Network Model

In this subsection, we describe the network model that we use to analyze the performance of AP-based WLANs. In these infrastructure-based WLANs, each wireless node only communicates directly with an AP in order to exchange data with another node inside or outside of the WLAN.

As in much of the existing literature [8,27], we base our analysis on the fluid traffic model, and thus are concerned with AggrThruput. However, the results in this section clearly indicate that when the task traffic model is used, the network efficiency in terms of AvgTaskTime is better under time-based fairness than under throughput-based fairness (see Section 2.1).

Let I be the set of competing nodes and n its cardinality. We define d_i and s_i as the data rate used and data packet size used by node i. For simplicity of analysis, we assume that d_i and s_i apply to data packets in both uplink and downlink directions of node i.

We define the channel occupancy time T(i), $0 \leq T(i) \leq 1$, of node i as the fraction of time a wireless node i is able to access the channel to either transmit or receive packets to and from the AP. The channel occupancy time necessary to transfer a data packet includes i) the transmission time of the data packet, ii) the transmission time of a synchronous ack, iii) the propagation delays, iv) the inter-frame idle periods necessary for a node to be idle before accessing the channel, and v) the amount of time required to perform retransmissions when necessary. Since we assume that the channel is busy all the time:

$$\sum_{i \in I}{T(i)} = 1$$ (1)

Let R(I) and R(i) be the total throughput achieved by all nodes in I and the achieved throughput of node i respectively. We can express R(i) in terms of T(i) as:

$$R(i) = T(i) \times \gamma(d_i,s_i,I)$$ (2)

where $\gamma(d_i,s_i,I)$ is the baseline throughput (that nodes experience) as a function of d_i, the data rate, and s_i, the packet size, holding all else equal. The baseline throughput $\gamma(d_i,s_i,I)$ equals the maximum total achieved throughput when all nodes (I) use the same packet size and data rate under similar loss characteristics. For instance, when two nodes simultaneously transfer files using 1500-byte TCP packets and a data rate of 11 Mbps, the baseline throughput (as shown in Figure 2) is 5.08 Mbps. However, the actual throughput R(i) node i depends upon the fraction of time i was able to access the channel, T(i). The total actual throughput of the network is simply:

$$R(I) = \sum_{i \in I}{R(i)}$$ (3)

Baseline throughput increases with the increase in data transmission rate as well as packet size. The latter is due to reduced per-packet overhead as a result of the larger number of payload bits per packet. By expressing R(i) in terms of $\gamma(d_i,s_i,I)$, we avoid dealing directly with other factors that affect the throughput such as the back-off periods and physical layer overhead, that are independent of the work covered in this paper. $\gamma(d, s,I)$ can be obtained both theoretically and experimentally. In Section 2.7, we report measured values of $\gamma(d, s,I)$ for various values of d. Furthermore, we do not deal with varying loss characteristics since our goal is in understanding how diverse data rates and packet sizes affect the network performance.