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frame num, maximum number of data frames allowed to be transmitted in a TXOP (transmission opportunity); lt ype , number of bits in a type frame; ttype , transmission time on the channel for a type frame; single-poll, the single polling frame in the single poll (i.e. CF-Poll frame); n, poll size (i.e. the number of poll records in a multipolling frame); n-poll, the multipolling frame with n poll records; ERRtype , probability that a type frame is dropped due to bit errors; , probability that an STA has no data to send when polled; , probability that an STA becomes a nonbehaved STA; h, number of PCs operating in the overlapping space; InitBT, initial backoff time; E, polling ef ciency.
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The following assumptions will be used in the analysis: (1) The PC (point coordinator) always performs the initial backoff before sending any polling frame. (2) The data frame is transmitted without any acknowledgment. When an STA is polled, the STA either sends a half of frame num data frames on average or sends a null data frame if there is no data to send.
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Figure 21.5 The state diagram of the multipolling mechanism. (Reproduced by permission of IEEE [43].) (3) There is an equal probability BER for a bit error to occur due to the channel noise (interference, fading or multipath). Hence, ERRtype can be expressed as 1 (1 BER)ltype . (4) An STA becomes a nonbehaved one if the STA fails to receive the CTS frame from the PC. That is, = ERRCTS . If AvgD and AvgT denote the total number of bits in the data frames successfully sent from the polled STAs and the average complete time in time units for a poll, respectively, then the polling ef ciency is de ned as E = AvgD/AvgT. This represents the average uplink data rate during a poll. In the single poll, a polled STA contributes data frames if the STA successfully receives a CF-Poll frame and has pending data frames to be successfully transmitted. The polled STA may suffer frame error due to interference from external STAs. Therefore, AvgD = (1 ) frame num/2 ldata frame (1 ERRdata frame ) (1 ERRsingle
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The polled STA will give a response to the PC after an SIFS period for a successful CF-Poll. If a polled STA does not respond to the PC after a PIFS period for a failed CF-Poll, the PC takes over the channel control and may send the next CF-Poll frame. In the HCF, the RTS/CTS frames should be exchanged before the data transmission to prevent the interference from other STAs. Since the HCF is being substituted for the PCF in the 802.11E, we consider the single poll of the HCF in our analysis. Therefore, AvgT = InitBT + (tsingle-poll + PIFS) ERRsingle-poll + [tsingle-poll + SIFS + tRTS + tCTS + 2SIFS + (1 ) frame num/2 (tdata + (tnull frame + SIFS)] (1 ERRsingle-poll )
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Next, we use a state diagram to represent the situation after sending a multipolling frame with poll size n. In Figure 21.5, the state m : fail(0 m n) represents the event that there are m STAs in the polling group which failed to receive the multipolling frame. Let Pn,m denote the probability of the state m : fail. Let Dn,m and Tn,m denote the amount of uplink data frames in bits and the total time duration in time units under the state m : fail, respectively. Generally, we have the following values: Pn,m = n m (ERRn poll )m (1 ERRn poll )n m
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