Capacity and QoS for a Scalable Ring-Based
Wireless Mesh Network
Jane-Hwa Huang, Li-Chun Wang, Senior Member, IEEE, and Chung-Ju Chang, Fellow, IEEE
Abstract—The wireless mesh network (WMN) is an economical
solution to support ubiquitous broadband services. This paper in-vestigates the tradeoffs among quality-of-service (QoS), capacity, and coverage in a scalable multichannel ring-based WMN. We sug-gest a simple frequency planning in the proposed ring-based WMN to improve the capacity with QoS support, and to make the system more scalable in terms of coverage. We develop a physical (PHY)/ medium access control (MAC) cross-layer analytical model to eval-uate the delay, jitter, and throughput of the proposed WMN, by taking account of the carrier sense multiple-access (CSMA) MAC protocol, and the impact of hop distance on transmission rate in the physical layer. Furthermore, the mixed-integer nonlinear pro-gramming optimization approach is applied to determine the op-timal number of rings and the associated ring widths, aiming at maximizing the capacity and coverage of a mesh cell subject to the delay requirement.
Index Terms—Capacity and coverage, cross-layer analysis,
quality-of-service (QoS), wireless mesh network (WMN) .
I. INTRODUCTION
T
HE WIRELESS MESH NETWORK (WMN) is apromising technology for next-generation wireless systems since it can enhance coverage with low transmit power [1]–[4]. The architecture for a WMN is illustrated in Fig. 1, where each user relays other users’ traffic toward the central gateway directly connected to the Internet. Compared with single-hop networks, the coverage of WMN is improved thanks to less propagation loss and shadowing. Moreover, WMN can be rapidly deployed in a large-scale area with less cabling engineering work.
However, multihop networking may face the scalability issue [3]–[5]. Specifically, the multihop communications can extend the coverage of an access point with more hops or longer hop distance. However, the repeatedly relayed traffic with more hops will easily exhaust the radio resource and degrade the quality-of-service (QoS), e.g., longer delay and higher jitter. In the mean-while, longer hop distance will also lead to lower data rate in the relay link between nodes. Besides, as the number of users increases, more collisions due to channel contention will further degrade the throughput. Therefore, one of the key challenges in Manuscript received October 1, 2005; revised March 4, 2006 and May 1, 2006. This work was supported in part by the National Science Council and the Program for Promoting Academic Excellence of Universities under Grant EX-91-E-FA06-4-4, Grant NSC 95-2752-E-009-014-PAE, Grant NSC 94-2213-E-009-030, and Grant NSC 94-2213-E-009-060. This work was presented in part at the IEEE International Conference on Communications (ICC) 2006, Istanbul, Turkey, June 2006.
The authors are with the Department of Communication Engineering, Na-tional Chiao-Tung University, Hsinchu 300, Taiwan, R.O.C. (e-mail: hjh@mail. nctu.edu.tw; lichun@cc.nctu.edu.tw; jchang@cc.nctu.edu.tw).
Digital Object Identifier 10.1109/JSAC.2006.881622
Fig. 1. Mesh cell architecture for a WMN.
a multihop network is to maintain the throughput and QoS while extending the coverage area.
In the literature, the performance issues for WMN have been studied from two directions [1], [2], [6]–[11]. On the one hand, by simulations, authors in [6] demonstrated the coverage advan-tage of a multihop WMN over a single-hop infrastructure-based network. On the other hand, from a throughput viewpoint, it was shown in [7] and [8] that the user throughput in an ad hoc net-work is scaled like , where is the total number of users. The authors in [2] pointed out that the achievable user throughput in a WMN will sharply decrease as due to the bottleneck at the central gateway. Furthermore, the au-thors in [9]–[11] investigated the throughput and delay trade-offs in ad hoc networks. These works [9]–[11] addressed the issue whether ad hoc networks can simultaneously achieve high throughput and guarantee the delay requirement. Fewer papers have considered both throughput and coverage performance is-sues for a WMN, except for [1] in the single-user case. In our previous work [12], the relation of throughput and coverage in a scalable WMN was investigated. However, the QoS issues (i.e., delay and jitter) are not considered in [12].
This paper investigates the optimal tradeoff among capacity, coverage, and QoS for a scalable WMN, as shown in Fig. 1. The proposed WMN is scalable thanks to the following two factors. First, the suggested frequency planning can reduce collisions as cell coverage and users increase. Second, the ring structure can 0733-8716/$20.00 © 2006 IEEE
facilitate the management of QoS, throughput, and coverage in WMNs. To find the optimal tradeoff among throughput, cov-erage, and delay, we first develop a physical (PHY)/medium access control (MAC) cross-layer analytical model to evaluate the throughput of the proposed WMN, considering the carrier sense multiple-access (CSMA) MAC protocol, the impact of the ring-based cell structure on frame contentions, and that of hop distance on transmission rate in the physical-layer. Secondly, we develop a queueing model to evaluate the delay and jitter in the considered WMN. Third, we apply the mixed-integer nonlinear programming (MINLP) optimization approach to determine the optimal number of rings in a cell and the associated ring widths, aiming at maximizing the cell capacity and coverage with the QoS requirement.
The rest of this paper is organized as follows. Sections II dis-cusses the proposed network architecture and the impacts of ring-based cell structure on frame contention. In Section III, we formulate an optimization problem to maximize capacity and coverage of a mesh network with a delay constraint. Section IV discuses the channel activity in the ring-based WMN. Section V elaborates the developed cross-layer MAC throughput model for the considered WMN. In Section VI, we analyze the delay and jitter. Numerical examples are shown in Section VII. Con-cluding remarks and future works are given in Section VIII.
II. SCALABLERING-BASEDWMN
A. Network Architecture
Fig. 1 shows the considered ring-based WMN. In the figure, a mesh cell is divided into several rings , de-termined by concentric circles centered at the central gateway
with radii . Users in the inner rings
will forward data for users in the outer rings toward the cen-tral gateway. Accordingly, the user in ring is connected to the central gateway via an -hop communication, and only the gateway connects to the backbone network. Clearly, the cabling engineering work required to deploy this WMN is reduced due to fewer backbone links.
The considered WMN operates in a multichannel fashion. We assume that each node is equipped with two radio interfaces, and therefore can concurrently receive and deliver the forwarded traffic as [3] and [4]. For example, a user in ring can concur-rently communicate with the users in rings and at two different channels and , respectively. A simple fre-quency planning is employed to avoid the co-channel interfer-ence. The simplicity of the frequency planning lies in the fact that only the width of each ring should be designed to obtain the co-channel reuse distance without interference.
Because the users in the inner rings near the central gateway will relay more traffic than the users in the outer rings, we also sectorize the congested inner rings and allocate different channel to each sector. Since the number of contending users is reduced, the throughput for the ring-based WMN can be further improved. Fig. 2 illustrates an example of a three-cell WMN, where the innermost rings of each cell are divided into three sectors. In this example, the ring-based frequency planning with 12 different channels ensures four buffer rings between
Fig. 2. Example of a three-cell WMN, where the congested ringsA and A of each mesh cell are sectorized.
two co-channel rings. Apparently, if more nonoverlapping channels are available, more inner rings can be sectorized to enhance cell capacity and coverage.
B. Scalability, QoS, and Robustness
Most traditional WMNs are not scalable to cell coverage be-cause throughput and QoS (delay) are not guaranteed with in-creasing collisions. By contrast, the proposed ring-based WMN is scalable in terms of coverage, because delay and throughput can be ensured by the ring-based frequency planning with ap-propriately designing the ring widths of the mesh cell. The re-maining important problem lies in the way to analytically de-termine the optimal ring widths so as to achieve the optimal tradeoff among delay, throughput, and coverage.
Due to multiple paths for each node, an appealing feature of WMN is its robustness. If some nodes fail, the mesh network can continue operating with slightly degraded performance by forwarding data traffic via the alternative nodes. Different from the conventional WMNs, the ring-based WMN can easily pro-vide capacity margin for each relay link by decreasing the ring width (and then the hop distance). By doing so, even if some nodes near the central gateway fail, throughput and delay can still be ensured.
C. Frame Contention Under Ring-Based Cell Structure
To describe frame contention under the ring-based cell struc-ture, we first define the mutually interfered region as an area in which any two users can sense the activity of each other. Fig. 3 shows an example of mutually interfered region in ring , such as the area including nodes and . Since each ring is allocated with different channel, a mutually interfered region is indeed the intersection of two circles and the associated ring, which is de-pendent on the locations of observed nodes and the interference distance. For simplicity, we assume that the mutually interfered region in ring can be approximated as an annulus sector with a central angle of . Suppose that the interference distance is
Fig. 3. Examples of wireless collision domain and mutually interfered region.
. Referring to Fig. 3, the central angle of a mutually in-terfered region in ring is equal to
(1)
If , we define which means that the
whole ring is in the same mutually interfered region. Clearly, the area of a mutually interfered region is
and is the area of ring .
Then, we define the wireless collision domain as the area in which at any instant at most one user can successfully transmit data traffic at a particular frequency. Referring to Fig. 3, the wireless collision domain in ring is also approximated as an annulus sector with a central angle of , and its area
is . The phenomenon of is
due to the fact that the four-way handshaking request-to-send/ clear-to-send (RTS/CTS) mechanism is employed to avoid the hidden node problem. As the example in Fig. 3, user in ring is sending data to user in ring . After the RTS/CTS exchange, node in ring determines that the channel is busy. In the meantime, since users and belong to different mutually interfered regions, user in ring can send an RTS frame to users . Nevertheless, user will not reply the CTS frame to because it has overheard the CTS of . As a result, nodes and are in the same wireless collision domain even though they are not in the same mutually interfered region. This fact means that the central angle of wireless collision do-main in ring is determined by the angle of mutually interfered region in the inner ring . That is, . The example in Fig. 3 also shows that the existence of trans-mitters in region invalidates the RTS request of . Hence, we define the region with a central angle of as the
working-in-vain region of . Such an impact of the ring struc-ture on frame contention will be incorporated into the cross-layer throughput model later.
In addition, note that the innermost ring is in the same wireless collision domain and , since all users in ring can overhead the CTS frame from the central AP. After sec-torizing ring as shown in Fig. 2, the number of contending
Fig. 4. Examples of the lowest rate links for a mesh cell withn = 4.
users is decreased by a factor of three since . Sim-ilarly, we can further sectorize ring , which will help resolve the bottleneck issue in this multihop network.
III. CAPACITY ANDCOVERAGEMAXIMIZATION
A. Problem Formulation
All the performance issues of throughput, coverage, and QoS will impact the design of WMNs. From the viewpoint of de-ployment cost, a larger coverage per cell is better because of fewer access points. From the standpoint of throughput, how-ever, a smaller cell is preferred since fewer users contend for the same radio channel. This paper mainly focuses on frame delay consisting of contention delay and queueing delay in each relay node. From the queueing delay perspective, a longer hop distance may be better due to fewer hops. From the contention delay viewpoint, however, a shorter hop distance is preferred due to fewer contending users. In the following, we formulate an optimization problem to determine the best number of rings in a cell and the optimal ring widths subject to the constraints on delay, throughput, and coverage.
To begin with, we discuss the constraints in the considered optimization problem.
• The capacity of the lowest-rate link in ring should be greater than the carried traffic load of each node, i.e.,
(2)
where is the width of ring and
rep-resents the link capacity between two nodes at a separa-tion distance . This constraint guarantees the minimum throughput for each user. As shown in Fig. 4, the lowest-rate link in ring is the link between nodes and
at a separation distance .
• The overall frame delay should meet the delay require-ment , i.e.,
• The ring width should be less than the max-imum reception range
(4) • The ring width should be greater than the average distance
between two neighboring nodes, i.e.,
(5)
where (m) is dependent on the user node
density . This constraint also represents the limit on the hop distance due to node density.
B. MINLP Optimization Approach
From the above considerations, the optimal capacity and cov-erage issues in a WMN can be formulated as a MINLP problem with the following decision variables: (the number of rings in a mesh cell) and . The objective function is to maximize the capacity of a mesh cell. In this scalable ring-based WMN, the ring-based frequency planning resolves the colli-sion issue as cell coverage increases. Accordingly, the optimal coverage and capacity will be achieved simultaneously, since more users in a mesh cell can also lead to higher cell capacity. The optimal system parameters for the ring-based WMN can be analytically determined by solving the following optimization problem:
subject to
(6) (7) (8) where is the user density, and is the traffic load generated by each user.
IV. CHANNELACTIVITY IN THERING-BASEDWMN From the viewpoint of a particular user, there are five types of channel activities in the considered ring-based WMN.
1) Successful frame transmission. 2) Unsuccessful frame transmission.
3) Empty slot, where all users are in backoff or idle. 4) Successful frame transmission from other users. 5) Unsuccessful frame transmission from other users. For clarity, the activity of a radio channel is described by a se-quence of effective time slots [13]–[15]. Subject to the backoff procedures, their durations are defined as
(9)
Fig. 5. The considered userP and two adjacent wireless collision domains, where userP is contending for the radio channel.
where is the duration of an empty slot, and are the suc-cessful transmission time and collision duration, respectively. Therefore, the average duration of an effective time slot can be written as
(10)
Here, is the corresponding probability for the channel activity type as calculated in the following, and .
A. Successful/Unsuccessful Transmission
In Fig. 5, user can successfully send data as long as no other user is transmitting in the adjacent wireless collision domains of . Consider user and its two wireless collision domains in-fluenced by two closest neighboring transmitters and , which are out of the mutually interfered regions of , as shown in Fig. 5.1Let and be the positions of and ,
re-spectively. If one of the transmitters and is within the working-in-vain regions of , i.e., , user can still send the RTS request to user , but user cannot reply the CTS acknowledgment (ACK), as discussed in Section II-C. Suppose that is the average probability (average fraction of time) of a wireless collision domain in which a user is delivering data, as defined in (33). Then, the working-in-vain probability
of user can be expressed as
(11) where note that accounts for the existence probability of transmitter which is affecting the considered area.
1In this ring-based WMN, the considered area of angle2 will be
influ-enced by at most two neighboring transmitters (e.g., nodesP and P in Fig. 5). Other transmitters (e.g., nodesP and P ) are too far away, and will not affect the considered area.
Now, we consider the case that both transmitters and are not in the working-in-vain regions of user , i.e.,
. In the considered area of angle , only the users in
the area can send RTS frames, as shown
in Fig. 5. Those users in regions and will not send their requests since they can sense the transmissions of and . Let be the average central angle for region , and be the area of a wireless collision domain of user .
Therefore, the average number of contending users in the con-sidered area of angle is equal to the average number of
users in the area of , i.e.,
(12)
where is the user density; is the area of
ring ; is the central angle of the mutually interfered
re-gion, as defined in (1); is
the central angle of region and is uniformly distributed in , as shown in Fig. 5. Subject to the RTS/CTS proce-dures, the frame collisions may only occur when the contending users concurrently deliver their RTS requests. Let be the av-erage probability of an active user sending the RTS request at the beginning of an effective slot. Suppose that is the av-erage probability of a user being idle due to empty queue. In-corporating the impacts of ring structure on frame contention, the unsuccessful transmission probability can be computed by
(13) In (13), the first term is the probability that at least one trans-mitter is inside the working-in-vain regions of . That is, user will not receive the CTS response. The second term repre-sents the probability that the RTS request from is collided with other RTS frames.
Thus, given that the considered user has a nonempty queue, the probability that this user successfully/unsuccessfully sends data frame in an effective slot can be expressed as
(14) (15)
B. Empty Slot
In Fig. 6, user observes an empty slot if all the users in the adjacent mutually interfered regions of user are silent. As shown in the figure, the users in regions and will not send RTS due to the transmissions of and . Let be the average central angle of region , and be the area of a mutually interfered region of user . The average number of contending users in the considered area of angel is equal to
Fig. 6. The considered userP and its two mutually interfered regions, where userP is in backoff at the current slot.
the average number of users in the area of , i.e.,
(16)
where is the central angle of
region , as shown in Fig. 6. Accordingly, from the viewpoint of the considered user, the empty-slot probability is
(17) where the first term is the probability of the considered user being in backoff, and the second term represents the probability that all the other users are in backoff or idle.
C. Successful/Unsuccessful Transmission From Other Users
To calculate the successful transmission probability from other users, we consider user and its two mutually inter-fered regions, as shown in Fig. 6. In the considered area of angle , the average number of contending users is as derived in (16). Given that user is in backoff at the current slot, the probability that at least one user sends RTS is equal
to . Suppose that is
the probability of the considered area being influenced by neighboring transmitters. Consequently, in the considered area of angle , the conditional probability that there is at least one successful transmission from other users is expressed as
where is the probability that the left-side mutually interfered region of user contains a suc-cessful transmission, and is the probability that each mutu-ally interfered region of contains a successful transmission. Then, from the viewpoint of the considered user, the probability of an effective slot containing successful/unsuccessful transmis-sion(s) from other users can be expressed as
(19) (20) The successful probabilities and will be derived in the appendix.
V. CROSS-LAYERTHROUGHPUTANALYSIS
This section suggests an analytical throughput model for the ring-based mesh network using the CSMA MAC protocol with RTS/CTS. Although the 802.11a wireless local area network (WLAN) is used as an example here, the developed analytical framework can be applied to various wireless systems, e.g., the IEEE 802.11/15/16 networks, as well as the free-space optics (FSO) systems [16].
A. Background
Now, we calculate the duration of a successful frame trans-mission and a collision in the IEEE 802.11a network. Let be the payload size of data frame, and be the transmission PHY mode for data frames and that for control frames, respec-tively. Subject to the IEEE 802.11 CSMA MAC protocol with RTS/CTS, the successful frame transmission time and colli-sion time are expressed as
(21) (22) where is the propagation delay; the durations of short inter-frame space (SIFS), distributed interinter-frame space (DIFS), and extended interframe space
are specified in [17]. [18].
In the IEEE 802.11a WLAN [18], a data frame includes the physical-layer convergence procedure (PLCP) sublayer
preamble , PLCP SIGNAL field ,
16-bit SERVICE field in the PLCP header and six tail bits, MAC header , as well as frame check sequence field
. The transmission time for a data
frame with payload size using PHY mode is given as
(23)
where is the number of data bytes in an OFDM symbol, and is an OFDM symbol duration. For RTS, CTS, and ACK control frames using PHY mode , their transmission durations can be written as
(24)
(25) where RTS and ACK are the lengths of RTS and ACK frames, respectively.
B. Carried Traffic Load of a User Node
The carried traffic load in each mesh node includes its own traffic and the forwarded traffic from other users. Assume that all the nodes in the inner ring share the relayed traffic from the outer ring . Suppose that the user density is . The average number of nodes in ring can be expressed as
(26) where and are the area and the width of ring , respectively. Let and represent traffic load generated by each node and the total carried traffic load per node in ring , respectively. Then, it is followed that
(27)
For the outermost ring .
C. MAC Throughput
To evaluate the MAC throughput in the ring-based WMN, we should consider the impacts of the physical-layer ring structure on frame contention. Consider a binary exponential backoff pro-cedure with the initial backoff window size of . Let be the maximum backoff stage. The average backoff time can be calculated by
(28) where is the unsuccessful transmission probability with con-sidering the impacts of ring structure in the physical layer, as defined in (13). Since a user sends RTS requests every
Fig. 7. State transition diagram for the considered user, where the state variable k is the number of frames queued at the considered user.
slots on average [19], the transmission probability for an ac-tive user can be written as
(29) From (13) and (29), we can obtain the unique solution of and for a given idle probability of a user. The idle probability
will be derived by the following queueing model.
Fig. 7 illustrates the proposed discrete-time queueing model for a user in ring , where the state variable represents the number of frames queued in the user. In each effective time slot, the probability for one user to successfully transmit a data frame is , as defined in (14). Consequently, the total con-tention delay spent for a frame (i.e., the frame service time) is a geometric random variable with a mean of effective slots. In a multihop network, this phenomenon means that the arrival process of relayed traffic is also Markovian since the interarrival time of relayed traffic is geometrically distributed. Let be the payload size of data frame. It is reasonable to assume that the frame arrivals at one user follow a Poisson process with a rate of frames/s. Here, is the total carried traffic load of a user in ring , including the local traffic of user and the forwarded traffic from others. From above considerations, the state-transition probabilities for the queueing model can be de-fined as
(30)
Therefore, the state probability can be obtained as
(31) where and the idle probability of a user can be given
as .
Now, we evaluate the MAC throughput of one user. With the effective slot concept, the average busy probability (average fraction of time) of one user being sending data and the channel utilization of a wireless collision domain can be expressed as
(32) (33) where is the probability that one user successfully sends a frame in an effective slot, is the time duration for successful frame transmission, is the average duration of an effective slot, and is the number of users in a wireless
Fig. 8. State transition diagram for the considered frame in a user, where the state variableh means the considered frame being placed at the (h+1) position of the queue.
collision domain. From (10), (14), and (31)–(33), and can be calculated by an iterative method. Then, the capacity of a mesh link between two nodes at a separation distance can be calculated by
(34) where is the payload size of data frame. It is noteworthy that the payload size of data frame is affected by the separation distance and the PHY mode , which will be discussed in the next section.
D. Impact of Hop Distance on Transmission Rate
In a multihop network, the hop distance will also impact the throughput of relay link. Generally, the radio signal is affected by path loss, shadowing, as well as multipath fading. With all these radio channel effects, we assume that the average recep-tion ranges for eight PHY modes are , where . In principle, two users with a shorter sep-aration distance can transmit at a higher data rate. Therefore, the transmission PHY mode is determined according to the separation distance between two users, i.e.,
(35) Furthermore, we suggest that all data frames have the same transmission time . That is, the payload size of data frame is determined by the adopted PHY mode . As in [20] and [21], the same transmission time for each data frame can achieve fairness and avoid throughput degradation due to low-rate transmissions.
VI. DELAYANALYSIS
This section presents an analytical method to evaluate the delay and jitter (delay variance) of a Markov process, without the need to derive the probability distribution of delay as in [22]. Consider a frame being placed at the th position of the first-come, first-serve (FCFS) queue of a user. The state-tran-sition diagram for the considered frame is illustrated in Fig. 8, which is obtained from the model in Fig. 7 by withdrawing the state transitions due to frame arrivals. In the figure, state represents the one that the considered frame is contending for the radio channel in the current effective slot. Moreover, state is defined as the one that the considered frame is suc-cessfully delivered. Let be the state transition from state to state in an effective slot. Then, the state-transition probability can be expressed as
Now, we deal with the time spent for a frame to enter state (i.e., be successfully transmitted) given that this frame is now at state . Clearly,
(37) where is expressed in effective slots. Therefore, the mean of
is equal to
(38)
Since , from (38), we can obtain
(39) By the conditional variance formula, the variance of can be expressed as
(40) From (37), it is followed that
(41) In addition, it is obvious that
(42) From (40) to (42) with some manipulations, we can obtain
(43)
where the initial condition is .
Hence, the mean and variance of the sojourn time for a frame spent in a relay node can be calculated by
(44)
(45)
TABLE I
SYSTEMPARAMETERS FORNUMERICALEXAMPLES
where and represents
the probability of having frames queued in the relay node at the instant a data frame arrives.
In a multihop network, the overall frame delay is defined as the elapsed time from the frame generated at the source node to the successful reception by the central AP. Consider a frame generated at a node in the outermost ring . Then, the mean and variance of overall delay for the considered frame can be calculated from
(46)
(47) where is the number of rings in a mesh cell.
VII. NUMERICALRESULTS
In this section, we investigate the interactions among delay, capacity and coverage in a ring-based WMN. The numerical results are analytically derived by means of the proposed cross-layer analytical model and the MINLP opti-mization approach. The system parameters are summarized in Table I. The RTS/CTS/ACK control frames are transmitted with PHY mode for reliability. We assume the
in-terference distance , where is 1.5. As in
[20], the chosen frame payload sizes for eight PHY modes are bytes. Referring to the measured results [23], the corresponding average recep-tion ranges are
meters. These reception ranges may vary for different environ-ments. However, the proposed optimization approach is general enough for different WMNs with various reception ranges.
A. Interactions Among Delay, Capacity, and Coverage
Figs. 9–11 investigate the interactions among the delay, ca-pacity, and coverage, where both rings and are sectorized. Fig. 9 illustrates the coverage performance against the number of rings in a mesh cell under different delay requirements. In the figure, it is obvious that the optimal cell coverage slightly decreases from 610 to 603 (m) at to meet the delay re-quirement (s). However, for a more stringent delay requirement (s), the optimal cell coverage will di-minish to 488 (m) at .
Fig. 9 also shows that the number of rings in a cell has a maximum value. In general, when increases, cell coverage
Fig. 9. Cell coverage versus the number of ringsn in a cell under different delay requirements, where the demanded traffic per user isR = 0:5 (Mb/s).
Fig. 10. Overall frame delayD versus cell capacity under different delay re-quirements.
also increases. For handling the increasing relay traffic as in-creases, the ring width will be reduced to shorten the hop dis-tance, thereby improving the link capacity. However, because the minimum allowable ring width is determined by the node density according to (8), there will exist a maximum value of . In this example, the maximum allowable number of rings in a cell is for the case with delay requirement , and for the other cases.
In Fig. 10, the overall frame delay versus cell capacity under different delay requirements is shown. The frame delay can be dramatically improved from to 0.1 (s) at , while the optimal cell throughput merely decreases from 58.6 to 57.2 Mb/s. The phenomenon of extreme delay is due to the fact that the link is fully utilized if without any delay constraint. From (44), for , the sojourn time of data frame will grow toward a very large value [22]. However, by shortening the hop distance, we can raise the link capacity to improve delay per-formance at the expense of a smaller cell coverage, as shown in
Fig. 11. Overall delay variance (jitter) versus the number of ringsn in a cell under different delay requirements.
Fig. 9. From Fig. 10, one can also see that the delay requirement (s) is fulfilled at the expense that the optimal cell capacity decreases to 37.4 Mb/s at .
Fig. 11 shows the variance of overall delay (jitter) against the number of rings subject to various delay requirements. As shown in the figure, the case without delay requirement has an extreme delay variance. However, if setting the delay require-ment (s), the delay variance can be also improved to about . For (s), the delay variance can be controlled to about .
In the above figures, we investigate the interactions among the delay, capacity, and coverage. It is shown that optimal cell capacity and coverage can be achieved simultaneously, and QoS (delay and jitter) can be provided at the expense of lower cell capacity and coverage.
B. Effect of Ring Sectorization
Fig. 12 compares the effect of ring sectorization on the cell capacity. As shown in the figure, when both rings and are sectorized, the optimal number of rings increases to
. Moreover, one can observe that if sectorizing ring , the optimal cell throughput can be improved by 35% over the case without sectorization. If both rings and are sectorized, the optimal cell throughput can be further improved by 37% over the case with only secterizing .
Obviously, the more the rings are divided into sectors, the better the cell capacity. For sectorizing more rings, however, a more sophistical frequency planning is needed to allocate more available channels to each mesh cell.
VIII. CONCLUSION ANDFUTUREWORKS
In this paper, we have investigated a scalable multichannel ring-based WMN with QoS support. Subject to the QoS require-ment, an optimization approach is proposed to maximize the cell capacity and coverage for the considered WMN.
From the system architecture perspective, the proposed WMN has two key elements. First, a simple ring-based fre-quency planning has been employed to improve the capacity
Fig. 12. Effect of ring sectorization on the cell throughput, for the delay re-quirementD = 0:01 (s).
with QoS support, and to make the system more scalable in terms of coverage. Second, sectoring the congested inner rings has been suggested to resolve the bottleneck issue of the WMNs.
From the system design perspective, this paper has other three important components. First, we have proposed a PHY/MAC cross-layer analytical model to evaluate the throughput of the proposed WMN. Second, we have developed a queueing model to analyze the delay and jitter. Third, we have applied the MINLP optimization approach to determine the optimal number of rings in a mesh cell and the associated ring widths in the proposed ring-based WMN. Numerical results have shown that the optimal system parameters (i.e., the number of rings and ring widths) can be determined analytically, and the goals of capacity enhancement and QoS support can be fulfilled at a slight cost of coverage performance.
Many interesting issues are worthwhile for further investiga-tion from this work. First, besides the bottleneck issue near the central gateway, the WMNs also need to resolve the energy fair-ness issue. In WMNs, most traffic is delivered either to or from the central gateway [2]. The users near the central gateway have to spend more energy to relay traffic than the other users, which leads to energy unfairness. Even worse, if the users near the cen-tral gateway rapidly exhaust their batteries, the mesh network will not function normally. Therefore, how to achieve energy fairness for WMNs is an important issue in the future.
Second, the impact of power control needs to be further inves-tigated. Although higher transmit power can increase the max-imum allowable hop distance and the data rate in relay link, it also increases contention collisions and lowers the efficiency of spatial frequency reuse. Hence, how to determine the proper transmit power to achieve the best tradeoff among energy ef-ficiency, QoS, capacity, and coverage in a ring-based WMN is an essential task. In addition, there are some other interesting topics, including how to support differentiated services with dif-ferent priorities, how to design the enhanced multichannel MAC protocol for WMN, and to evaluate the impacts of cooperative communications on the ring-based WMN.
APPENDIX
SUCCESSFULPROBABILITIES, AND
Now, we derive the probabilities and mentioned in Section IV-C. In Fig. 6, suppose that the considered area of angle is influenced by two neighboring transmitters. Let
represent the position of the contending user and be the positions of the neighboring transmitters and . Accordingly, the central angles for regions and
can be written as
and , respectively.
Suppose that is the effective transmission prob-ability for one user. Then, given the positions , and , the conditional probability that the left-side mutually interfered region of user contains a successful transmission can be ex-pressed as
(48) In (48), the term represents the probability that only user sends an RTS request in the left-side mutually interfered region of user . The term
accounts for the probability that all the users except for and in the adjacent wireless collision domains of are in backoff or idle, where
and in the same way . In addition, the condition for means that both the neighboring transmitters and are not inside the working-in-vain regions of .
By the same method, the conditional probability that each mutually interfered region of user contains a successful trans-mission can be obtained from
(49) Here, the term within brackets represents the probability that the right-side mutually interfered region of user also contains a successful transmission, where
and
.
By averaging over the positions and , the
probabil-ities and for can be computed by
(50) In this section, we take the case of as an example to evaluate the successful probability . By the same reasoning, one can also calculate the probabilities for . Thus, the detailed derivations are omitted here.
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Jane-Hwa Huang received the B.S., M.S., and Ph.D. degrees in electrical engineering from the National Cheng-Kung University, Tainan, Taiwan, R.O.C., in 1994, 1996, and 2003, respectively.
He joined the Department of Communication En-gineering, National Chiao-Tung University (NCTU), Hsinchu, Taiwan, as a Postdoctoral Researcher from 2004 to January 2006, and a Research Assistant Professor since January 2006. His current research interests are in the areas of wireless networks, wire-less multihop communications, and radio resource management.
Li-Chun Wang (S’92–M’96–SM’06) received the B.S. degree from the National Chiao-Tung Univer-sity (NCTU), Hsinchu, Taiwan, R.O.C., the M.S. degree from the National Taiwan University, Taipei, Taiwan, and the M.Sci. and Ph.D. degrees from the Georgia Institute of Technology, Atlanta, in 1986, 1988, 1995, and 1996, respectively, all in electrical engineering.
From 1990 to 1992, he was with the Telecom-munications Laboratories of the Ministry of Trans-portations and Communications, Taiwan (currently, the Telecom Laboratories of Chunghwa Telecom Company). In 1995, he was affiliated with Bell Northern Research, Northern Telecom, Inc., Richardson, TX. From 1996 to 2000, he was with AT&T Laboratories, where he was a Senior Technical Staff Member in the Wireless Communications Research Department. Since August 2000, he has been an Associate Professor with the Department of Communication Engineering, National Chiao-Tung University. He is the holder of a U.S. patent with three more pending. His current research interests are in the areas of cellular architectures, radio network resource man-agement, cross-layer optimization, and cooperation wireless communications networks.
Dr. Wang was a corecipient (with G. L. Stuer and C.-T. Lea) of the 1997 IEEE Jack Neubauer Best Paper Award for his paper “Architecture Design, Frequency Planning, and Performance Analysis for a Microcell/Macro-cell Overlaying System,” which appeared in the IEEE TRANSACTIONS ON VEHICULARTECHNOLOGY(best systems paper published in 1997 by the IEEE Vehicular Technology Society). He is currently an Associate Editor for the IEEE TRANSACTIONS ONWIRELESSCOMMUNICATIONS.
Chung-Ju Chang (S’81–M’85–SM’94–F’05) was born in Taiwan, R.O.C., in August 1950. He received the B.E. and M.E. degrees in electronics engineering from National Chiao-Tung University (NCTU), Hsinchu, Taiwan, in 1972 and 1976, respectively, and the Ph.D. degree in electrical engineering from National Taiwan University (NTU), Taipei, Taiwan, in 1985.
From 1976 to 1988, he was with Telecommunica-tion Laboratories, Directorate General of Telecom-munications, Ministry of ComTelecom-munications, Taiwan, as a Design Engineer, Supervisor, Project Manager, and then Division Director. There, he was involved in designing digital switching system, RAX trunk tester, ISDN user-network interface, and ISDN service and technology trials in Sci-ence-Based Industrial Park. In the meantime, he also acted as a Science and Technical Advisor for the Minister of the Ministry of Communications from 1987 to 1989. In 1988, he joined the Faculty of the Department of Communi-cation Engineering and the Center for TelecommuniCommuni-cations Research, College of Electrical Engineering and Computer Science, NCTU, as an Associate Pro-fessor. He has been a Professor since 1993. He was Director of the Institute of Communication Engineering from August 1993 to July 1995, Chairman of Department of Communication Engineering from August 1999 to July 2001, and the Dean of the Research and Development Office from August 2002 to July 2004. Also, he was an Advisor for the Ministry of Education to promote the education of communication science and technologies for colleges and uni-versities in Taiwan during 1995–1999; he is acting as a Committee Member of the Telecommunication Deliberate Body, Taiwan. His research interests in-clude performance evaluation, wireless communication networks, and broad-band networks.
Dr. Chang is a member of the Chinese Institute of Engineers (CIE). He serves as Editor for the IEEE Communications Magazine and Associate Editor for IEEE TRANSACTIONS ONVEHICULARTECHNOLOGY.
