This paper presents an analytical model for network throughput of WLANs, taking into account heterogeneous conditions, namely network nodes transmit different length frames with various offered load individually. The airtime concept, which is often used in multihop network analyses, is firstly applied for WLAN analysis. The proposed analytical model can cover the situation that there are saturation and nonsaturation nodes in the same network simultaneously, which is the first success in the WLAN analyses. This paper shows the network throughput characteristics of four scenarios. Scenario 1 considers the saturation throughputs for the case that one or two length frames are transmitted at the identical offered load. Scenarios 2 and 3 are prepared for investigating the cases that all network nodes transmit different length frames at the identical offered load and identical length frames at the different offered loads, respectively. The heterogeneous conditions for not only frame length but also offered load are investigated in Scenario 4.

This paper aims to investigate the performance of the IEEE 802.11-based tree-topology network, where a wireless node is within the others' carrier sensing ranges. In such a network, the concurrent transmission is a dominant cause of frame collisions. Moreover, the relay nodes (RN) (i.e., in the tree) likely cause the coexistence of non-saturated and saturated nodes in the networks. Those conditions have not been addressed in the previous works yet. As a solution, this work proposes new analytical expressions of delay and throughput in the investigated scenario. The presented analytical model incorporates the Bianchi model and airtime concept to formulate operations of the IEEE 802.11 nodes. First, by leveraging Bianchi-based analysis, the proposed model gives the frame collision probability caused by concurrent transmission. Second, by using airtime concept analysis, the ratio of frame numbers of each flow in a relay node (RN) is expressed to represent the buffer state of RN. As a result, we can obtain the network throughput, the throughput, and the delay of each flow. The validity of the analytical expressions is confirmed by the quantitative agreement between the analytical and simulation results.