3.2.1 Gap Processing Time
To measure the performance of the stall avoidance schemes, we define a new perfor-mance measure – gap processing time (GPT). It is the duration from the occurrence of a Type II gap until a stall avoidance scheme recognizes the existence of nonrecov-erable gaps. The gap processing time is an important performance metric to evaluate the quality of service (QoS) for HSDPA. On the one hand, when the gap processing time is shorter than the RLC timeout, with the help of the stall avoidance scheme an
RLC retransmission can be initiated sooner when the Type-II gap is detected. This is especially important for the delay sensitive services. On the other hand, without the help of the stall avoidance scheme, the excessive gap processing time may be longer than the RLC timeout. When a packet is sent out, an RLC timer is started at the transmitter. If the acknowledgement is not received correctly before the RLC timer is expired, the transmitter sends the packet again. When a Type-II gap halts the received packets at the MAC layer to be delivered to the RLC layer and the excessive gap processing time is longer than the RLC timeout, the so called “spurious” RLC retransmission occurs. In this situation, the RLC timeout triggers the retransmis-sion of some already received packets, which are halted at the MAC layer due to an unrecoverable Type-II gap. Therefore, the analysis of gap processing time offered in the paper can be helpful in setting an appropriate value of the RLC timeout from a viewpoint of the receiver’s MAC layer performance.
Although the probability of the NACK-to-ACK error is 0.01 [53, 54], the high allowable packet error rate in the MAC layer of HSDPA can still lead to serious stall problems. To boost the transmission rate, the packet error rate of the first transmission can be higher than 40% because a high level modulation and coding scheme is adopted [65]. For example, when the probability of a NACK-to-ACK error is equal to 0.01, average packet error rate is equal to 0.3, and the transmission time interval of 2 milli-seconds, the stall problem occurs 7.5 (5/0.002 × 0.3 × 0.01) times within five seconds. Thus, the impact of the NACK-to-ACK error cannot be ignored, especially for supporting delay sensitive services.
The stall problem affects the performance of the parallel HARQ mechanism in two folds. From the goodput aspect, the end-to-end goodput from the receiver’s upper-layer viewpoint can be seriously degraded due to the long gap processing time.
From the delay aspect, the end-to-end data delivery delay can also become longer due to the gap processing time. Referring to the analytical model in [86], the packet
delivery delay (denoted by Td) in the third-generation (3G) WCDMA with transport control protocol (TCP) can be decomposed as
Td= Qd+ Rd+ Nd , (3.1)
where Qd, Rd, and Nd are the queuing delay, reordering delay, and the wireline network delay, respectively. However, the packet delivery delay of (3.1) does not consider the effect of ACK errors. To incorporate the effect of NACK-to-ACK errors into packet delivery delay, Td can be modified as
Td= Qd+ Rd+ Nd+ GP T . (3.2)
Note that the reordering delay Rd is caused by Type-I gaps while the GP T is caused by Type-II gaps. Clearly, a longer period of gap processing time causes longer packet delay because Type-II gaps halt the procedure of forwarding the received packets to the upper layer.
A longer period of gap processing time also results in more accumulated packets in the MAC layer. As a result, the overflow probability of the reordering buffer is increased. Moreover, as more received packets are forwarded to the RLC layer due to longer gap processing time, a larger buffer in the RLC layer is required to accommodate these packets. With large enough buffers of both MAC and RLC layers, the received packets can be accommodated in the receiver. In this chapter, we focus on the analysis of the gap processing time for the three stall avoidance schemes. Gap processing time is influenced by the physical layer parameters, such as packet error rate (Pe) and the probability of a NACK becoming an ACK (PN →A), and the MAC layer parameters, e.g. the size of the reordering buffer and the number of processes in the parallel SAW HARQ mechanisms.
3.2.2 Assumptions
Being a function of both physical layer and MAC layer parameters, gap processing time is difficult to be computed analytically. To make the analysis tractable, we make the following assumptions:
1. Because a NACK-to-ACK error usually occurs when a mobile terminal moves at high speeds, it is assumed that the fast changing channel is modelled by an independent Rayleigh fading channel from one packet to another packet.
2. All packets are assumed to have the same priority.
3. All transmit processes in the HARQ mechanism always have packets ready for transmission.
4. Effects of incremental redundancy and Chase combining are not considered.
The provided analysis in this chapter can be viewed as the worst-case analysis.
5. Assume the modulation and coding scheme and the packet length are not changed during the period of the gap processing time.
6. The feedback delay is not taken into account of the gap processing time.