Reduction Factor

information has been considered as a part of the network dimensioning process in this document.

Timeslot Utilisation

Timeslot utilization takes into account the average number of timeslots that are available for packet switched traffic. It is a measure of how much the network is loaded with data services. Networks with timeslot utilisation close to 100% are close to saturation and the end-user performance is likely to be very poor.

In Atoll this parameter is termed as the Load (Traffic load for circuit switched traffic and packet switched traffic load for packet switched traffic). It is described in more detail in the Network dimensioning steps section.

Reduction factor takes into account the user throughput reduction due to timeslot sharing among many users. The figure below shows how the peak throughput available per timeslot is reduced by interference and sharing.Reduction factor is a function of the number of timeslots assigned to a user (N_u), number of timeslots available in the system (N_s) and the average system packet switched traffic load (L_p) (utilization of resources in the system). Data Erlangs or data traffic is given by:

More precisely, the reduction factor is a function of the ratio N_s/N_u (N_p). N_p models the equivalent timeslots that are available for the packet switched traffic in the system. For example, a 24-timeslot system with each user assigned 3 timeslots per connection can be modelled by a single timeslot connection system with 8 timeslots in total.

The formula for reduction factor can be derived following the same hypotheses followed by Erlang in the derivation of the blocking probability formulas (Erlang B and Erlang C).

Let X be a random variable that measures the reduction factor in a certain system state:

Where n is the instantaneous number of connections in the system. The throughput reduction factor is defined as:

Or,

Here, P(X=n) is the probability function of having n connections in the system. Under the same assumptions as those of the Erlang formulas, the probability function can be written as:

Hence the reduction factor can finally be written as:

This formula is not directly applicable in any software application due to the summations up to infinity. Atoll uses the following version of this formula that is exactly the same formula without the summation overflow problem.

Figure 5.8Reduction of Throughput per Timeslot Data Erlangs = L_PN_S

The default quality curves for the Reduction Factor have been derived using the above formula. Each curve is for a fixed number of timeslots available for packet switched traffic (N_p) describing the reduction factor at different values of packet switched traffic load (L_p). The figure below contains all the reduction factor quality curves in Atoll. The Maximum reduction factor can be 1, implying a maximum throughput, and the minimum can be 0, implying a saturated system with no data throughput.

Each curve in the above figure represents an equivalent number of packet switched timeslots, N_P.

5.6.1.2.2 Delay

Delay is the time required for an LLC PDU to be completely transferred from the SGSN to the MS, or vice versa. As the delay is a function of the delays and the losses incurred at the packet level, the network parameters, such as the packet queue length, and different protocol properties, such as the size of the LLC PDU, become important. It is also quite dependent upon the radio access round trip time (RA RTT) and has a considerable impact on the application level performance viewed by the user.

The delay parameter is a user level parameter rather than being a network level quantity, like throughput per cell, timeslot capacity, TBF blocking and reduction factor, hence it is difficult to model and is currently under study. Hence, no default curve is presently available for delay in Atoll.

5.6.1.2.3 Blocking Probability

In GPRS, there is no blocking as in circuit switched connections. If a new temporary block flow (TBF) establishment is requested and there are already M users per timeslot, M being the maximum limit of multiplexing per timeslot (Multiplexing factor), the request is queued in the system to be established later when resources become available.

Supposing that M number of users can be multiplexed over a single timeslot (PDCH), we can have a maximum of M * N_p users in the system. This implies that if a new TBF is requested when there are already M * N_p users active, it will be blocked and placed in a queue. So the blocking probability is the probability of having M * N_p + 1 users in the system or more, meaning,

as in this case n is always greater than N_p, we have,

Figure 5.9Reduction Factor for Different Packet Switched Traffic Loads (L_p, X-axis) RF

L_PN_P

 ⁿ

---n!

n=1 N_P



^N^P

N_P+1

 

N_P!

--- ln1–L_P L_Pⁿ ---n n=1

N_P



 

 

 

 –

L_PN_P

 ⁿ

---n!

n=1 N_P



^^L^P^^N^P^

N_P

N_P!

--- L_P 1–L_P

--- +

---=

P X = n for n = M N _P 1+

So, the Blocking Probability can be given as:

Eliminating the summations to infinity, the blocking probability can be stated in a simpler form:

The above formula has been used to generate the default quality curves for blocking probability in Atoll.

These graphs are generated for a user multiplexing factor of 8 users per timeslot. Each curve represents an equivalent number of packet switched timeslots, N_P.

The curves depict the blocking probabilities for different number of available connections (N_p) at different packet switched traffic loads (L_p) for a fixed user multiplexing factor of 8. The figure below contains all the blocking probability curves for packet switched traffic dimensioning in Atoll. The blocking probability increases with the packet switched traffic load, which implies that as the packet switched traffic increases for a given number of timeslots, the system starts to get more and more loaded, hence there is higher probability of having a temporary block flow placed in a waiting queue.

Figure 5.10Blocking Probability for Different Packet Switched Traffic Loads (L_p, X-axis)

Reference:

T. Halonen, J. Romero, J. Melero; GSM, GPRS and EDGE performance – Evolution towards 3G/UMTS, John Wiley and Sons Ltd.

5.6.2 Network Dimensioning Process

The network dimensioning process is described below in detail. As the whole dimensioning process is in fact a chain of small processes that have there respective inputs and outputs, with outputs of a preceding one being the inputs to the next, the best method is to detail each process individually in form of steps of the global dimensioning process.

5.6.2.1 Network Dimensioning Engine

During the dimensioning process, Atoll first computes the number of timeslots required to accommodate the circuit switched traffic. Then it calculates the number of timeslots to add in order to satisfy the demand of packet switched traffic.

This is performed using the quality curves entered in the dimensioning model used. If the dimensioning model has been indicated to take all three KPIs in to account (throughput reduction factor, delay and blocking probability), the number of timeslots to be added is calculated such that:

3. The throughput reduction factor is greater than the minimum throughput reduction factor, 4. Delay is less than the maximum permissible delay defined in the service properties, and

5. The blocking probability is less than the maximum allowable blocking probability defined in the service properties.

The figure below depicts a simplified flowchart of the dimensioning engine in Atoll.

On the whole, following are the inputs and outputs of the network dimensioning process:

5.6.2.1.1 Inputs

• Circuit switched traffic demand

• Packet switched traffic demand

• Timeslot configurations defined for each subcell

• Target traffic overflow rate and Half-rate traffic ratio for each subcell

• Service availability criteria: minimum required throughput per user, maximum permissible delay, maximum allowable blocking probability etc.

• Dimensioning model parameters: Maximum number of TRXs per transmitter, dimensioning model for circuit switched traffic, number of minimum dedicated packet switched timeslots per transmitter, maximum number of TRXs added for packet switched services, KPIs to consider, and their quality curves.

5.6.2.1.2 Outputs

• Number of required TRXs per transmitter

• Number of required shared, circuit switched and packet switched timeslots

• Traffic load

• Served circuit switched traffic

• Served packet switched traffic

• Effective rate of traffic overflow

• Actual KPI values: throughput reduction factor, delay and blocking probability

5.6.2.2 Network Dimensioning Steps

This section describes the entire process step by step as it is actually performed in Atoll. Details of the calculations of the parameters that are calculated during each step are described as well.

5.6.2.2.1 Step 1: Timeslots Required for CS Traffic

Atoll computes the number of timeslots required to accommodate the circuit switched traffic assigned to each subcell.

Atoll takes the circuit switched traffic demand (Erlangs) either user-defined or calculated in the traffic analysis and assigned to the current subcell and the maximum blocking probability defined for the circuit switched service, and computes the required number of timeslots to satisfy this demand using the Erlang B or Erlang C formula (as defined by the user).

If the user-defined target rate of traffic overflow per subcell, O_Target, is greater than the maximum blocking rate defined in the services properties, it is going to be taken as the Grade of Service required for that subcell instead of the maximum blocking rate of the service.

For the blocking probability GoS and circuit switched traffic demand TD_C, Atoll determines the required number of timeslots TS_{req. C} for each subcell using formulas described below. In fact, Atoll searches for TS_{req. C} value until the defined grade of service is reached.

Figure 5.11Network Dimensioning Process

For Erlang B, we have:

For Erlang C, we have:

Atoll considers the effect of half-rate circuit switched traffic by taking into account a user-defined percentage of half-rate traffic. Atoll computes the effective equivalent number of full-rate timeslots that will be required to carry the total traffic with the defined percentage of half-rate traffic.

If the number of timeslots required to accommodate the full-rate circuit switched traffic is TS_{req. FR}, and the percentage of half-rate traffic within the subcell is defined by HR, then the effective number of equivalent full-rate circuit switched timeslots TS_eff. that can carry this traffic mix is calculated by:

Atoll employs this simplified approach to integrating half-rate circuit switched traffic, which provides approximately the same results as obtained by using the half-rate traffic charts.

5.6.2.2.2 Step 2: TRXs Required for CS Traffic and Dedicated PS Timeslots

This stage of the network dimensioning process computes the number of TRXs required to carry the circuit switched traffic demand through the number of required timeslots calculated above and the timeslot configuration defined by the user in the network settings. Atoll distributes the number of required circuit switched timeslots calculated in Step 1 taking into account the presence of dedicated packet switched timeslots in each TRX according to the timeslot configurations.

If a timeslot configuration defines a certain number of dedicated packet switched timeslots pre-allocated in certain TRXs, those timeslots will not be considered capable of carrying circuit switched traffic and hence will not be allocated. For example, if 4 timeslots have been marked as packet switched timeslots in the first TRX and Atoll computes 8 timeslots for carrying a certain circuit switched traffic demand, then the number of TRXs to be allocated cannot be 1 even if there is no packet switched traffic considered yet.

The total numbers of timeslots that carry circuit switched and packet switched traffic respectively are the sums of respective dedicated and shared timeslots:

and

5.6.2.2.3 Step 3: Effective CS Blocking, Effective CS Traffic Overflow and Served CS Traffic

In this step, the previously calculated number of required TRXs is used to compute the effective blocking rate for the circuit switched traffic. This is performed by using the Erlang B or Erlang C formula with the circuit switched traffic demand and the number of required TRXs as inputs and computing the Grade of Service (or blocking probability). It then calculates the effective traffic overflow rate, O_eff..

In case of Erlang B formula, the effective rate of traffic overflow for the circuit switched traffic is the same as the circuit switched blocking rate. While in case of the Erlang C model, the circuit switched traffic is supposed to be placed in an infinite-length waiting queue. This implies that there is no overflow in this case.

From this data, it also computes the served circuit switched traffic. This is the difference of the circuit switched traffic demand and the percentage of traffic that overflows from the subcell to other subcells calculated above. Hence, for an effective traffic overflow rate of O_eff. and the circuit switched traffic demand of TD_C, the served circuit switched traffic ST_C is computed as:

5.6.2.2.4 Step 4: TRXs to Add for PS Traffic

This step is the core of the dimensioning process for packet switched services. First of all, Atoll computes the number of TRXs to be added to carry the packet switched traffic demand. This is the number of TRXs that contain dedicated packet switched and shared timeslots.

To determine this number of TRXs, Atoll calculates the equivalent average packet switched traffic demand in timeslots by studying each pixel covered by the transmitter. This calculation is in fact performed in the traffic analysis process or is user-defined in the subcells table. Knowing the traffic demand per pixel of the covered area in terms of kbps and the maximum attainable throughput per pixel (according to the C and/or C/I conditions and the coding scheme curves in the GPRS/EDGE configuration), Atoll calculates the average traffic demand in packet switched timeslots by:

GoS

The average timeslot capacity of a transmitter is calculated by dividing the packet switched traffic demand over the entire coverage area (in kbps) by the packet switched traffic demand in timeslots calculated above.

With the number of timeslots required to serve the circuit switched traffic, the timeslots required for packet switched traffic and their respective distributions according to the timeslot configurations being known, Atoll calculates the number of timeslots available for carrying the packet switched traffic demand. These timeslots can be dedicated packet switched timeslots and the shared ones. So, following the principle that shared timeslots are potential carriers of both traffic types,

The packet switched traffic load is calculated by the formula:

The second important parameter for the calculation of Reduction Factor, Delay and Blocking Probability is the equivalent number of available timeslots for packet switched traffic, i.e. N_P. This is computed by dividing the total number of timeslots available for carrying packet switched traffic by the number of downlink timeslots defined in the mobile terminal properties.

So, N_P is calculated at this stage as:

Where, TS_Terminal is the number of timeslots that a terminal will use in packet switched calls.

The number timeslots that a terminal can use in packet switched calls is the product of the number of available DL timeslots for packet-switched services (on a frame) and the number of simultaneous carriers (in case of EDGE evolution).

The number of timeslots that a terminal will use in packet switched calls is determined by taking the lower of the maximum number of timeslots for packet switched service defined in the service properties and the maximum number of timeslots that a mobile terminal can use for packet switched services (see above).

and

Here, the min(X,Y) function yields the lower value among X and Y as result.

Now, knowing the packet switched traffic load, L_P, and the equivalent number of available timeslots, N_P, Atoll finds out the KPIs that have been selected before launching the dimensioning process using the quality curves stored in the dimensioning model.

This particular part of this step can be iterative if the KPIs to consider in dimensioning are not satisfied in the first try. If the KPIs calculated above are within acceptable limits as defined by the user, it means that the dimensioning process has acceptable results. If these KPIs are not satisfied, then Atoll increases the number of TRXs calculated for carrying packet switched traffic by 1 (each increment adding 8 more timeslots for carrying packet switched traffic as the least unit that can be physically added or removed is a TRX) and resumes the computations from Step 3. It then recalculates the packet switched traffic load, L_P, and the equivalent number of available timeslots, N_P. Then it recomputes the KPIs with these new values of L_P and N_P. If the KPIs are within satisfactory limits the results are considered to be acceptable. Otherwise, Atoll performs another iteration to find the best possible results.

The calculated values of all the KPIs are compared with the ones defined in the service properties. The values for maximum Delay and Blocking probability are defined directly in the properties but the minimum throughput reduction factor is calculated by Atoll using the user’s inputs: minimum throughput per user and required availability. This calculation is in fact performed during the traffic analysis process, but since it is relevant to the dimensioning procedure, it is displayed in a column in the dimensioning results so that the user can easily compare the minimum requirement on the reduction factor KPI with the resulting one. If dimensioning is not based on a traffic analysis, the minimum throughput reduction factor is a user-defined parameter.

In document Atoll 2.8.3 RF Technical Reference Guide E2 (Page 168-174)