Chapter 4 Proposed Power-Conserving Scheduling Algorithms 14
4.2 Maximal Power-Conserving (MPC) scheme
The objective of the proposed MPC scheme is to provide a QoS-guaranteed scheduling algorithm in order to maximize the power efficiency under the multi-connection scenar-ios. The MPC algorithm is primarily designed for the connections with power-saving class of Type II due to its most stringent QoS requirement comparing with the other two types. Nevertheless, the connections with either Type I or III traffic can also be scheduled and assigned in the case that there are remaining time slots after the schedul-ing process for the Type II traffic has been completed. Even though the MPC scheme is illustrated to design for a single BS/MSS pair, the IEEE 802.16e PMP scenario between a single BS and multiple MSSs can easily be extended with appropriate assignment of
the bandwidth requirements from the BS to each MSS.
It is assumed that there are N connections existed between a single BS/MSS pair. The QoS requirements for the MSS is defined as Q = {Qi| ∀i, 1 ≤ i ≤ N} = {(Di, τi) | Di > 0, τi ≥ 0, ∀i, 1 ≤ i ≤ N}, where the parameter i denotes the ith con-nection between the BS and the MS. Di represents the DL delay constraint for the ith connection. On the other hand, the parameter τi indicates either the average DL data requirements per frame for the ith connection (with unit in time slots).
The primary purpose of the proposed MPC scheduling algorithm is to obtain the number of sleep frames per period by maximizing the power efficiency based on the various QoS requirements. Considering that the sleep and listen intervals are denoted as TS and TL (both have units in ms) respectively, the first constraint C1 based on the QoS delay requirements can be acquired as
C1 : TS+ TL≤ min
∀i {Di} (4.1)
Fig. 4.4 illustrates the schematic diagram of the solution set and the corresponding QoS constraints by exploiting the proposed MPC scheduling algorithm. The sleep interval TSand the listen interval TLare considered as the y-axis and x-axis respectively.
It can be observed that the constraint C1 is drawn in the first quadrature since the delay constraint Di is considered greater than zero.
On the other hand, the bandwidth requirement is utilized as the second constraint for the design of the MPC scheme. The total DL data requirements (in time slots per frame) for an MSS can be obtained by summing the average data requirements for each connection as ΓD = PN
i=1τi. Based on the resource allocation, the total DL and DL bandwidth allowances for each MSS that are assigned by the BS is pre-specified as BD in time slots per frame, i.e. ΓD < BD. It is noticed that even with the inclusion of additional connection within the MSS, the extended data requirement should still be
less than the allowable bandwidth assigned by the BS. Furthermore, in the case with multiple MSSs, the concept can be extended in a similar manner. Different values of BD will be assigned by the BS to each MSS based on its resource allocation policy.
Since the main design concept is to compress the total data requirements from the original (TS + TL) time duration into the listen interval TL for power-saving purpose, the following inequality has to be satisfied:
TS+ TL TL ·
XN i=1
τi ≤ BD (4.2)
With appropriate arrangement of (4.2), the second constraint C2 for the QoS band-width requirements can be obtained as
C2 : TS
TL ≤ {BD− ΓD
ΓD } (4.3)
The bandwidth constraint C2 is also denoted as in Fig. 4.4. It can be observed that the C2 line passes through the origin point in the two-dimensional coordinate; while the slope of C2 is positive and is dependent to both BD and ΓD. Consequently, the main target of the MPC scheduling is to obtain the corresponding listen and sleep intervals by maximizing the power-saving efficiency subject to the QoS constraints, i.e.
(TL∗, TS∗) = arg max
It is noted that that optimization process is subject to the delay and the bandwidth constraints (i.e. C1 and C2 as acquired from (4.1) and (4.3)) associated with the condi-tions that TL > 0 and TS > 0. Based on the constraints, the solution set (TL∗, TS∗) will be confined within the shaded triangular region as shown in Fig. 4.4. After computations
and intuitive observations, the optimal sets of the listen and sleep intervals (TL∗, TS∗) are obtained to constitute the continuous line segment of C2, i.e. the bolded black line segment as shown in Fig. 4.4.
However, the listen and sleep intervals should be integer multiplier of a frame dura-tion. As a result, it is necessitate to obtained the discretized suboptimal set of solution M = {(m∗L(ζ), m∗S(ζ)) | ∀ζ}. As illustrated in Fig. 4.4, the grids in the two-dimensional space indicate the integer multiplier of the frame duration. Intuitively, the brute-force method can be utilized by searching all the grid points within the shaded region for ob-taining the suboptimal solutions. However, excessive computation cost will be incurred by the extensive searching algorithm. Intuitively, the number of discretized suboptimal solution can be reduced by considering the grid points based on the optimal set (TL∗, TS∗) as defined in (4.4), i.e.
(m∗L(ζ), m∗S(ζ)) =
where the suboptimal solution m∗L(ζ) and m∗S(ζ) are denoted as the numbers of listen and sleep frames per iterative period. It is noted that (m∗L(ζ), m∗S(ζ)) should be chosen within the confined rectangular region. As shown in Fig. 4.4, it can be observed that there are three discretized suboptimal solutions associated with the continuous optimal line, i.e. (m∗L(ζ), m∗S(ζ)) = (2, 1), (3, 2), and (5, 3) for ζ = 1, 2, and 3. Two schemes are proposed for the selection of the suboptimal solution (m∗L(ζ), m∗S(ζ)) as follows:
For the purpose of achieving maximal power-saving, the proposed MPC scheme is to obtain the suboptimal solution which has the shortest distance to the optimal line segment (TL∗, TS∗) as indicated in Fig. 4.4, i.e.
(m∗L, m∗S)M P C = min
∀ζ {Dist [(m∗L(ζ), m∗S(ζ)), (TL∗, TS∗)]} (4.6)
Delay Constraint Bandwidth Constraint
Feasible Area
C1
TL TS
Candidate for Suboptimal Solution Optimal Line
Segment
MPC
C2 Frame Duration
Figure 4.4: Schematic diagram of the solution set and the QoS constraints by adopting the proposed MPC scheduling algorithm.
where the function Dist[a, b] in (4.4) corresponds to the shortest distance from point a to line b. The main concept of the MPC approach is to acquire a suboptimal solution which is considered to have the shortest distance to the original optimal solution. As can be observed from Fig. 4.4, the suboptimal solution obtained from the MPC scheme becomes (m∗L, m∗S)M P C = (3, 2). The MPC selection algorithm requires certain amount of computational cost for the calculation of the Dist[a, b] function. However, it it intu-itive to observe that the solution exploited by the MPC scheme is served as the best selection among the other suboptimal solutions for power-saving purpose.