MAC protocols over wireless mesh networks: problems and perspective

J. Parallel Distrib. Comput. 68 (2008) 387 – 397 www.elsevier.com/locate/jpdc MAC protocols over wireless mesh networks: problems and perspective V. Loscrì D.E.I.S. Department, University of Calabria, 87036 Rende, CS, Italy Received 31 October 2006; accepted 7 May 2007 Available online 16 May 2007 Abstract The wireless mesh network (WMN) has been an emerging technology in recent years. Because the transmission medium used in networking backhaul access points (APs) is radio, the wireless mesh network is not only easy and cost effective in deployment, but also has good scalability in coverage area and capacity. This paper provides an overview of distributed medium access control (MAC) protocols, discusses their features and suitability for WMNs and identifies potential challenges and open research issues. Specifically, we overview the technical medium access control of the new standard for WMNs, the mesh deployments of the IEEE 802.16 MAC and we focus on the coordinated distributed scheduling (CDS) scheme of this. Moreover, we assess the fitness of the IEEE 802.11 over wireless mesh networks. Through the study of existing solutions, we analyze the previous work and sketch the contours of the directions to achieve the throughput and the latency that must be guaranteed in WMNs. In this context we suggest future enhancements to the standard that could increase throughput, while also increase the robustness, without complexity increases and propose and evaluate a new distributed scheduling scheme (DSS). We compared the CDS and the DSS and simulations studies document and confirm the positive characteristics of the proposed scheme. Furthermore, we proposed an analytical model to assess a lower bound in terms of delay. © 2007 Elsevier Inc. All rights reserved. Keywords: Wireless mesh networks (WMNs); MAC; IEEE 802.11; IEEE 802.16; Coordinated distributed scheduling; TDMA 1. Introduction The wireless mesh networking has emerged as a promising technology for future broadband wireless access [1,4]. Although the notion of mesh networking has been discussed extensively in wireline and optical networks [7,9], the research mainly focuses on restoration of link failure and/or design of survivable and healing networks. When applying mesh networking techniques over shared wireless medium with limited radio spectrum, many new challenges are raised such as fading mitigation, effective and efficient medium access control (MAC), quality of service (QoS) routing, call admission control, etc. Wireless mesh networks (WMNs) consist of wireline gateways, mesh routers and mesh clients, organized in a three-tier architecture [1,16] as shown in Fig. 1. A mesh client network can be formed in an ad hoc manner and connected to one or more mesh routers. The mesh routers in fixed sites comprise a wireless mesh backbone to provide relay service to the mesh client networks and other access networks such as cellular networks, wireless E-mail address: [email protected]. 0743-7315/$ - see front matter © 2007 Elsevier Inc. All rights reserved. doi:10.1016/j.jpdc.2007.05.002 local area networks (LANs), etc. The wireless mesh backbone provides a platform to integrate the wireless LANs, so that a multi-mode mobile station with multiple air interfaces can roam freely among the access networks and select desired services. For WMNs, due to the limited radio bandwidth, MAC is essential to coordinate the transmissions from/to the mesh routers and clients in an effective and efficient manner. MAC for wireless networks can be categorized into two groups: centralized and distributed MAC, according whether the access to the medium is coordinated in a centralized or distributed fashion. Centralized MAC is usually designed for infrastructure-based networks such as cellular networks. On the other hand, distributed MAC is suitable for infrastructure-less networks such as mobile ad hoc networks without a pre-existing central controller, where each node determines its own access to the medium according to its local observation of the channel [5]. Due to the self-organization nature of WMNs, it is desired to apply distributed MAC to achieve efficient resource utilization. Without central coordination, distributed MAC is more challenging than centralized MAC as contention and hence transmission collision are generally inevitable. There are extensive research results on 388 V. Loscrì / J. Parallel Distrib. Comput. 68 (2008) 387 – 397 Fig. 1. An illustration of wireless mesh network. distributed MAC over mobile ad hoc networks in the literature [12,15]. Although organized in an ad hoc manner, the WMNs are quite different from traditional mobile ad hoc networks. In fact, the wireless mesh backbone is with low (or no) mobility and has no power constraint and the wireless clients may form a network attached to fixed mesh routers, thus with only limited mobility. The traffic volume in the wireless mesh backbone in a large-scale WMN can be very large and can vary from one mesh router to another, thus posing significant challenges on the MAC design. Therefore, it may not be effective or efficient to directly apply existing MAC protocols proposed for ad hoc networks (i.e., the Evolutionary-TDMA, E-TDMA [22,23]) to the wireless mesh backbone and the mesh client networks. This paper is to provide a comprehensive overview on distributed MAC protocols, discuss their suitability for WMNs, and present new solutions while discussing further research issues in this area. The rest of the paper is organized as follows. In Section 2 we give an overview of the IEEE Std 802.11. The IEEE Std 802.16 and specifically the coordinated distributed scheduling scheme (CDS) is described in Section 3. In Section 4 we present a new totally distributed scheduling scheme (DSS) for WMNs. In Section 5 we propose an analytical approach to evaluate the delay in a TDMA protocol. This analytical model will be used in Section 6 to compute a delay lower bound. Moreover, in Section 6 we discuss performance comparisons between the differ- ent solutions presented and open research issues are discussed in this section. Finally, the conclusion remarks are given in Section 7. 2. The std IEEE 802.11: problems and challenges in a WMN 2.1. The IEEE 802.11: some details The 802.11 protocol covers the MAC and physical layers. The standard currently defines a single-hop MAC which interacts with three PHYs (all of them running at 1 and 2 Mb/s) as follows: frequency hopping spread spectrum in the 2.4 GHz band, direct sequence spread spectrum in the 2.4 GHz band, and infrared. The MAC layer defines two different access methods, the distributed coordination function (DCF) and point coordination function (PCF). The basic access mechanism, the DCF, is basically a carrier sense multiple access with collision avoidance (CSMA/CA) mechanism. A CSMA protocol works as follows. A station desiring to transmit senses the medium. If the medium is busy (i.e., some other station is transmitting), the station defers its transmission to a later time. If the medium is sensed as free, the station is allowed to transmit. These kinds of protocols are very effective when the medium is not heavily loaded, since it allows stations to transmit with minimum V. Loscrì / J. Parallel Distrib. Comput. 68 (2008) 387 – 397 delay. But there is always a chance of stations simultaneously sensing the medium as free and transmitting at the same time, causing a collision. The latter case will cause significant delay. In order to overcome the collision problem, the 802.11 uses a CA mechanism coupled with a positive acknowledge scheme, as follows: • A station wanting to transmit senses the medium. If the medium is busy, it defers. If the medium is free for a specified time, called the distributed interframe space (DIFS) in the standard, the station is allowed to transmit. • The receiving station checks the cyclic redundancy check (CRC) of the received packet and sends an acknowledgement packet. Receipt of this ACK indicates to the transmitter that no collision occurred. If the sender does not receive the ACK packet, it retransmits the frame until it receives an ACK or throws it away after a given number of retransmissions. According to the standard, a maximum of seven retransmissions are allowed before the frame is dropped. In order to reduce the probability of two stations due not hearing each other, the well-known “hidden node problem”, the standard defines a virtual CS mechanism: a station wanting to transmit a packet first transmits a short control packet called request to send (RTS), which includes the source, destination, and duration of the intended packet and ACK transaction. The destination station responds, if the medium is free, with a response control Packet called clear to send (CTS), which includes the same duration information. All other stations receiving either RTS or the CTS set their virtual CS indicator, called a network allocation vector (NAV), for the given duration and use this information together with the physical CS when sensing the medium. This mechanism reduces the probability of the receiver area collision caused by a station that is “hidden” from the transmitter during RTS transmission, because the station overhears the CTS and “reserves” the medium as busy until the end of the transaction. A hidden node is one that is within the interfering range of the intended destination but out of the sensing range of the sender. Hidden nodes can cause collisions on data transmissions. Wireless packet networks also face the exposed node problem. Exposed nodes are complementary to hidden nodes. An exposed node is one that is within the sensing range of the sender but out of the interfering range of the destination. As consequence, the available bandwidth is underutilized. In the 802.11 MAC layer protocol, there is no scheme to deal with this problem. This might cause a serious problem when it is used in multihop wireless networks. 2.2. The IEEE 802.11: problems and challenges in a WMN A WMN is a dynamic collection of backhaul routers. It is similar to an ad hoc network, but the topology, composed of backhaul routers, is static. The backhaul router has more functionality than an AP. However the IEEE 802.11 MAC protocol, CSMA/CA, is originally designed for single-hop WLAN environment, not for multihop wireless networks. The backhaul networking of a WMN must have the following concerns: capacity, throughput, latency, and reach. Based on the analysis on 389 previous works [21,11], CSMA/CA cannot meet the requirements of backhaul networking. In [21], the authors discovered that CSMA/CA did not function well in a wireless multi-hop environment. The results revealed that not only the instability problem of throughput occurred in the TCP connections, but also a serious unfairness existed among TCP connections. This is caused by the hidden terminal problem, the exposed terminal problem, and the binary exponential backoff scheme of the IEEE 802.11. In Section 6 we will show results that confirm results obtained in [21,11]. 3. IEEE 802.16 mesh mode 3.1. General description of IEEE 802.16 Almost all the existing works about the IEEE 802.16 are on the PMP mode [10,6,20]. The main difference between PMP and Mesh mode is that in the PMP mode, traffic only occurs between the base station (BS) and subscriber stations (SSs), while in the Mesh mode, traffic can be relayed via other SSs, and also can occur directly between SSs. Comparing with the tree-based multi-hop network topology of 802.16 tree-based mobile multihop relay (MMR) [17,3], 802.16 mesh mode places more challenges on the link scheduling algorithms. In order to achieve efficient collision-free multi-hop data transmission, the Mesh mode defines three scheduling schemes, i.e., centralized, coordinated distributed, and uncoordinated distributed scheduling, to resolve wireless interference occurred in the 2-hop neighborhood of a node. Each frame in the IEEE 802.16 standard is divided into two parts: (i) a control sub-frame consisting of MSH_CTRL_LEN (0–15) transmission opportunities (XmtOps in the standard) and (ii) a TDM data sub-frame consisting of up to 256 minislots. All the XmtOps are in fixed length of 7 OFDM symbols (Ts). There are two types of control sub-frame, i.e., schedule control sub-frame and network control sub-frame. In the following we will describe details of the CDS. 3.2. Coordinated distributed scheduling (CDS) CDS scheme [13,14] is designed to achieve collision-free periodical transmissions for two types of control messages, i.e., MSH-NCFG and MSH-DSCH, respectively. Since the exact same algorithm is used independently for these two types of messages in separate XmtOps (transmission opportunities), we can simply analyze the behavior of one, and the result is applicable to the other. In this part, a general introduction of the IEEE 802.16 distributed scheduling behavior is given. In the 802.16 scheduling algorithm, the control messages and data packets are allocated in different time slots in a frame. The allocation of the data time slots is performed through the control message exchange so that there is no contention in the data time slots. In the distributed scheduling, a node selects its next transmission time in the current one. Because other nodes may also transmit in the selected time slot so that the node uses an election algorithm to compute whether it can win or not. The general concept of CDS is to let nodes running the scheduling algorithm independently derive pseudo-random but predictable 390 V. Loscrì / J. Parallel Distrib. Comput. 68 (2008) 387 – 397 behaviors by exchanging two-hop (or three-hop) neighborhood schedule information with each other. Both randomness and predictability are achieved by dynamically constructing random generator seeds for each node according to a common rule. The seed for a node is based on its unique node ID and the index (or timestamp) of a candidate XmtOp.Given the neighborhood information, the random number generated locally will be the same with the corresponding one generated at a neighboring node. In distributed scheduling, the scheduling information for each station is described by two parameters:  NextXmtXm :: 5 bits, XmtHoldoff Exponent :: 3 bits. Given these two parameters of a specific neighbor, a node can determine a bounded interval for NextXmtTime (the next slot in which a node will transmit) as well as the following: NextXmtXm ∗ 2XmtHoldoffExponent ≺ NextXmtTime (NextXmtXm + 1) ∗ 2XmtHoldoffExponent , (1) EarliestSubsequentXmtTime = NextXmtTime +2XmtHoldoffExponent+4 . (2) Since the exact scheduled XmtOp of the neighborhood is unknown, as implementation issue, one may define NextXmtTime to be the last XmtOp within the interval when calculating EarliestSubsequentXmtTime. The holdoff exponent value decides the channel contention time of node so it is an important parameter that can affect the system performance. In the mesh mode, every station calculates its NextXmtTime using the distributed election algorithm defined in the standard [14]. In this algorithm, one station sets the first transmission slot after the holdoff time as the temporary next transmission opportunity and then competes this slot with all the competing nodes in the two-hop neighborhood. At the previously scheduled XmtOp, a node (the local node, LN) will run an election algorithm to find its next collision-free XmtOp. Based on the calculated NextXmtTime time interval and EarliestSubsequentXmtTime, a node can exclude a subset of neighboring nodes. In this way the utilization of XmtOps is improved. The local node will increment the candidate XmtOp and running the same election algorithm until it wins the election. Based on the above description, we can see that the probability a node winning a contention is determined by the total number of competing nodes, and the total number of competing nodes is related with the number of neighbor nodes and their topologies and exponent value. So, in this algorithm the choice of the exponent value is crucial, but different results can be obtained for different network density and topology. Values of XmtHoldoffExponent and NextXmtXm can be optimal for a type of network with certain topology and density characteristics but they have to be changed when different topologies and densities are considered. In this way the CDS is not robust. 4. A new topology-free scheme: the DSS In this section we describe some potential enhancements to mesh deployment of 802.16 that are well within reach. The proposed advances should increase the average throughput and the robustness of the CDS scheme of 802.16. We do not modify the structure frame of the standard and do not add complexity, so the hardware of the standard must not be changed. 4.1. Details of the DSS The proposed scheme differs from the IEEE 802.16 CDS scheme in the selection of the new XmtOp. In fact, a node transmitting in the current XmtOp uses a random function instead of the hash function (the MeshElection function defined in the IEEE Std 802.16) to compute the next XmtOp. The frame structure is shown in Fig. 2. The DSS scheduling mechanism for LN is described in Fig. 3. In Fig. 3 random function randomly picks-up an available slot. A slot is available if the state in the next frame of the LN is Idle. The access is conflict-free because the LN uses the current XmtOp slot computed in a conflict-free fashion in the previous frame. Whether a node LN did not find an available XmtOp slot in the previous frame or lost this slot for some reasons as shown in Fig. 4 it will apply a redistribution function. This function is an Hash Function in which a node, which needs a XmtOp for the current frame, analyzes a set of available slots (that is, the state of the LN is Idle in this slot). The hash function will be applied to the onehop neighbors of the LN. In this way, all the neighbors that do not have a valid XmtOp slot in the current frame will apply the same function with the same information (slot number, neighbor ID and address of the node applying the function) and only one node will win the competition. The main advantage of the DSS mechanism is that no parameters must be set, and in this way the protocol is robust for different topologies and network scenarios. Each node considers a number of XmtOp (opportunities) that is 16 as well as in the IEEE 802.16 Std and this is the number of opportunities (in the control frame) to transmit updated schedule, send data slots reservation requests and reserve another XmtOp. Specifically, with constraints required by conflict-free TDMA transmissions, the activity of a node ni in a slot s can be classified into the following states: • TX: Transmits to a set of neighbors R: (state(s) = Transmit, target(s) = R). • RX: Receive from a neighbor nj : (state(s) = Recv, target(s) = nj ). If a node is not transmitting or receiving in this slot, it is in one of the following (passive) states: • Blocked from transmitting because at least one of its neighbors receives from another node, and none of its neighbors transmits: (state(s)Block_TX). • Blocked from receiving because at least one neighbor is transmitting to another node, and none of its neighbors receives: (state(s) = Block_RX). 391 V. Loscrì / J. Parallel Distrib. Comput. 68 (2008) 387 – 397 Control Round Data Round Control ReDistribution Round Control Round Re-allocation Phase Allocation Phase Redistribution Function …… … … . Information Frame 1 IS1 Next Ctrl Schedule (Random Function) …… ISL Information Frame M IS1 …… ISL Data Frame Allocation Fig. 2. Frame structure of distributed scheduling scheme (DSS). At the beginning of each control frame, a control re-distribution round is applied, it will be applied to the nodes that do not have a valid XmtOp in the current frame. The redistribution function considered in this work is the same Hash function considered in the IEEE Std. 802.16e. In the control round each node applies a random function to compute the next XmtOp and sends updated information in the current XmtOp. Data slots allocation takes place in the control round. Each node in its current XmtOp can send data slots reservation requests. LN: Is it the current XmtOp my XmtOp? NO YES LN is in a Passive State in the current XmtOp Random Function: LN selects an available next XmtOp for the next frame YSE Did LN find a new next NO YES XmtOp slot? Is LN in Receive State in the current XmtOp? LN receives updated scheduling from neighbours and loses LN uses the current XmtOp to the next XmtOp make data slots reservation YES computed in the current requests and to update frame neighboring nodes Redistribution Function: at the beginning of the next frame LN applies an Hash Function to the set of available slots. A slot is available if the current state in the frame of LN LN receives updated schedule from1-hop neighbor in Transmit State in the current XmtOp slot is Idle. Fig. 3. Flow chart of local node (LN) scheduling mechanism of DSS. 392 V. Loscrì / J. Parallel Distrib. Comput. 68 (2008) 387 – 397 Current Schedule Next Schedule S4 S7 S5 S11 4 23 5 4 S11 23 5 Fig. 4. Current schedule: node 4 is transmitting in the slot S4, node 23 is transmitting in the slot S7 and node 5 is transmitting in the slot S5. Node 4 reserves the slot S11, in the current schedule for the next schedule, as XmtOp. This reservation takes place in the slot S4. Node 4 transmits the updated schedule to its neighborhood. Node 23 is notified with the updated schedule. In the next slot, S5, node 5 reserves the same slot S11 (selected randomly). Node 5 will be notified that this slot is already reserved by another neighbor node (node 4) in the slot S7 by node 23. • Both blocked from transmitting because at least one neighbor is receiving, and blocked from receiving because at least another neighbor is transmitting: (state(s) = Block_TX_RX). • Experiencing a collision when it is supposed to receive from a neighbor (state(s) = Collision). • Idle, when none of its neighbors transmits or receives in this slot: (state(s) = Idle). Of course these states are mutually exclusive. The state of the slots in which a node transmits is called active state, state in which a node does not transmit is a passive state. The channel is partitioned in two sub-portions: a control round where the schedules are updated and data round where user data transmission takes place (Fig. 2). The state of the nodes in each slot is updated during the control round when each node in the current XmtOp computes the next XmtOp and sends the updated information to the neighbors. The data schedule will be updated at the beginning of each new frame; in this way different transmission requirement nodes can be accommodated. Two different informations are considered in the control round: (1) current information (or current schedule) and (2) next information (or next schedule). The current schedule is the actual schedule used by the node to transmit and to compute another NextXmtTime (in accordance with the IEEE 802.16 notation, that is the next XmtOp). The mechanism used to compute a new transmission time (NextXmtTime) will be the random function in DSS. After the random function is called and the NextXmtTime is computed a node updates its schedule and sends this (the updated schedule) to its neighborhood through the message (MSH-DSCH) where the request of a certain bandwidth is contained. In the mechanism described above, it can happen that a node, acquired a conflict-free broadcast slot, loses it because it will receive some other information from some neighbors after it reserved the slot. When this latter situation occurs, a node will contend for an unassigned slot at the beginning of the next frame (the state of the node in the slot must be Idle). A typical situation that may occur is described in Fig. 4 and a node (node 5, in the specific case) will be not able to use the XmtOp computed in the next frame. For this reason at the beginning of each frame, where the partial schedule is ready and all the nodes acquired information from the neighborhood, each node that does not have a XmtOp will run a redistribution function to try to use the control broadcast slots unused. In order to ensure that no two neighbor nodes grab the same slot, an hash function based on the ID of the nodes and a timestamp (slot) is used. Of course, the redistribution function will be applied only for the broadcast slots in which the node state is Idle. This new scheduling mechanism ensures that the schedules are conflict-free and a node has not to wait for any particular order to reserve a new broadcast control slot. 5. Delay bound computation The performance metrics of interest in the MAC layer include the throughput and delay. In the IEEE 802.16 mesh mode, the details of the data sub-frame reservation are left unstandardized and to be implemented by the vendors; and the control subframe is independent of the data sub-frame. In this section we develop an analytical delay model that gives a lower bound. The following analysis aims at providing an approximation of the end-to-end data transmission delay. For the analysis we make the following assumptions: • The wireless backbone network and the wireless access network operate on different channels. Therefore we assume that there is no interference between the data transmissions between the access points (APs) and the transmissions between the mobile nodes and the APs. • The APs are uniformly distributed. • All the APs have similar transmission capabilities. This assumption makes the analysis more tractable (and the same assumption is maintained in the simulation campaigns). • Time is slotted and synchronization is maintained by the APs (i.e., through the periodic transmission of beacon messages). • The medium access is performed in a conflict-free fashion through a TDMA protocol which operates in two different channels: a control channel and a data channel (this assumption is coherent with the CDS of the 802.16 and the DSS introduced in this paper). The control channel is characterized by the same number (16 control slots) of control slots used in the CDS scheme and the DSS introduced in this work. We assume that the TDMA protocol used for our analysis is optimal. To produce the optimal schedule (where optimality is measured in terms of bandwidth efficiency; i.e., we desire schedules with the minimum number of TDMA slots) is NP-complete [2,18,8]. With the term optimal we signify that the distribution of both the control and the data slots is realized in an optimal fashion, that is maximizing the assignment of the slots maintaining the conflict-free property of the schedules. The evaluation of the delay has been computed considering different components of the delay (propagation delay, transmission delay and queuing delay) and considering the delay introduced by the transmission of the packets between two APs (in a multi-hop environment). In order to conduct this analysis we assume that there is a total knowledge of the topology and some centralized coordinator is able to manage the distribution of slots in a TDMA fashion. In this way the distribution of the bandwidth resource is only constrained by the density of the network. V. Loscrì / J. Parallel Distrib. Comput. 68 (2008) 387 – 397 Table 1 Parameters used for the analytical model R r N′ N P PropSpeed Bandwidth Data packet dimension Queuing buffer dimension TTS (slot duration) TPS Tdata−frame Tctrl−frame Range of the network Transmission radius of an AP Number of 1 and 2 hop neighbors Number of nodes in the network Network density 3 × 108 m/s 1 Mb/s 64 bytes 50 pkts (in the simulations) 1.54 × 10−4 (s) 1.2264 × 10−2 (s) 9.8 × 10−3 (s) 2.464 × 10−3 (s) The end-to-end delay is computed considering the 1-hop transmission delay between APs. The parameters introduced in our evaluation are reported in Table 1. In order to consider a more accurate model all kinds of delays have been taken into account, as said: • Propagation delay: It has been computed as the ratio of the distance between two nodes (APs) and the propagation speed PropSpeed. As the distance between two nodes may vary between  (>0) (we assume two nodes are not exactly at the same location) and r (transmission radius of a node), the average inter-nodes distance da can be computed as follows:  √ r r2 − ε da = , that is da ≈ 2 , (1) 2 2 393 of our analysis it is not important the particular passive state associated with a node but it is only important whether a node grab a slot to transmit or not. A packet transmission is complete when two data slots are assigned, because each slot is 32 bytes and a data packet is 64 bytes. In the ideal case we assume do not have any overhead. In the simulation campaigns we take into account an overhead of 20 byte and the real dimension of a data packet is 84 bytes. We are assuming backlogged sources. Let p be the probability that a saturated AP transmits a packet in a frame (control − frame + data − frame). In an ideal TDMA paradigm this probability is related with the total number of neighbors (1 and 2-hop neighbors) and can be written as ⎧ NCS NDS ⎪ p= ′ if NCS < (N ′ − 1) ⎪ ⎪ ′ − 1) ⎪ N − 1 2(N ⎪ ⎪ ⎪ and NDS < 2(N ′ − 1), ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ NDS ⎪ ⎪ if NCS(N ′ − 1) ⎪ ⎨ p = 2(N ′ − 1) (3) and NDS < 2(N ′ − 1), ⎪ ⎪ ⎪ ⎪ ⎪ NCS ⎪ ⎪ p= if NCS < (N ′ − 1) ⎪ ′ − 1) ⎪ (N ⎪ ⎪ ⎪ ⎪ and NDS 2(N ′ − 1), ⎪ ⎪ ⎪ ⎩ p=1 otherwise, where NCS is the number of control slots and NDS is the number of data slots. Let N1 be the number of 1-hop neighbors (it is the number of nodes in the coverage area of an AP). N1 can be expressed as N1 = r 2 where  is the network density and can be expressed as  = NR 2 . N ′ is the number of 2 (2) 1 and 2-hop neighbors and can be computed as N ′ = 4N Rr 2 . By considering the equilibrium state, each transition can be straightforwardly computed as follows: • Transmission delay: It is related with the number of control and data slots used. When the number of control and data slots is higher than the number of nodes in the network the delay is related to the duration of the frame and the duration of the slot, otherwise the transmission delay is related with the density of nodes in the network. • Queuing delay: It is related with the number of packets that have to be sent from an AP. ⎧ ′ P(PS)(PS) =(1−p)N ⎪ ⎪ ⎪ ⎨ P(PS)(TX) =1 if p=1, ⎪ ⎪ (Tdata−frame +Tctrl−frame ) ⎪  ⎩ (TTS ) otherwise, P(PS)(TX) =p (1−p)B(d) (4) delayprop da Distance . = = PropSpeed 3 × 108 (m/s) The computation of the delay between APs follows a similar approach as in [12]. As represented in Table 1 r is the radius of an AP (for simplicity we assumed all the APs have the same radius) and N the number of the APs uniformly distributed over an area of diameter k. The data transmission process involves two different schedules: the control and the data schedules. In the control schedule a node, with a certain probability p, acquires a control slot. This control slot is used to update the schedule, to send the updated schedule to the neighbors and to reserve data slots. Data slots are allocated in the control schedule. Two different states are associated with each node (in a simplified version): Passive (PS) state and a Transmitting (TX) state. In the PS state a node can be blocked to transmit in a certain slot because another neighbor is transmitting in the same slot or can be Idle or can be in a receiving state. To the scope where TTS is the duration of a slot, Tctrl−frame is the duration of the control frame and Tdata−frame is the duration of the data frame. For a given transmission, the area B(d) where nodes may potentially interfere with the transmitting node can be computed as (d is the inter-nodes distance) [6]: ⎞ ⎛  2 d d d ⎠ , (5) B(d) = r 2 − 2r 2 arccos ⎝ − 1− 2r 2r 2r ⎛ ⎜ delayAP−AP = ⎜ ⎝ 1− P(PS)(TX) (Tctrl−frame +Tdata−frame ) ⎞ P(PS)(TX) (Tctrl−frame +Tdata−frame ) +TPS ⎟ ⎟ ⎠ P(PS)(TX) (Tctrl−frame +Tdata−frame ) P(PS)(TX) (Tctrl−frame +Tdata−frame ) +TPS ∗ (Tctrl−frame + Tdata−frame ) , (6) 394 V. Loscrì / J. Parallel Distrib. Comput. 68 (2008) 387 – 397 where d is the same as da computed in (1). The delay can be derived as in (6). TPS is the time a node is in a passive state. Let us remember that a PS is the state in a generic slot in which a node is not transmitting, that is a node can be in receiving state, blocked to transmit, blocked to receive, blocked to transmit and receive, collision or idle. We are evaluating the end-to-end data transmission delay and for this reason the TPS is evaluated considering the average time a node spends in a passive state before to acquire the right to transmit in a data slot time. Let us assume that the distribution of the AP is uniform, the transmissions are scheduled in a round robin fashion and the transmissions are multi-hop transmissions, that means that each intermediate AP would have to transmit its traffic as well as the traffic of its children. With these assumptions, the average number of node ni at each hop level i can be expressed as  ir N ni = 2x dx, (7) R 2 (i−1)r  R Nr 2  2 2 k+1 R 2 k − (k − 1) (8) pk =   , Nr2 k 2 − (k − 1)2 R2 ni =  N 2 2 r 2. i − (i − 1) R2 (9) Let kmax be the maximum number of hops and pk the number of packets that an AP has to forward. Then, if we consider k < kmax , pk can be expressed as  kavg  2 2 k+1 k − (k − 1)   , pk = (10) k 2 − (k − 1)2 qk = pk ∗ delayAP−AP (11) delayTOT = qk + delayAP−AP + delayPROP , (12) kavg in (11) is the average number of hops that a packet has to traverse in order to be delivered to the destination. We evaluated the parameter kavg considering different scenarios generated with ns. It is interesting to observe that increasing the number of nodes in the network (considering the same dimension of the area), the parameter kavg decreases because higher is the number of nodes that link a source to the destination. Of course, when the number of nodes increases the possibility of conflicts in the network increases too and the latency to acquire a slot increases. So, the queuing delay qk can therefore be approximated by (11). The total average delay can be written as (12). 6. Performance results In this section results pertaining to the performance of an 802.16 system in a distributed mesh deployment are presented in comparison with the new totally DSS presented in Section 4 and the IEEE Std 802.11. Results about IEEE 802.11 are shown in order to confirm simulation results obtained in other works [21,11]. Furthermore, the analytical approach developed in Section 5 has been used to compute a delay lower bound. In the current MAC modules for ns-2 no 802.16 MAC module is available yet, so we implement a new MAC module for the IEEE 802.16 mesh mode. The module consists of the scheduling controller that handles the signalling channel contention and in the current transmission slot contends the next transmission time using the election mechanism defined in the standard based on the collected neighbors’ information. Another fundamental component of this module is the data channel that receives and transmits data packets in the allocated time slots. Identical XmtHoldoffExponent and NextXmtXm have been used for all scenarios as far as the IEEE 802.16 is concerned. Specifically, different simulation campaigns have been conducted with the same traffic load and the same topology and different XmtHoldoffExponent and NextXmtXm values and the better values, in terms of delay and throughput, have been selected. The parameters evaluated in this section are: • Throughput: is the percentage of delivered packets over the total packets sent in the networks. • Delay: intuitively, the delay of a packet in a network is the time it takes the packet to reach the destination after it leaves the source. We take into account queuing delay at the source because we consider multihop transmissions and a node can be involved in different simultaneous transmissions. Moreover, the delay has been computed considering the different components of the delays, that is propagation delay, transmission delay and queuing delay. • Unused slot: this parameter has been introduced as a kind of measure of the effectiveness of the scheduling scheme used. In fact, we will show how the CDS manages the bandwidth resources in a fashion the conflict-free property of the schedules created to be guaranteed, but a certain amount of slots in each frame is unassigned. In this way, the efficiency of the network decreases. In this paper, we evaluated performance of WMNs in treebased architectures. The node 1 works as a gateway and the others nodes work as APs. We simulated traffic of terminal users with varying traffic load among the APs. In all the plots 802.16 is the CDS of the IEEE 802.16, DSS developed in this work, 802_11 is the IEEE Std 802.11 and analytical scheme is the ideal, analytical scheme developed in Section 5. Comparisons of the CDS scheme, the DSS and the IEEE 802.11 are done in terms of average throughput and average end-toend data packets delay in different density network conditions, obtained considering a different number of nodes in the network. Specifically, we varied the number of nodes in a grid of 1000 × 1000, between 25 and 70. In order to estimate the system performance of 802.16 CDS, DSS and 802.11, results were obtained using a well-known simulator, the ns-2 [19]. Parameters used in the simulation campaigns are shown in Table 2. In Fig. 5 is shown the average throughput for different network densities (varying the number of nodes among 25, 30, 40, 50, 60 and 70 in the same area network). Concerning the 802.16 CDS we had to set the parameters, the better values of NextXmtTime and XmtHoldoffExponent in order to obtain the better throughput and the minimum delay. This represents a drawback of the CDS scheme, because by changing the network density and the topological characteristics of the network we need to set up the values of these parameters and for this reason we defined 395 V. Loscrì / J. Parallel Distrib. Comput. 68 (2008) 387 – 397 Table 2 Simulation parameters 802.16 DSS 30 40 Analytical Scheme 802_11 1.2 Input parameters Simulation area Traffic sources Number of nodes Sending rate Size of data packets Transmission range Simulation time Delay (sec.) 1 1000 × 1000 CBR 25, 30, 40, 50, 60, 70 4, 40, 400 packets/s 64 bytes 250 m 500 s 0.8 0.6 0.4 0.2 0 20 50 60 70 80 70 80 Nodes Number Mobility model Mobility model Pause time Mobility average speed Random way point 10 s Static network Simulator Simulator Medium access protocol Routing protocol Link bandwidth Confidence interval NS-2 (version 2.1b6a) 802.16 (CDS), DSS AODV 1 Mbps 95% Fig. 7. Average end-to-end data delay. P(PS)(TX) PPS Unused Control Slots (%) 802.16 DSS 30 25 20 15 10 5 0 20 30 40 50 60 Nodes Number TX PS Fig. 8. Percentage of control slots unassigned vs the number of nodes in the network. Fig. 5. Two states are associated with each node for a generic slot S. PS is the passive state and TX is the transmitting state. Throughput (%) 802.16 DSS 802_11 75 70 65 60 55 50 45 40 35 30 25 20 30 40 50 60 70 80 Nodes Number Fig. 6. Percentage of packets delivered over packets sent. our scheme topological-free scheme. In fact, in DSS we do not have to set any parameters to select the next XmtOp. In Fig. 6 we show the delivery ratio of data packets. As we expected [21,11], the performance of IEEE 802.11 MAC protocol is not satisfactory in a wireless multi-hop environment. Concerning the performance comparisons between the CDS of the IEEE Std 802.16 and the DSS, we can see how our scheme permits more data packets to be delivered to the destination. Above all with a higher density of the network (50, 60 and 70 nodes in the same area), our scheme delivers a higher percentage (10%) of data packets than the CDS. In order to understand why we obtain better results in terms of throughput (Fig. 6) and delay (Fig. 7), by using our scheme, we can observe the parameter in Fig. 8, unused control slots. This latter represents the degree of utilization of the control broadcast slots (opportunity to transmit XmtOp) in the network. In practice, with this parameter we tried to measure the capability, in both of the schemes, the XmtOp to be assigned. Of course, we assumed that each node tries to acquire a XmtOp in each frame but there is a higher number of unassigned slots in the CDS scheme. This is due to the mechanism used by the CDS scheme. In fact, it is based on a hash function, the MeshElection, that permits both randomness and predictability to be guaranteed but, on the other hand, this mechanism does not guarantee that each XmtOp in each frame will be assigned, that is, although some node require a XmtOp in a certain frame and there are some XmtOp “free”, available to be assigned, the XmtOp will be unassigned. Concerning scenarios where a smaller number of nodes in the network is considered (25, 30 and 40 nodes) we can see that the degree of under-utilization in both the schemes is higher, but this is due to the fact that not all the XmtOp have to be used. In fact, the number of neighbors (one and two-hop neighbors) in the networks is much smaller than the number of XmtOp(that are 16), in the simulated scenarios and in the analytical model (see Table 3). Considering that we can re-use some XmtOp, in this case the parameter does not reflect exactly the under-utilization in the network. The underutilization of the XmtOp is well reflected when the number of nodes in the network increases. In fact, considering 50, 60 and 70 the number of neighbors in the simulated scenarios is higher than the number of opportunity to transmit considered, so in this case in each frame each node tries, in average, to acquire a different XmtOp. Obviously, in this latter case is very important that for each frame we reduce the number of unassigned slots 396 V. Loscrì / J. Parallel Distrib. Comput. 68 (2008) 387 – 397 Table 3 Number of neighbors (1 and 2-hop) for different number of nodes in the network # Nodes in the network N ′ (Analytical) N ′ (Simulation) 25 30 40 50 60 70 6.25 7.5 10 12.5 15 17.5 8.2 7.6 11.3 17 20 22 and we realized this in our scheme. In fact, in our scheme, the degree of under-utilization is almost close to zero. On the contrary, in the CDS we have an under-utilization degree of 10% and 5% for 50, 60 and 70 nodes, respectively. This behavior is reflected in the throughput and delay plots. In fact, DSS works well also when the density of the network increases. Also in this case, the latency introduced is smaller than those introduced with the CDS scheme. Smaller latency also increases the reactivity of the network and decreases the average end-to-end delay. Remember that we show the under-utilization of the control slots in Fig. 8 and the delay of data packets in Fig. 7, but these two parameters are strictly related. In fact, a node (i.e., LN) that has to reserve data slots needs a XmtOp to make new reservations and to exchange updated schedules. When the latency of the scheme that manages the “distribution” of the XmtOp increases as in the case of the CDS scheme, LN will be able to reserve data slots in more time (with a more amount of delay) and performance of the network degrade. This is due to the fact that the network is much more reactive when we distribute in a more efficient fashion the XmtOp, that is, the under-utilization degree in the network concerning the broadcast control slots is smaller. Concerning the analytical scheme we show the delay of this in Fig. 7 and we based the estimation of the number 2 of neighbors on the formula N ′ = 4N Rr 2 , used in Section 5. Actually, an under-estimation is obtained in this way when the number of nodes in the network increases. In fact, as shown in Table 3, for 50, 60 and 70 nodes the number of neighbors is higher than the number of XmtOp used. We used these values and not the values obtained considering the simulation scenarios because the scope of the evaluation of the analytical delay was to establish a lower bound in terms of delay and how much the schemes that have been analyzed in this work are close to these analytical results. In this way for 50 and 60 nodes our evaluation does not take into account the interference area and the number of neighbors. In fact, the probability p a broadcast control slot to be acquired is 1 and the P(PS)(TX) that is the transition from a passive state (PS) to an active state (TX) is 1. In this way the delay is only related with the duration of the slot and the duration of the frame (control frame and data frame). The better distribution of control slots permits the latency of our scheme to be reduced in comparison of the latency introduced by the CDS. For this reason the average end-to-end data packets delay is smaller in our scheme, because the reactivity of the network is higher when the degree of under-utilization (of control slots in this case) is smaller. Moreover, we introduced more robustness in our scheme because the behavior of our scheme does not depend on the particular network conditions, as the density of the network or the topological characteristics of the network. 7. Conclusions CSMA/CA did not function well in a wireless multi-hop environment. The causes include the hidden terminal problem, exposed terminal problem and binary exponential backoff scheme, which results in transmission problems much worse in wireless multi-hop networks. The backhaul networking needs capacity, throughput, latency and reach guarantee. For this reason other MAC protocols have been proposed for wireless mesh networks (WMNs) and, specifically, we analyzed the coordinated distributed scheduling scheme (CDS) of the mesh deployment of the IEEE Std 802.16 for tree topologies. We tried to sketch some “drawback” of this scheme and we concluded that this scheme does not manage well the opportunities to transmit and introduces an excessive degree of under-utilization concerning the XmtOp (broadcast control slots). Related to these considerations we introduced a new scheme that permits the hardware characteristics of the Std 802.16 to be maintained and introduces a variation as far as the selection of a new XmtOp to be concerned. We show how the new distributed scheduling scheme (DSS) permits a better management of the broadcast control slots to be realized and this is translated in a smaller degree of under-utilization of XmtOp. This smaller under-utilization permits better performance in terms of throughput and end-to-end data packets delay to be realized and we avoid the inconvenience introduced by the CDS to have to set some parameters. 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Valeria Loscrì received his M.S. in computer science and Ph.D. degrees from University of Calabria, Italy in 2003 and 2006, respectively. Since early 2003, she has been with the telecommunications research group of the University of Calabria where she is fully involved in a number of projects concerning the multimedia wireless communications. She is currently research fellow at University of Calabria in the Department of Electrical and Information System (D.E.I.S.). Her research interests include quality of service and medium-access control, performance analysis, Ad hoc Networks, Wireless Sensors Networks and Wireless Mesh Networks.