system counts the number of events not continuously but only at particular times. This leads to some uncertainty for the measurement results. Nevertheless, the error performed can be estimated using statistical methods. In general, the smaller the scanning interval the higher the precision of the measurement. Typical scanning intervals are 100 ms or 500 ms.


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5 Network Dimensioning

5.1 Dimensioning of TRX

The dimensioning of the number of TRXs per cell should be based on traffic estimations for this area and should be performed for the busy hour. Using:

the number of subscribers in the corresponding area (for the busy hour) the expected averaged traffic per subscriber (for the busy hour) the offered

traffic A results from: A = No of subscribers x traffic load per subscriber Using the Erlang B look up table the number of TRXs can be derived. Hint: This number also depends on the amount of half rate being used in the cell

5.2 Dimensioning of Control and Traffic Channels

The first step of this task is to estimate the SDCCH traffic, since the need of SDCCHs can vary substantially between network due to e.g. subscriber behavior and parameter settings. An optimum manual SDCCH configuration, for every cell, can only be achieved by looking at cell statistics. The following procedures have an effect on the SDCCH load:

Mobility Management procedures, i.e. Normal Location Updating, Periodic Registration and IMSI attach/detach.

Connection Management, i.e. Call set-up, Short Message, Service point to point (SMS p-p), Fax set-up and Supplementary Services.


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Capacity Planning

The second step is to decide the channel configuration. There are two different types of 51-multiframe as described before:

combined BCCH: includes 4 SDCCH subchannels uncombined BCCH: requires additional SDCCH timeslot (each one

containing 8 SDCCH subchannels) The SDCCHs are possible to configure in a limited set of ways and there are some limitations on the number of SDCCHs that is possible to have in a cell. These possible configurations and limitations apply both for SDCCH dimensioning. If an SDCCH/4 is chosen it is automatically allocated at time slot 0 on the BCCH carrier. For the SDCCH/8s the time slot number and channel group can be specified. The number of TRXs limits the possible number of SDCCH/8s in a cell; i.e. it is not possible to have more SDCCH/8s in a cell than the number of TRXs.

SACCH multiframe (containing 2 BCCH multiframes)

downlink BCCH + CCCH + 4 SDCCH / 4, F = FCCH, S = SCH

uplink R = RACH + SDCCH / 4 Fig.3

Total blocking probability: Assuming traffic offered to connection management is A, Traffic offered to mobility management procedure is A *, According to their different blocking rate, traffic carried by TCH and SDCCH are shown in the following:


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Capacity Planning

Fig. 4 Traffic lost and traffic carried for TCH and SDCCH 5.3 Dimensioning of terrestrial interfaces

LAPD signalling links: O&M signalling for BTSM: LPDLM TRX signalling: LPDLR Signalling for TRAU: LPDLS Rules of thumb: 1. LPDLM and LPDLR are counted as one LAPD-link 2. In case of 1 or 2 TRX, 16 kbit/s are sufficient for LPDLM+LPDLR 3. Otherwise 64 kbit/s are required 4. LPDLS always uses 64 kbit/s Processor capacity: Traditional BSC: One PPLD processor handles up to 8 LAPD links One PPCC processor handles up to 4 CCSS7 links


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High capacity BSC: Two PPXX processors handle up to 248 signaling links load sharing (LAPD and maximum 8 CCSS7)

Fig.5 Interface and signaling

Fig. 6 Assignment of timeslots on Abis and Um interface


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Fig. 7 Assignment of timeslots on Asub and A interface


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5.4 CCSS7 Dimensioning If the types of mobile subscribers are different, the traffic models will be different too. The following is the traffic Model with following assumptions for busy hour (standard subscriber):

And traffic Model with following assumptions for busy hour (highly mobile subscriber):

According to these two different models,SS7 Signalling load per subscriber will be as the following:


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Capacity Planning

5.5 Signalling Load Per BSC

The first step is to calculate total number of subscribers. If the total traffic capacity and traffic per subscriber are known, the number of subscriber can be easy calculated: Number of subscriber = Traffic capacity / Traffic per subscriber For example: 2000 Erlang / (0.025 mErlang/subscriber) = 80 000 subscribers Then if signaling load per subscriber is known, the total required signaling load per BSC can also be calculated: Signalling load = Number of subscribers * Signalling load per subscriber Example 1:if the required CCSS7link capacity: 80 000 subscribers * 600 byte / 3600 sec = 13.3 kbyte/sec CCSS7 link single capacity 64 kbit/s = 8 kbyte/sec Consequence: 2 CCSS7 links required Example 2: if the required CCSS7link capacity : 80 000 subscribers * 1100 byte / 3600 sec = 24.5 kbyte/sec CCSS7 link single capacity 64 kbit/s = 8 kbyte/sec Consequence: 4 CCSS7 links required

Fig. 8 Assignment of timeslot for ss7 on Asub and A


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Capacity Planning

5.6 TRAU Capacity The capacity of TRAU depends on cell sizes. Assume 120 traffic channels can be handled per TRAU and Blocking of A interface has to be taken into account, The following table lists the TRAU capacity for different cell size.

5.7 Capacity and Cell Radius In capacity limited areas of the network: Cell radius is smaller than would be for coverage limited situation to satisfy the traffic demand.

Fig.9 Capacity and cell radius


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6 Exercise 1.Consider a call rate of 1000 calls per hour. The mean holding time is 90 sec. What is the Traffic Offered in Erlang? 2.Consider a Traffic Offered of 30 Erlang and a mean holding time of 120 sec. How many calls per hour do you expect?


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3. Consider 1 BTS with 2 TRXs and full rate channels. Assume 1% blocking. Assume a typical TCH load of 25 mErl per subscriber per hour. Furthermore, assume a typical SDCCH load of 10 mErl per subscriber per hour. Compare configurations A and B: Which one offers the higher capacity?


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Capacity Planning

4.Consider a telephone system with N=6 trunks and a time period of 10 time units (0,1,...,10). Subscriber 1 makes a call from t1 to t3. Subscriber 2 makes a call from t2 to t4. Subscriber 3 makes a call from t3 to t7. Subscriber 4 makes a call from t4 to t8. Subscriber 5 makes a call from t4 to t9. Subscriber 6 makes a call from t5 to t9. Subscriber 7 makes a call from t6 to t8. Subscriber 8 makes a call from t7 to t10. a) Draw the number of used trunks as function of time. b) Draw the number p of simultaneous occupations in the trunk group as function of the total time with exactly p occupations. c) What is the traffic offered in Erlang? d) What is the traffic carried in Erlang? e) What is the lost traffic in Erlang?


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Capacity Planning

5.Consider a pure delay system and a group of 10 trunks belonging to a trunk group. Assume that all these trunks are available (full availability). Assume a traffic offered of 4 Erlangs and a mean holding time of 100 seconds. The queue discipline shall be first come, first served(ordered queue). a) What is the probability to be queued? b) What is the mean waiting time of queued calls? c) What is the mean waiting time of offered calls? d) What is the probability that call are queued for longer than 1 minute?


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6.Consider a pure loss system and a group of 10 trunks belonging to a trunk group. Assume full availability. What is the traffic in Erlangs which can be offered to this system if the probability to be blocked should be maximum 1%, 3%, 5% and 7% ?


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120759241 capacity planning gsm (3)

Documents

traffic systems

traffic lost

traffic intensity

traffic channels

traffic forecasting

traffic measurements

traffic distribution

periods of high traffic