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- Open Access
Medium access behavior analysis of two-flow topologies in IEEE 802.11 wireless networks
- Muhammad Zeeshan^{1}Email authorView ORCID ID profile and
- Anjum Naveed^{1}
https://doi.org/10.1186/s13638-016-0535-2
© Zeeshan and Naveed. 2016
- Received: 26 July 2015
- Accepted: 21 January 2016
- Published: 9 February 2016
Abstract
Impact of medium access control (MAC) on throughput of IEEE 802.11-based multi-hop wireless networks is not completely understood despite numerous research efforts. Researchers have explored the MAC interaction of two-flow topologies in order to better understand the MAC behavior of nodes in generic multi-hop wireless network. Prior research has considered two flow interactions under the assumption of same transmission and carrier sensing range. This research extends and completes the existing body of work by relaxing the assumption of same transmission and carrier sensing range to realize more practical and realistic two-flow topologies. Twenty-five unique possible two-flow topologies can exist in general multi-hop wireless networks. The topologies have been classified into six categories based on MAC layer behavior and per flow throughput. Closed-form expressions for occurrence probabilities of the identified categories have been derived with particular observation that carrier sensing range-based categories have high occurrence probability and cannot be ignored. MAC behavior of each category is discussed. It is observed that different transmission and carrier sensing ranges significantly affect the MAC behavior and the throughput of flows. Based on the behavior, exact throughput of the two single hop flows is analytically computed. The results achieved through analysis have been compared with the simulated results to verify the accuracy of analysis. This research will serve as basis for MAC behavior analysis of generic multi-hop wireless networks.
Keywords
- Wireless mesh networks
- Multiple access interference
- Two-flow interference analysis
1 Introduction
Interference in wireless networks significantly limits the network capacity. Among a set of interfering links using a common frequency channel, transmission of a link is successful only if all other links remain silent for the entire period of transmission. Medium access control (MAC) protocol is employed to arbitrate the access to the wireless channel among competing links. IEEE 802.11 networks use carrier sense multiple access with collision avoidance (CSMA/CA) as MAC protocol. The random access mechanism of CSMA/CA does not ensure interference-free transmissions, specifically when the sender nodes of the interfering links are not within the transmission range of each other. Consequently, many transmission opportunities are wasted when more than one interfering links simultaneously attempt transmissions. Thorough MAC behavior analysis can reveal the impact of interference on the achievable throughput of the interfering links.
Analysis of two-flow topologies is widely used in literature to understand the complex interactions in general multi-hop wireless networks, and analysis of subset of four nodes is suitable to explain all types of interaction that can exist in realistic wireless network deployments. Currently, most deployments of wireless mesh network uses carrier sense multiple access (CSMA) as their MAC protocol. For fully connected topologies where all four nodes or at least both transmitters are within single transmission range, CSMA with or without RTS/CTS demonstrates fair throughput and channel access performance between contending flows. The rest of two-flow topologies in WMN, where both transmitters are not in single transmission range, exhibit severe throughput imbalances between two contending flows and few well-known topologies have been investigated by researchers in the past including hidden and exposed terminal problems. Two-flow topologies in WMN that results in throughput imbalances suffer from problems including severe short- and long-term unfairness between contending flows.
This work further widens and completes the body of work on two-flow interaction analysis for multi-hop wireless network. In this work, two-flow topologies have been classified by separately considering the transmission and the carrier sensing ranges. The interaction between the two single hop flows is considered under CSMA/CA protocol for throughput estimation of two-flow topologies. It is observed that the presence of sender or receiver of interfering link within the carrier sensing range results in a significantly different MAC behavior compared to the presence of the two nodes outside the carrier sensing range. This research divides the two-flow topologies into six categories, depending upon CSMA/CA interaction. Occurrence probability of each category has been computed using spatial analysis. For this purpose, possible geometric area where the nodes of the particular topology can exist has been considered, compared to the overall geometric area of occurrence for two interfering links. Analysis shows that the categories that are based on interference interactions from within the carrier sensing range only have high occurrence probability values (aggregate of 0.69). Finally, throughput achieved by the two links under each category has been computed analytically based on MAC protocol behavior. Analytically computed throughput values have been compared with the simulation throughput values using Opnet-based simulations. The comparison shows near perfect match in analytical and simulated values, suggesting the completeness of the categorization.
The rest of the paper is organized as follows. Section 2 discusses the related work. Section 3 enlists the two-flow categories and possible geometric placement of nodes under each category. Expressions for occurrence probabilities of the categories have been derived in Section 4. Interference type based on MAC protocol and the throughput achieved by each link has been derived for each category in Section 5. Section 6 concludes the paper.
2 Related work
Literature relating MAC behavior analysis and capacity estimation can be grouped into three sets. The first set consists of interference models and ensuing MAC behavior analysis that considers interference from within the transmission range. These models consider the impact of interference from different links to be same, irrespective of their relative geometric location [1–4]. The second set comprises of location-based MAC behavior and interference analysis [5–8]. Literature in this group focuses on change in MAC behavior because of changing geometric relation of the interfering links. The final set consists of capacity estimation based on physical characteristics of wireless channel.
Capacity estimation of CSMA-based wireless networks was first performed by Boorstyn et al. [9]. Authors used Markov chain-based model to compute exact throughput in multi-hop CSMA-based wireless networks. However, the analysis was limited to few nodes, given the complexity of computation. Bianchi [10] computed the achievable throughput by individual nodes, given that all interfering nodes are within a transmission range. Bianchi showed that in the absence of hidden node problem [11] and with perfect channel capture, wireless nodes exhibit fairness for all nodes contending for channel access. Although restricted to only one type of two-flow interactions (i.e., coordinated interfering links), Bianchi computed exact throughput values for different IEEE 802.11 DCF mode parameters. Protocol and physical models of interference are well-known interference models [1] that have been used frequently in literature for capacity estimation as well as MAC protocols and channel assignment research. Both models lead to inaccurate interference estimation.
Given a link and its interfering link, the placement of the sender and the receiver of the interfering link within transmission or carrier sensing range defines the MAC behavior and its impact on achievable throughput of the two links. Garetto et al. [5] have analyzed the MAC behavior of the two interfering links under different geometric placements inside and outside transmission range. The authors have categorized the two-flow topologies with different geographic placements into three categories. Under the assumption of the same transmission and carrier sensing range, the analysis carried out by Garetto et al. [5] accurately predicts the impact of MAC behavior and interference on throughput of the two single hop flows. However, the study does not consider the impact of carrier sensing range on the MAC behavior and the resultant throughput. Razak et al. [7] have extended this research by considering separate carrier sensing and transmission ranges; however, the simulation results show that the topologies within the single category do not share the same throughput profile. Furthermore, important categories based on nodes within carrier sensing range have not been considered.
Garetto et al. [5] have considered the two-flow interactions and classified possible topologies into three categories of sender connected (SC), asymmetric incomplete state (AIS), and symmetric incomplete state (SIS) based on MAC behavior and throughput imbalances. In their extended work, Garetto et al. [6] computed per link forwarding capacity for general multi-hop wireless networks using two-flow interactions. In cases where transmission and sensing ranges are considered same, the analytical results accurately predict throughput achieved through simulations. However, the model does not capture the impact of interference from links within sensing range. The work has been extended by Razak et al. [7, 8, 12]; however, significant gap exists between analytical and simulated results. Research presented in this document is focused on differentiating between interference introduced from transmission range and from carrier sensing range. This results in new categories that have high occurrence probability in realistic multi-hop wireless networks.
Among capacity estimation literature, Li et al. [13] have performed the throughput analysis of a single access point for IEEE 802.11g radios. Dinitz [14] has proposed distributed algorithms for wireless nodes to achieve optimal throughput in distributed multi-hop wireless networks. The author have used protocol and physical models for interference. Kawade et al. [15, 16] have compared the performance of IEEE 802.11g and 802.11b radios under co-channel interference by considering the physical layer characteristics. The authors have concluded that IEEE 802.11g networks are more resistant to co-channel interference while channel separation improves the performance of both types of networks. Weber et al. [17] have computed the upper and lower bound network capacity for multi-hop wireless networks using different physical channel conditions. The authors have computed maximum physical transmission capacity and optimal number of nodes that achieve the maximum capacity.
Fu et al. [18] have analyzed the general CSMA protocol and proposed the concept of cumulative interference model where hidden node problem can be avoided. The authors have also proposed incremental power carrier sensing that can help nodes identify the distance from potential interfering nodes and better plan the transmissions. Vitturi et al. [19] have proposed new techniques for rate adaptation to cater the collision problem and compared the performance with automatic rate fallback technique. The authors have shown that the performance of new techniques is better in terms of retransmissions required. Qiao et al. [20] have also proposed transmit power control and rate adaptation to achieve low energy consumption in IEEE 802.11a/h systems. The objective is to minimize consumed energy, although throughput gains have also been reported.
Focus of this research is the analysis of two-flow interference interactions, impact of geometric location on MAC behavior, and its impact on throughput of the two single hop flows.
3 Two-flow topology categorization
Within a multi-hop network, a sender receiver pair (referred as flow throughout the rest of the paper) interacts with multiple flows in the neighborhood. Each interaction impacts the throughput of the flows, resulting in complex chain of interactions. In order to understand such interactions and the resulting impact on the achievable throughput of each flow, it is important to understand the possible interactions between two flows in isolation. Based on this understanding, a general model for wireless interactions in a multi-hop wireless network is conceivable, which can predict the achievable throughput of individual single hop flows. In this section, possible interactions of two flows are categorized based on geometric location of the nodes of the flows. The differences of proposed categorization from the categories defined in prior work [5, 7] are highlighted. In the subsequent sections, the achievable throughput is discussed based on the MAC behavior.
3.1 Terminology
The Euclidean distance between two nodes A and B is given as d(A,B). A node can have three possible placements with reference to another node depending upon the signal strength received from the other node. If node B is placed around node A such that it can successfully decode the transmissions from node A, then the node B is within the transmission range (TR) of node A, i.e., d(A,B)≤TR. Such placement is referred as connected in this paper. On the other hand, if node B can sense the channel to be busy when node A transmits but cannot successfully decode the information because of weak radio signals, then the node B is outside transmission range but within the carrier sensing range (CSR) of node A, i.e., TR<d(A,B)≤CSR. This placement is referred as sensing. Finally, if node B cannot sense the transmissions of node A, then node B is outside the carrier sensing range of node A, i.e., d(A,B)>CSR. This placement is referred as disconnected. The placement is referred as not connected if it is either sensing or disconnected. The placements are referred as interference interactions throughout the rest of the paper.
3.2 Two-flow topologies
Based on the interference interactions, there are a total of 3^{4}(81) possible two-flow topologies while 53 of these topologies are unique. Given the restriction that the transmitters of flows must be within the transmission range of the respective receivers and the fact that carrier sensing range is ≈2.7 times the transmission range (through simulations and experimentations), only 25 topologies are physically realizable in a multi-hop wireless network. Remaining 28 topologies have zero occurrence probability. The 25 unique possible topologies have been classified into six categories, depending upon the types of the four interference interactions and the MAC behavior. The following sections explain the interference interactions of the categories.
3.2.1 Sender connected (SC)
3.2.2 Symmetric sender receiver connected (SSRC)
3.2.3 Asymmetric sender receiver connected (ASRC)
This category exists with the name of asymmetric incomplete state in the categorization of Garetto et al. [5] and Razak et al. [7]. However, an additional topology (Fig. 6 a) is part of this category in the proposed categorization because of the different sensing range and transmission range.
3.2.4 Receiver connected (RC)
3.2.5 Symmetric not connected (SNC)
3.2.6 Asymmetric not connected (ANC)
4 Category occurrence probabilities
How frequently the topologies belonging to each category can exist in a general multi-hop wireless network? Specifically, what is the occurrence probability of the newly identified categories? Answers to these questions are important in identifying the impact of each category on interference profile of the links in general multi-hop wireless networks. Geometric analysis has been employed to find out the occurrence probability of the categories. Perfect circular disks are assumed for area under transmission range, carrier sensing range, and the network with the disk radii defined as r _{tr}, r _{csr}, and r _{n}, respectively. Network radius is assumed to be r _{n}=0.5×(2×r _{tr}+r _{csr}) which covers maximum possible distance for a valid placement of the nodes such that the resulting flows are interfering. Note that at times, the carrier sensing range of nodes can be outside the total network area; however, the ratio of area of interest and the total area remains unaffected.
For each category, four interference interactions AB, Ab, aB, and ab are considered individually. For each pair of nodes within the interference interaction, one node is assumed to be at a fixed location. The area around the first node where the second node can possibly exist is computed, given the placement constraints introduced by the specific category. Under the assumption of circular disk ranges, the area is mostly equivalent to either the area of a disk or the area of intersection of two disks with known radii. The ratio of computed area to the maximum possible network area gives the probability of occurrence of the interference interaction. Multiplying the occurrence probabilities of four individual interactions gives the occurrence probability of the category.
The occurrence probability of each category is computed in the subsequent section using the two listed expressions. For sake of brevity, the final expression for probability of each category is given with brief description of the expression.
4.1 Sender connected
4.2 Symmetric sender receiver connected
where r=d=r _{tr}.
4.3 Asymmetric sender receiver connected
where r=d=r _{tr}.
4.4 Receiver connected
where r=d=r _{tr}.
4.5 Symmetric not connected
4.6 Asymmetric not connected
4.7 Occurrence probability values
Figure 15 shows that the occurrence probability is significantly high for the categories that are purely based on interactions because of carrier sensing range (SNC = 0.45 and ANC = 0.24). In the subsequent section, we show that these interference interactions significantly affect the throughput of interfering links. Therefore, the categories cannot be ignored.
5 Interference and throughput analysis
IEEE 802.11 wireless interfaces use carrier sense multiple access (CSMA) with collision avoidance (CA) protocol for acquiring wireless channel access. This section starts with brief explanation of the CSMA/CA protocol as used in IEEE 802.11 (Only extended mode is explained). Parameters affecting the throughput are discussed, and the throughput expressions derived by Bianchi [10] and Kumar et al. [21] are listed. Subsequently, the expressions for the parameters in the throughput expressions are derived for the two flows for each category, throughput for different packet sizes is computed, and the computed values are compared with simulated results to highlight the accuracy of the categorization and the throughput analysis.
5.1 CSMA/CA protocol behavior
In IEEE 802.11 MAC, time is considered to be slotted and the slot interval is represented by σ. Based on the CSMA protocol, when a node has data to transmit, it sets a back-off counter by selecting a random value from the range [0,W _{ i }−1]. For the first attempt, W _{0}=16 for IEEE 802.11a/g radios. The counter is decremented whenever the channel is found idle for the slot interval. If the channel is not idle because of an ongoing transmission from a neighboring node, the back-off counter freezes. When the counter reaches zero and the channel is idle, the node initiates transmission by sending ready-to-send (RTS) frame. The transmitting node waits for the response from intended receiver, which is in the form of clear-to-send (CTS) frame. If the CTS is not received within a certain period of time (SIFS + 2*propagation delay), the RTS is assumed to be lost (due to collision or because of busy channel at receiver end). In case of collision, the node resets the back-off counter by selecting a random value from the range [0,2^{ i }∗W _{0}−1] where i is the number of retransmission attempt and is known as a back-off stage. The entire procedure of channel access is repeated. If the CTS is received, the channel is reserved for the particular transmission and the node proceeds with transmission of data packet, followed by ACK from a receiver. The four frames RTS, CTS, DATA, and ACK are separated by Short Inter-Frame Space (SIFS) while ACK frame is followed by DCF Inter-Frame Space (DIFS). In case of IEEE 802.11g radios, every frame is followed by signal extension, which is idle interval of 6 μs, necessary for proper reception of signal. The nodes other than the transmitter and receiver that correctly receive the RTS or CTS frame set the NAV for remaining period of transmission and freeze their activity on the channel.
Parameters (ERP IEEE 802.11g)
Parameter | Value |
---|---|
Data rate | 54 Mbps, 216 bits/symbol |
Basic rate | 6 Mbps, 24 bits/symbol |
W _{0} | 16 |
W _{max} | 1024 |
m | 6 |
m ^{′} | 6 |
Symbol duration | 4 μs |
σ | 9 μs |
SIFS | 10 μs |
DIFS | 28 μs |
PHY | 20+6 μs (including signal extension) |
RTS, CTS, MAC, ACK | 20, 14, 34, 14 bytes at basic rate |
(ceil(bits/(bits/sym)) × 4 μs) + PHY | |
DATA | at data rate, measured in symbol duration |
T _{ s } | RTS + CTS + DATA + ACK + |
3 SIFS + DIFS | |
T _{ c } | RTS + DIFS |
In the following, the MAC behavior based on interference interactions for the identified categories is explained and the known parameters are computed to compute the achievable throughput for both flows of each category.
5.2 Sender connected
5.3 Symmetric sender receiver connected (SSRC)
The senders A and B of the two flows in this category (and all subsequent categories) are not within the transmission range of each other. Therefore, the RTS frame transmitted by sender A is not successfully decoded by sender B and vice versa. However, the channel is sensed busy during RTS transmission, preventing the other sender from initiating a transmission. This is different from SIS category proposed by Garetto et al. [5] where senders are assumed to be outside the sensing range and cannot sense the RTS transmitted by sender of the alternate flow. The receivers of both flows are within the transmission range of the alternate senders, i.e., interference interactions Ab and aB are connected. This means that the receivers can successfully decode the RTS frame transmitted by the alternate senders resulting in setting NAV at alternate receiver. Similarly, senders can successfully decode the CTS packet transmitted by the alternate receivers. Therefore, collision can only occur if one sender starts transmission of RTS during the idle interval between RTS and CTS transmission of the alternate flow.
Parameters (SSRC computation)
Parameter | Value |
---|---|
Throughput | \(\frac {p_{s}T_{s}}{p_{s}T_{s} + p_{c}T_{c} + p_{I}\sigma + p_{s}T_{s}}\) |
p _{ s } | \(\frac {\Sigma _{i,j}\pi _{(i,j)}\gamma _{i}(1-\gamma _{j})^{f}}{\Sigma _{i,j}\pi _{(i,j)}(\gamma _{i}(1-\gamma _{j})^{f} + \gamma _{i}\gamma _{j})}\) |
p _{ c } | \(\frac {\sum _{i,j}\pi _{(i,j)}\gamma _{i}\gamma _{j}}{\sum _{i,j}\pi _{(i,j)}(\gamma _{i}(1-\gamma _{j})^{f} + \gamma _{i}\gamma _{j})}\) |
p _{ I } | \(\sum _{i,j}\pi _{(i,j)}(1-\gamma _{i})(1-\gamma _{j})\) |
γ _{ i } | \(\frac {2}{W_{i} + 1}\) |
f | ceil((SIFS + 6) /σ) =2 |
Throughput | 0.0011 pkts /μs |
5.4 Asymmetric sender receiver connected (ASRC)
In this category, the two senders A and B are outside the transmission range of each other. The receiver of flow Bb is within the transmission range of sender A while receiver of flow Aa is either within carrier sensing range or outside the range of sender B. This results in different view of channel for each flow. If RTS frame is transmitted by sender A, it is received by receiver b, which sets the NAV and remains silent for the entire transmission of the flow Aa. The transmission of flow Aa can be unsuccessful if sender B starts the RTS transmission during the interval between RTS and CTS frames of flow Aa, which is sensed idle by sender B. In case of topology in Fig. 6 b, this interval increases by the duration of CTS frame because sender B cannot sense the activity of receiver a. This information is used to compute collision probability of flow Aa. This behavior of the category is significantly different from AIS category proposed by Garetto et al. [5] where conditional packet loss probability of flow Aa is zero because of assumption that the two senders are outside the range of each other. Note that transmission of flow Bb in all these scenarios will not be successful given the fact that receiver b has set the NAV after receiving RTS frame from sender A. Flow Bb can have a successful transmission only when the RTS frame from sender B is initiated while flow Aa is in back-off stage. In this case, sender A senses RTS frame and assuming the channel to be busy, it does not initiate transmission. Subsequently, it receives CTS frame and sets the NAV resulting in busy period for flow Aa and successful transmission on flow Bb. The probability of this event is computed by considering the available transmission opportunities for sender B that can lead to successful RTS transmission.
where D= signal extension + DIFS. Using this equation, packet loss probability of flow Bb can be computed in terms of all known variables. Replacing p _{ B } in Eq. 9 gives transmission probability τ _{ B } for flow Bb. Throughput computation of flow Bb also requires the value of busy probability b _{ B } which is equal to the transmission probability τ _{ A } of flow Aa. Therefore, we need to compute the transmission probability of flow Aa in order to compute the throughput of flow Bb.
Transmission probability τ _{ A } of flow Aa is dependent upon the conditional packet loss probability p _{ A }. In case of ASRC category, RTS frame transmitted by sender A is sensed by sender B as busy period. However, signal extension + SIFS interval following RTS transmission is sensed as idle by sender B. If sender B initiates RTS transmission during this event, it will result in unsuccessful reception of CTS from a at sender A, which is the event of collision for flow Aa. Therefore, probability of packet loss for flow Aa can be computed by modeling the probability of the event of RTS transmission by sender B during interval signal extension + SIFS between RTS and CTS transmission by flow Aa. This event can be modeled as one-dimensional Markov model with m states. The expressions in Table 2 are valid for the purpose with the difference of number of states and the variable γ _{ j } replaced by τ _{ B }. Note that variable f includes additional interval of CTS for the topology in Fig. 6 b. Conditional packet loss probability for flow Aa is given by the expression for p _{ c }. Computed value can be used to compute the value of τ _{ A } using Eq. 9. Given that busy probability b _{ B } of flow Bb is equal to the transmission probability τ _{ A } of flow Aa and busy time is equal to T _{ s }− DIFS − signal extension, all parameters for throughput computation of flow Bb are known. Equation 10 can be used to get the throughput value for flow Bb.
5.5 Receiver connected (RC)
5.6 Symmetric not connected (SNC)
Topologies belonging to this category do not have any of the interference interactions as connected. Placement of flow Bb within the carrier sensing range of flow Aa is possible within a large area of carrier sensing range. Therefore, the distances d(A,B),d(a,B),d(A,b), and d(a,b) can be as small as slightly greater than transmission range and as large as exactly equal to carrier sensing range (which is ≈2.7 times the transmission range) or even outside carrier sensing range. The throughput of the two flows under this category is driven by the fact that frames transmitted by an interferer from closer location within carrier sensing range are sensed as busy periods. On the other hand, the frames transmitted by the interferer at relatively distant location within carrier sensing range may cause errors but otherwise can be rejected as interference, without making the channel busy. Keeping this in view, the MAC behavior can be divided into two parts. The first part comprises of region where a node can sense the frame transmission from other node as busy period. The second part comprises of the region where such transmissions cause errors; however, signal strength is not high enough to make channel busy. Empirical analysis shows that area around a sender up to r _{csr}−0.5r _{tr} comprises of the first part while the presence of interfering nodes within the region beyond this threshold form the second part. Significant area of occurrence of the topology in Fig. 10 a exists in the first part. For all remaining topologies belonging to this category, approximately half of the area of occurrence lies within the first part while the remaining half of the occurrence area lies in the second part.
Parameters (SNC computation)
Topology | Parameter | Value |
---|---|---|
a,b | f | ceil((signal extension + SIFS) /σ) |
a,b | T _{ b } | T _{ s }− DIFS |
a,b | T _{ c } | RTS + SIFS + CTS + DIFS |
c,d | f | ceil((RTS + SIFS) /σ) |
c,d | T _{ b } | CTS /ACK |
c,d | T _{ c } | RTS + DIFS |
e,f,g | f | ceil((CTS + SIFS − signal extension) /σ) |
e,f,g | T _{ b } | (DATA + ACK − 2*signal extension) 0.5 |
e,f,g | T _{ c } | RTS + SIFS + CTS + DIFS − signal extension |
The impact of interference from far sensing range on throughput of the flows can be estimated by considering the received signal strength, its impact on bit error rate and packet error rate. Ideal channel conditions are assumed where the only factor affecting the unsuccessful reception of frame is the interference from the other flow. Although extremely simplifying, even under this assumption, throughput of the two flows can be predicted accurately. This assumption allows the computation of packet error probability for RTS frame. Near sensing range analysis is used as basis while the conditional packet loss probability and busy probability of the flows are adjusted by the packet error probability to achieve the throughput of the two flows that interfere from within far sensing range.
5.7 Asymmetric not connected (ANC)
Topologies belonging to this category have interference interaction Ab as sensing while the interference interaction aB is disconnected. Like ASRC category, asymmetric channel view of the two flows results in imbalance among achievable throughput with one flow Aa getting dominant portion of channel capacity while the other flow Bb getting negligible throughput. Similar to SNC category, the distance between nodes of two flows affects the achievable throughput. The MAC behavior of the category predicts the initial throughput of the two flows at minimum possible distance. With the increasing distance, the impact of one flow on the other is mitigated, gradually making two flows independent of each other. For the throughput computation, the MAC behavior is defined first and the throughput of the two flows is computed. Subsequently, the results because of the SNR-based adjustments to the behavior are reported, similar to SNC category.
For the analysis purposes, interference interaction Ab is considered as sensing while the interference interaction aB is considered to be disconnected. The conditional packet loss probability of flow Bb can be computed by considering the interval during which RTS transmission from B will be received successfully by b. This interval is given by D+i σ where D= signal extension + DIFS and i is the average number of back-off slots. There is a difference between MAC behavior of the topologies. For topologies in Fig. 13 a, b, sender A can sense RTS transmission from sender B; therefore, B only needs to initiate the RTS transmission within the specified interval for its transmission to be successful. On the other hand, for topologies in Fig. 13 c, d, Senders A and B are outside the sensing range; therefore, sender B must complete the transmission of the entire RTS frame during the specified interval for the transmission to be successful. For the later case, D is updated to D= signal extension + DIFS − RTS. Given the value of the interval, Eq. 11 can be used to compute the conditional packet loss probability for flow Bb. The busy probability of two group of topologies also differs. For topologies in Fig. 13 a, b, busy probability b _{ B }=τ _{ A } because of the fact that B can sense the transmissions of A. Busy interval is equal to T _{ s }− (SIFS + ACK + DIFS). On the other hand, busy probability of flow Bb for topologies in Fig. 13 c, d is zero. Throughput of flow Bb can be computed in terms of all known parameters using Eq. 10, provided the value of τ _{ A } is known.
6 Conclusions
This work has investigated the MAC behavior of two single hop IEEE 802.11 standard-based interfering flows. All possible two-flow topologies have been identified using realistic transmission and carrier sensing ranges. The identified categories have been divided into six categories based on the MAC behavior as well as geographic placement of the four interfering nodes. Closed-form expressions for occurrence probabilities of all identified categories have been computed to show that all categories have significant probability of occurrence in a general multi-hop wireless network. MAC behavior of each category is thoroughly discussed with the key observation that the presence of interfering nodes within the carrier sensing range has significant impact on the behavior and the throughput of five out of six identified categories. Based on the MAC behavior, extensive throughput computations are performed for both flows under each category. This work completes the research efforts towards defining the MAC behavior of two-flow topologies and its impact on the throughput of links. The work can be extended to general capacity analysis of multi-hop wireless networks and can serve as the basis for modified MAC protocol that can better mitigate the impact of interference, specifically the interference from within carrier sensing range.
Declarations
Open Access Thisarticle is distributed under the terms of the Creative Commons Attribution 4.0 International License(http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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