Transmission Efficiency of ARQ Protocols

In the previous sections we already introduced the performance differences between Stop-and-Wait, Go-Back-N, and Selective Repeat ARQ protocols. In this section we discuss performance results for these protocols and present a quantitative comparison of their transmission efficiency. We show that the delay-bandwidth product, the frame error rate, and the frame length are key parameters in determining system performance.

For simplicity we focus here on the case where the information is unidirectional and where the reverse channel is used only for acknowledgments. We also assume that all information frames have the same length and that the transmitter always has frames to transmit to the receiver. Figure 5.23 shows the components in the basic delay t0 that transpires in Stop-and-Wait ARQ from the instant a frame is transmitted into the channel to the instant when the acknowledgment is confirmed. The first bit that is input into the channel appears at the output of the channel after a propagation time tprop; the end of the frame is received at station B after ty additional seconds. Station B requires tproc seconds to prepare an

Arq Delay Diagram
FIGURE 5.23 Delay components in Stop-and-Wait ARQ

acknowledgment frame that will require tack seconds of transmission time. After an additional propagation delay, the acknowledgment frame is received at station A. Finally, tproc additional seconds are required to carry out the CRC check. The basic time to send a frame and receive an ACK, in the absence of errors, is then given by nf na t0 2tprop H 2tproc H tf H tack 2tprop H 2tproc H ~R H ~R

where nf is the number of bits in the information frame, na is the number of bits in the acknowledgment frame, and R is the bit rate of the transmission channel.

The effective information transmission rate of the protocol in the absence of errors is then given by number of information bits delivered to destination nf no

Re-ff total time required to deliver the information bits t0

where no is the number of overhead bits in a frame and is given by the total number of bits in the header and the number of CRC check bits. The transmission efficiency of Stop-and-Wait ARQ is given by the ratio R^f to R:

nf nf

The preceding equation identifies clearly the sources of inefficiency in transmission. In the numerator the ratio n0/nf represents the loss in transmission efficiency due to the need to provide headers and CRC checks. In the denominator the term na/nf is the loss in efficiency due to the time required for the acknowledgment message, where na is the number of bits in an ACK/NAK frame. Finally, the term 2(tpr0p + tpr0C)R is the delay-bandwidth product, which was introduced earlier in the section.

Table 5.1 shows the efficiencies of Stop-and-Wait ARQ in a number of scenarios. We first assume a frame size of 1024 bytes (8192 bits) and n0 = na = 8 bytes. We consider three values of reaction time tpr0p + Ipr0C: 5 ms, 50 ms, and 500 ms. Because the speed of light is 3 x 108 meters/second, these

30 kbps 0.005 0.95

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