Proposed Linear Search Method

The objective of the linear search method presented in this chapter is to enable the selection of a policy level that balances QoS and energy efficiency satisfactorily. In order to achieve this, the energy consumption rating (ECR), average file transfer delay and blocking probability performances for different traffic loads are estimated for different policy levels. This represents a training phase for the network, which can be carried out at the earlier stages of operation of the network. The goal is to

meet a target blocking probability while keeping ECR and average file transfer delay low. More than one policy level might satisfy the blocking probability at a given traffic load, however some might lead to low delay but high ECR while others might lead to high delay but low ECR. The search is done to find a policy level that avoids these two extremes but instead balances the delay and ECR such that it is not the lowest ranked in either delay or ECR performances. As much as possible, it should be close to the top in ranking in both delay and ECR performances. The blocking probability, ECR and average file transfer delay performance metrics can be obtained from traffic statistics and key performance indicators stored at the Operation Support System (OSS) which are obtained from event and performance counters at the base stations in a similar manner as explained in Chapter 6.

The average file transfer delay increases with the order of policy level because delay increases with the order of choice restrictions as shown in Chapter 4, whereas, sleep state prohibition is shown to lead to better delay than sleep state permission in Chapter 5. The ECR is stored in the database rather than the energy reduction gain (ERG) or effective energy saving (EES) since it can be evaluated without considering a baseline scenario like the other two. Hence, the database creation and consequently selection of a policy level that balances QoS and energy efficiency can be done independently of a baseline scheme. The ERG is proportional to the ECR as earlier stated in (2.9) in Chapter 2.

Therefore, for a given baseline value, , the ERG depends only on the ECR value of the test scheme. In this case, evaluation of the system under different policy levels constitutes consideration of different test schemes. From (2.9) it can be deduced that the higher the ECR of the test scheme the lower the ERG and vice versa. At low traffic load, the ERG increases with the order of policy level since ERG increases with the order of choice restriction and sleep state permission leads to better ERG than its prohibition as shown in Chapters 4 and 5 respectively. Therefore, at low traffic load, ECR decreases with the order of policy level due to the inverse relationship between ERG and ECR. Beyond low traffic load, the ERG does not exhibit this linear relationship with the order of policy level, since as also established in Chapter 4, a low order choice restriction is eventually better than a higher order

choice restriction at some medium traffic load. Hence, the ECR does have a linear relationship with policy level beyond low traffic region.

For each traffic load, a set of measured delay and ECR values,

and are created.

is the number of policy levels that satisfy the blocking probability target. The policy levels that do not satisfy the blocking probability target are not considered in the selection process. The set of considered policy level, , in increasing order of level is defined as . Furthermore, policy levels are sorted in ascending order of delay, , and ECR, , to create delay and ECR sets of policy levels respectively. The delay policy level set, Q, and the ECR policy level set, Z, are

defined as and

respectively; where . Since , , and are all ordered set (ascending order), When is compared with or with , for if then always; while if then or . This is because the delay policy level set, Q, will always have the same element in the same position as the considered policy level set,

, since delay increases with increasing order of policy level. Whereas the ECR policy level set, Z, may or may not have the same element in the same position as the considered policy level set, , since ECR does not always increase with the order of policy level.

The linear search is conducted along the elements of ECR policy level set, Z, which is not always sequential. This is done one element at a time and at each step the current element and the preceding elements are checked for matches over the same range in the delay policy level set, Q. For each step m of the search, corresponding to the mthelement of , a subset of ( is created such that:

(7.1)

; (7.2)

This is compared to the same range of the delay policy level set to find a policy level with low delay and low ECR (which is equivalent to high energy efficiency). Similarly, a subset of ( is created such that:

(7.3)

; (7.4)

As mentioned earlier, policy levels in both delay and ECR policy level sets are arranged in ascending order of the magnitude of their delay and ECR measurements. Hence, if a match between the two sets is found at an early stage of the linear search, the choice of policy level will lead to low delay and good energy efficiency. The matched policy level set, P, at the mth stage of the linear search is given by:

(7.5)

If that is no match found, the search progresses onto to the (m+1)th step. However, if then one match is found and the final policy level selected,

, is given by:

; (7.6)

If more than one match is found. Hence the matched policy level set, P, is a set of policy levels as follows:

; (7.7) The equation in (7.7) implies that the policy levels in can be any of the policy levels, however the number of element of cannot exceed the total number of policy levels considered. In this situation, where more than one match is found, the policy level with the lowest delay measurement is selected to achieve the best QoS as explained below.

Assuming is set of the order of the matched policy levels in (7.7), then and . Since the delay increases with the order of policy

level, the policy level with the lowest order should be selected. Hence, the order of the selected policy level, , is given by:

∗; ∗ (7.9)

In Figure 7.2 shown below, a typical mapping scenario is shown for illustration purposes. The policy levels are arranged in ascending order of the delay and ECR measurements in the delay and ECR rows respectively. The search is started with the first element of the ECR row, which is policy level 4. When this is compared with the first element of the delay row no matching is found since this element is policy level 1. Thus, the search is continued and in the next step the second element and the first element of the ECR row, i.e. policy levels 3 and 4 respectively, are checked for a match in the delay row considering similarly the second and first elements of this row. Also, no match is found at this at this step and the search is continued. At the third step, the third, second and first elements of the ECR row are compared with the third, second and first elements of the delay row. In this case two matches are found as the policy level 3 and policy level 2 are both found in the delay row at this stage. Since policy level 2 has lower delay it is selected as the suitable policy for the traffic load for which the mapping is being carried out and the mapping is stored in the database.

Ranking

Delay

Records Policy Level 1 Policy Level 2 Policy Level 3 Policy Level 4 Policy Level 5

ECR

Records Policy Level 4 Policy Level 3 Policy Level 2 Policy Level 1 Policy Level 5

Matching at the third step of linear

search

1st 2nd 3rd 4th 5th

Figure 7.2 Policy Selection with Linear Search

The flowchart for the implementation of this approach is shown in Figure 7.3 for any given traffic load with related average file transfer delay, blocking probability and ECR measurements already in the database. The database is assumed to be available at the Operation Support System (OSS) and readily accessible to the central node,

QEPU, as explained in Chapter 6. It is important to note that the partially centralised paradigm of RRM and TM is still maintained. The QEPU only sets policies for long timescale average traffic load while ZBSs make RRM and TM decisions at short timescale of user arrivals and departures. The mapping of policy levels to traffic load is done over a range of traffic load and utilise for policy selection for different traffic load not already characterised by the system. How this is achieved is explained next.

Start

Sort policy levels in ascending order of average

delay in Delay Row

Sort policy levels in ascending order of ECR

in ECR Row

Initialize Search Step, N=1

Are policy levels in nth position or lower in ECR row in nth position or

lower in Delay row?

Matched policy level > 1?

Select the single matched policy level

Select policy level with lowest average

delay End Yes No N=N+1 No Yes