P ROPOSED THREE - DIMENSIONAL AARF M ARKOV C HAIN

CHAPTER 3. ARF AND AARF ALGORITHMS

3.4 P ROPOSED THREE - DIMENSIONAL AARF M ARKOV C HAIN

Again, it is paid much attention to obtain the transition probabilities of each mode.

Therefore, we have done the same thing to AARF algorithm, that is, to derive the corresponding Markov chain. The Markov chain of AARF becomes to three-dimension now.

The first and the second dimension are just the same as ARF and the third dimension indicates the different thresholds. Since it will become a mess if the complete three-dimensional behavior of AARF is plotted; here, only the differences between ARF and AARF are shown.

The first difference is that when the transmission of the probing packet fails, not only is the

rate switched to the previous lower one (as in ARF), but also the threshold is multiplied by two. Figure 3-2 illustrates this behavior. Besides, there are two situations when the threshold should be reset to its default value. Figure 3-3 illustrates the first one that when the rate is decreased due to two consecutive failed transmissions, the threshold becomes 10. And Figure 3-4 shows that when the transmission of probing packet succeeded, the threshold should also be reset.

Once the AARF Markov chain is obtained, it is feasible to calculate each state’s steady probability. And with these state probabilities, we could calculate the transit-down probability (Pdown) and transit-up (Pup) probability for each mode under various SNR values, similar to those that have been done to ARF. These two parameters become important keys while designing Call Admission Control algorithm for real-time traffic, and we show each of the calculations below. In the following section, there will also be some discussions about how they play their roles.

( ) ( )

where

m - the current mode of the station b - the state probability

P - the successful transmission probability of a packet s

Pf - the failed transmission probability of a packet d - the corresponding value of the third dimension T - the corresponding value of threshold d

Threshold=10

Chapter 4.

Proposed Scheduling and Call Admission Control Algorithm

4.1 Proposed Scheduling Algorithm

From section 2.4, it is noticed that there are still a few flaws in simple algorithm. The simple algorithm is intended as a reference only and it just respects the minimum requirements; so, it is somehow inefficient.

First, the TXOP duration of each station is always the same and corresponds to the transmission time of an M-sized (maximum MSDU size, i.e., 2304 bytes) packet at a certain PHY rate. While this may be suitable for traffic types that present small bursts of constant size (e.g., voice over IP, VoIP), some traffic types like MPEG-4 video present bursts of variable size formed by several packets (e.g., an MPEG-4 I-frame is usually much larger than a P-frame or B-frame). In other words, these types of traffic have various packet sizes and various packet inter-arrival times. With the simple algorithm, transmission of a long burst packet can lead to significant transmission delay, even cause packet drop. While for packet whose size is much smaller than M, TXOP calculation is too conservative so that waste of wireless resource becomes more severe. Moreover, the adoption of rate adaptation technique is not taken into consideration in simple algorithm either. Stations under continuous changing channel are using different transmission rate, hence they ought to occupy different TXOP from time to time.

Real-time scheduling theory has already proven that Earliest Deadline First (EDF) or Earliest Due Date (EDD) is optimal in a wide set of real-time scheduling problems [28][29].

For this reason, EDD is chosen to be the framework of our scheduling method. Besides, two

different concepts should be introduced when we design the EDD-based scheduler. They are discussed as follows, respectively.

Approach one

Before a station is allowed to use the medium, a polling message should be broadcasted and this message is regarded as an overhead. Approach one in scheduler design allows a station to transmit multiple packets for one poll. The simple algorithm we have introduced belongs to this kind of approach. Obviously, this approach maximizes the system capacity due to the minimization of the amount of overhead. Besides, after a certain station is polled and the first packet in its buffer (or the most urgent packet) is delivered, the remaining packets could be delivered consecutively without other polls. It results in the situation that the time occupied by those remaining packets might retard the process of other stations’ packets, which may be more urgent, from making themselves on time. Therefore, the disadvantage of this approach is that packet loss rate might suffer from the negative impact.

Approach one allows multiple packet transmissions. But what should the number of packets that is granted for one poll be? We suggest that it could be equal to the total amount of data in the buffer. People might wonder if there is a situation that the amount of data in the buffer is too much and it takes such a long time to complete all of their transmission, so that all packets from other stations will be dropped because of missing deadlines. Actually, we do not have to worry about this situation, because with our properly designed CAC (Call Admission Control) Algorithm, it will never happen. In other words, this issue is addressed in the proposed CAC algorithm, and each station’s QoS would be achieved not by the scheduler, but by the proposed CAC algorithm. The detailed discussion of the proposed CAC will be presented in the next section.

Back to the scheduler design approach one, TXOP for a station depends on the total amount of data and the current physical transmission rate. Hence the TXOP calculation for traffic stream j becomes to:

∑ ( )

where Np indicates the number of packets in the buffer; noverhead is the total amount of PHY and MAC header and tail (in terms of byte); lj,k is the size of the kth packet of traffic stream j.

Toverhead present as the time spent on polling, acknowledgement, and SIFS (Short InterFrame Space). Tsym is the symbol time, e.g., 4us in IEEE 802.11a standard. BpS(mj) stands for Byte-per-Symbol information for PHY mode mj and its values are given in Table 4-1.

The capacity performance could be even better when Packet Concatenation (PAC) protocol [30] is adopted. This technique intends to make multiple MAC packets to share the same control messages, which are Physical Layer Convergence Protocol (PLCP) preamble, PLCP header, and the tail. Since these control messages are always BPSK modulated, which is the most conservative way, the wasted on wireless resources for these messages is quite large. Multiple MAC packets sharing the same control message further reduces the amount of overhead. Last, if PAC protocol is utilized in our scheduler design approach one, the TXOP calculation for traffic stream j becomes to:

( )

j ^sym ^overhead

On the other hand, the second approach allows only one packet transmission for a single poll. Unlike approach one which takes only the first packet’s delay bound in each station’s buffer as the metric of scheduling priority, in approach two, each packet’s delay bound is

treated as the same, no matter what station they belong to. Therefore, the information is more sufficient and the schedule arrangement will be more precisely. This behavior has an influence which is just opposite to that of approach 1: larger overhead, smaller capacity, but better packet loss performance. The formula for TXOP in approach two is shown below.

( )

_j ^j ^sym ^overhead

where lj,1 indicates the size of the traffic stream j’s first packet, or the size of the most urgent packet, in the traffic stream j’s buffer.

Table 4-1 Mode dependent parameters of IEEE 802.11a PHY [1]

Mode per subcarrier

(NBPSC)

4.2 Proposed Call Admission Control Algorithm for Real-time Traffic

In this section, the second tier call admission control algorithm for real-time traffic is presented. It is mentioned before that the scheduler should be designed to have more flexibility because the characteristics of certain traffics are quite unstable. This concept should also be introduced in Call Admission Control Algorithm. Each TXOP now is a varying value, and the duration between two polls of a station is changing also. Therefore, in order to fulfill the Delay Bound (DB) requirement of each traffic stream, we bring up an idea of adaptive

“buffer time” (BT) to compensate the variation of each TXOP. A few parameters introduced in our Call Admission Control algorithm are defined as follows. And we suggest checking Figure 4-1 while reading the definitions.

¾ SI (Service Interval)

( )

DB i

SI =min _i ∀ (4-4)

SI is set as the smallest Delay Bound (DB) among all traffic streams.

¾ G (Summation of each TXOP)

∑

= ^k

TXOPi

(4-5) G indicates the total amount of time occupied by all stations within a SI interval.

¾ BT (Buffer Time)

(

^× ⁻ ^×

)

⁺^∆

∑

= k

up up

down down

i L P _i_m _i_m P _i_m _i_m

N BT

, ,

, δ δ (4-6)

Ni and Li are as same as the definitions in the simple algorithm. Just like the description above, BT is a period of time in order to compensate the variation of each station’s TXOP. In section 3, we have already discussed the rate adaptation technique, AARF, which traces the channel condition continuously to achieve the maximum effective throughput. For each station under a certain SNR value, there is a corresponding transit-down and transit-up probability, denoted as Pdown and Pup respectively. Moreover, while the mode increases or decreases, there will be a

time difference even for a fixed amount of data. Table 4-2 shows these time differences compliant to IEEE 802.11a. δ_down denotes the time difference for one bit when mode decreases, and δ_updenotes that when mode increases. The last term, ∆, intends to compensate the unpredictable characteristics of each traffic stream, especially for variable bit rate (VBR) traffic. Although Traffic Specification (TSPEC) provides some traffic statistics (e.g. user priority, maximum MSDU size, mean data rate, etc), VBR traffic usually does not follow this feature exactly. Hence we add a ∆ in BT calculation to reserve an extra period of time in order to balance this unstable property. By combining the parameters described, BT is able to accommodate the timing variation caused by rate adaptation and variation of the packet size and packet inter-arrival time.

Table 4-2 Time differences between modes

Deadline is the boundary we set to detect whether the system still has the ability to

compensate the expansion of each TXOP. If the summation of each TXOP, G, exceeds the Deadline, it implies that G in the next SI interval might goes beyond the SI, which is the smallest Delay Bound. This means packet drop will occur and the performance will degrade.

TXOP k TX OP l

TXOP j

TXOP i

Deadline DB_min

TXOP k TXOP l

TXOP i

Deadline DB_min

TXOP m

TXOP k TXOP l

TXOP j

TXOP i

BT G>Deadline Red Alert!!!!!!

if RD <= N_reject n=n+1;

else

Reject All Request!

Note:

TXOP is various in each SI

Figure 4-1 Scheduling and Call Admission Control Algorithm

It should be noticed that, at the beginning of each SI interval, Pdown and Pup should be updated according to each station’s previous SNR; and the Buffer Time, BT, should also be updated to a new value. Once G is greater than Deadline, it implies that at the next SI interval, G has a certain probability to exceed SI because of the decrease of transmission rate, hence cause packet drops.

Besides the four parameters, a counter n also shows up. Once the summation of each TXOP (G) goes beyond the Deadline, n should add itself by 1. Another parameter called

“Reject Density”, RD, is defined as n divided by the observation interval (in terms of second).

It implies the density of budget violation (G>Deadline) in a certain time duration. If RD is greater than a pre-defined value, Nreject, the incoming traffic should be rejected. Recall that for handoff design in UMTS [31], there is a hysteresis along with a timer in order to avoid ping-pong effect. This is the concept to avoid sudden change of a station’s SNR. RD in our

algorithm shares the same idea and further extends its function to accommodate different required Packet Loss Rate (PLR). Obviously, if the requirement of PLR is loose, Nreject could be set larger and allows higher Reject Density, and vice versa. This concept and the proper setting of Nreject will be discussed in section 5.2. In conclusion, the criterion to decide whether a new traffic stream could join the system or not is:

(

G >Deadline

)

∩

(

RD>Nreject

)

Î Reject (4-8)

Recall that in scheduler design in the previous section, approach one allows multiple packet transmissions. And we suggest that the number of packets that is granted for one poll could be the total amount of data in the buffer. People might wonder if the amount of data in the buffer is too much and it takes such a long time to complete all of their transmission, so that all packets from other stations will be dropped because of missing deadlines. Actually, we do not have to worry about this situation. In our CAC algorithm, a parameter SI (Service Interval) is introduced and equals to the smallest Delay Bound among all traffic streams.

Combining the scheduler and the corresponding call admission control, it is guaranteed that a traffic stream will be polled at least once per SI, and the amount of data accumulated in the buffer during SI should within a certain range, which we have already taken into consideration. In other words, we achieve each station’s QoS by the proposed CAC algorithm, but not scheduler.

Note: It is obvious that the Call Admission Control described above corresponds to the scheduler design approach one, which allows transmitting multiple packets per poll. To accommodate approach two, the only modification required in our CAC algorithm is to replace the SI by the lowest mean value of packet inter-arrival time, and substitute Ni in BT calculation for 1.

Chapter 5.

Simulation Results

IEEE 802.11a is adopted as the background in the following simulations. The critical parameters that have been defined in IEEE 802.11a standard and have been used in the simulations are concluded in Table 5-1 to make it clear.

Table 5-1 IEEE 802.11a parameters [1]

Parameter Value

N_SD: Number of data subcarriers 48

N_SP: Number of pilot subcarriers 4

N_ST: Number of subcarriers, total 52 (NSD + N_SP)

∆F: Subcarrier frequency spacing 0.3125 MHz (=20MHz/64)

TFFT: IFFT/FFT period 3.2 µs (1/∆F)

TSlot: Slot time 9 µs

TSIFS: SIFS time 16 µs

T_DIFS: DIFS time 34 µs (=TSIFS + 2×TSlot)

CWmin: minimum contention window size 15 CWmax: maximum contention window size 1023

T_PREAMBLE: PLCP preamble duration 16 µs (TSHORT+ TLONG)

T_SIGNAL: Duration of the SIGNAL BPSK-OFDM symbol 4.0 µs (T_GI+ T_FFT) TGI: Guard interval duration 0.8 µs (T_FFT/ 4) TGI2: Training symbol guard interval duration 1.6 µs (T_FFT/ 2)

TSYM: Symbol interval 4 µs (TGI + T_FFT)

T_SHORT: Short training sequence duration 8 µs (10 × TFFT / 4) T_LONG: Long training sequence duration 8 µs (TGI2 + 2 × TFFT)

5.1 IEEE 802.11a PHY Simulation Results

In this section, the first tier of the proposed Call Admission Control Algorithm, which refers to the function unit “PHY and MAC Measurement and Test” labeled as 1 in Figure 1-1, is evaluated. IEEE 802.11a uses OFDM and supports eight different data rates or eight different modes, ranging from 6 Mbps to 54 Mbps. Four modulation schemes, BPSK, QPSK, 16QAM, 64QAM, along with two convolution coding rates, 1/2 and 3/4, form these eight modes. Besides, in each communication system, it is always crucial to inspect the transmission reliability, and Bit Error Rate (BER) is one of the metrics that is commonly used to determine the performance of a certain communication system. In this study, we simulate the BER performance of the four modulation schemes mentioned above not only under AWGN, but also under different Rayleigh fading channels with moving speed equals to 2m/s, 10m/s, 20m/s, and 50m/s, respectively. The following figure (Figure 5-1) shows the simulation results. As it is mentioned before, OFDM system is sensitive to the time variation of mobile radio channels. Therefore, once the fading process becomes more severe, the performance degrades significantly. From the results, we observed that when the channel is not stable, it is not appropriate to select 16QAM or 64QAM as the modulation scheme at all.

It is also concerned that for different fading channels, the throughput performance will change dramatically due to degraded BER performance.

Figure 5-2 shows the simulation results for Mode1 to Mode4 under AWGN, Rayleigh fading channel with moving speed equals to 2m/s, 10m/s, 20m/s, and 50m/s. Here the performances for Mode5 to Mode8 are not shown because Rayleigh fading makes all these throughputs zero. This consequence has just matched the simulation results in Figure 5-1, which displayed that the BER for 16QAM and 64QAM approach to 0.5, hence no throughput could be obtained.

Figure 5-1 BER vs. Eb/No (a) BPSK (b) QPSK (c) 16QAM (d) 64QAM

(a) (b)

Figure 5-2 Throughput under different fading channels (a) Mode1 (b) Mode2 (c) Mode3 (d) Mode4

Except BER performance, throughputs of each mode in IEEE 802.11a under DCF MAC mechanism are also simulated, as shown in Figure 5-3. In the simulation, AWGN environment and 2000 bytes payload size are assumed when calculating the throughputs. Obviously, if rate adaptation is adopted, the maximum throughput could be achieved while SNR value is varying.

(a) (b)

Figure 5-3 Link Adaptation

Since DCF is a contention based access mechanism, it is apparent that when the number of users increases, the collision probability also raises. Figure 5-4 shows this consequence.

Moreover, the impact from number of users is shown in Figure 5-5 and Figure 5-6. As predicted, the throughput performances degrade gradually while the loading becomes heavier, resulting from the higher collision probability. The curves from top to down in Figure 5-5 (a) and Figure 5-6 (a) represent the throughputs for number of users from 1 to 20 under different SNRs. Besides, the individual saturation throughputs from number of users 1 to 200 are picked out and associate with each other to emphasize the influence of number of users.

Figure 5-5 (b) and Figure 5-6 (b) illustrate this effect.

Figure 5-4 Collision Probability

Figure 5-5 Mode1~4 (a) Individual throughput for number of users 1~20 (b) Individual saturation throughput

(a) (b)

Figure 5-6 Mode5~8 (a) Individual throughput for number of users 1~20 (b) Individual saturation throughput

(a) (b)

5.2 Proposed CAC Algorithm for Non-real time Traffic

From Figure 5-4, it is observed that when number of users increases, the collision probability becomes higher. This phenomenon results in larger inter-packet delay and smaller channel utilization. Although delay is usually not a great issue when dealing with non-real time traffic, there are still some delay constraints for certain of specific applications. Taking TCP for example, the delay between the packet transmitting and the acknowledgement receiving should be within the value of Retransmission Timeout (RTO), or the control unit would regard this as network congestion and retransmit the data segment. Therefore, the objective of CAC for non-real time traffic would not only to maximize the throughput and the number of granted users, but also to satisfy the delay constraints.

Figure 5-7 shows the relationship between the average inter-packet delay and the collision probability. It is straightforward that when collision probability is larger, the user would have to wait longer to get the medium. The wasting time results from the collision instances and the repetition of DCF MAC backoff mechanism as described in section 2.2 and 2.3.

Figure 5-7 Average Inter-packet Delay vs. Collision Probability Mode8 Mode1

The channel utilization is also provided. Figure 5-8 shows its relation with the average inter-packet delay. Obviously, the trend is very similar with that in Figure 5-7, which would have an exponential growth. It is observed in Figure 5-8 that when the channel utilization is about lower than 15%, the delay would increase dramatically. Therefore, the operation range for the CAC control may around 10%~20% for the channel utilization and the corresponding value of the average inter-packet delay is about 10. Under this condition, the collision probability is around 0.8 and the supporting number of users is around 150 according to

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