Acknowledgment. Abstract. 2 System Model Introduction PHY and MAC System Model Our approach to QoS...

Transcription

1 Abstract In this report we address the problem of providing end-to-end quality of service (QoS) to real and data applications passing through a multihop mesh network based on the IEEE WiMax standard. It builds on the scheme proposed in [33]. An important addition is the spatial channel reuse in the mesh. This can substantially improve the system performance. Other new elements are to include multiple channels and radios in the setup and also to support limited mobility. These are the important extra features from practical point of view. Finally we also consider the possibility of supporting the QoS when the last hop is an IEEE based wireless LAN. ii

2 Contents Acknowledgment Abstract i ii 1 Introduction Introduction Problem Definition Literature Survey Our Contribution Organization of report System Model Introduction PHY and MAC System Model Our approach to QoS Routing and Scheduling in Mesh Networks Introduction Optimization problem Transmission Constraints Approximate Solution and Algorithms Algorithms for optimal solutions Example iii

3 CONTENTS iv 3.4 Slot Assignment Problem Algorithm Interference-Aware tree structure routing and scheduling Tree routing structure Interference-aware tree route construction Algorithm Scheduling Simulations MC-MR networks Channel,node and interference constraints Providing QoS Introduction QoS for Real Time Traffic Scheduling of CBR traffic Scheduling of VBR Traffic QoSforTCPTraffic Joint Scheduling of UDP and TCP Flows Simulations Admission Control Mobility Support Introduction Mobility model Providing QoS to mobile nodes Simulations QoS through WLAN-WiMax interconnected network Introduction MAC Fluid model of MAC Simulation QoS through an interconnection of WLAN and WiMax mesh... 66

4 CONTENTS v 6.5 Simulation Example Summary and Future directions Summary Future Directions Bibliography 75

5 List of Figures 3.1 A sample network Multiple TCP flows through multiple queues with fixed rates Overall Scheduling of TCP and UDP flows to provide QoS. UDP flows get priority over TCP flows in each queue. RED applied on TCP flows at entry nodes. (We have separated UDP flows and TCP flows in each queue by a dotted line indicating each queue might be implemented via two queues.) Network used in simulations Number of TCP connections Number of UDP connections Random walk model An LAN downloading data files WLAN scenario Simulation results Internet of WLAN and Wimax mesh Network seen by the flows from the MBS to the AP Interconnected Network of WLAN and Wimax mesh vi

6 List of Tables 3.1 Comparision of routing strategies β Physical Layer Parameters Burst Profiles Performance of UDP Flows Performance of TCP Flows when maximum window size is set to E[w] Performance of TCP Flows when E[w] window is controlled by RED Performance of static UDP Flows Performance of mobile UDP Flows Performance of TCP static flows Performance of TCP mobile flows Performance of UDP Flows Performance of TCP Flows when maximum window size is set to E[w] Performance of TCP Flows when E[w] window is controlled by RED.. 69 vii

7 Chapter 1 Introduction 1.1 Introduction It is difficult to buy a laptop computer today that doesn t come with a Wi-Fi chip: a built-in radio that lets users surf the Web wirelessly from the boardroom, the bedroom, or the coffee bar. Wi-Fi has become popular because a single base station a box with a wired connection to the Internet, such as a DSL, cable, or T1 line can broadcast to multiple users across distances as great as 100 meters indoors and 400 meters outdoors. These systems are based on the IEEE b protocol. However, the media access controller (MAC) and physical layer (PHY) specifications for this protocol are suboptimum for outdoor citywide wireless networks or metropolitan area networks (MAN). This means that the technology has very little range and capability in a metropolitan setting or over any substantial distance. However a new technology called WiMax has arrived which provides wireless broadband Internet connections at speeds similar to Wi-Fi s, but over distances of up to 50 kilometers from a central tower. WiMax is a second-generation protocol that allows for more efficient bandwidth use, interference avoidance, and is intended to allow higher data rates over longer distances. Wireless Interoperability for Microwave Access or WiMax is a wireless 1

8 Chapter 1. Introduction 2 digital communications system, also known as IEEE , that is intended for wireless metropolitan area networks. WiMax can provide broadband wireless access up to 30 miles for fixed stations, and 3-10 miles for mobile stations. In contrast, the WiFi/ wireless local area network standard is limited in most cases to only feet. With WiMax, data rates like those of WiFi are easily supported, but the issue of interference is lessened. WiMax operates on both licensed and non-licensed frequencies, providing a regulated environment and viable economic model for wireless carriers. Although WiMax, has been designed to provide wireless broadband access in the Metropolitan Area Network (MAN), delivering performance comparable to Wifi, traditional cable, DSL or T1 offerings. To provide the coverage and data rates envisioned, even on uneven terrain, the use of multihop communication seems desirable. Hence WiMax supports a Mesh mode (the other mode being point to multipoint) in which unlike the traditional cellular systems, the nodes can communicate without having a direct connection with the base station. 1.2 Problem Definition In a IEEE d Mesh network, a node that has a direct connection to backhaul services outside the Mesh network, is termed a Mesh Base Station (MBS). All other nodes of a Mesh network are termed Mesh Subscriber Stations (MSS). In IEEE d standards these nodes are stationary, i.e., the standards do not support mobility (see however e amendment [2] to the standard which supports the mobility). The standard specifies a centralized scheduling scheme for mesh networks. Under this scheme, the SSs notify the MBS their data transfer requirements and the quality of their links to their neighbours. The MBS uses the topology information along with the requirements of each MSS to decide the routing and the scheduling. The

9 Chapter 1. Introduction 3 MAC scheme used is TDMA and the resource allocation is in terms of time slots within a frame. The standard does not specify an algorithm for scheduling of the slots to different MSSs; neither does it specify any routing algorithm. Scheduling and routing will have significant impact on the performance of the system and will largely decide the end to end QoS to different users. We will focus on these problems. The WiMax standard also supports a distributed scheduling scheme in which each mesh node uses the local topology, channel and traffic information to decide which channel to use. The distributed approach is simple and robust as compared to the centralized approach. However it results in lower channel utilization and will provide less control over QoS. Thus it is recommended ([11]) that the distributed scheduling be used only for unlicensed spectrum while the centralized for licensed. The standard recommends centralized scheduling for the traffic entering/leaving the mesh while distributed scheduling for Intra-net traffic. A part of the frame can be reserved for centralized scheduling and another for distributed scheduling and these can be configured. Since most of the traffic is expected to be Internet traffic we will concentrate on centralized mode. IEEE based WLAN has been becoming quite ubiquitous. This technology has matured over the years and its equipment has become quite cheap. However, as commented before the media access controller (MAC) and physical layer (PHY) specifications for this protocol(802.11) are suboptimum for outdoor citywide wireless networks or metropolitan area networks (MAN). An attractive scenario in the future is that the last hop of the network will be an based WLAN and it will be connected to a WiMax network to access the broadband Internet. The WiMax network might be a P-MP single hop network or a mesh network. therefore, providing end-toend QoS to different applications in such an interconnected network is an important research issue.

10 Chapter 1. Introduction Literature Survey In the following we survey the literature on scheduling and routing for wireless networks. Scheduling algorithms to provide QoS in single hop (point to multipoint) IEEE networks are considered in [13], [18], [36] and [40]. See also ([19]) for a performance analysis. The problem of scheduling and routing in adhoc multihop wireless networks has been extensively studied in recent years (see [4], [15], [26] for general surveys and tutorials). Scaling laws for fundamental limits on information transfer in multihop wireless networks are surveyed in [42]. The dominant MAC (multiple access control) protocols being considered for multihop networks are the CSMA/CA based IEEE and the TDMA based IEEE Since technology is much more mature and cheaper, most of the current mesh network deployments are based on it. However, due to co-channel interference it does not provide satisfactory performance ([28], [41]). See [21] for a recent contribution to provide QoS in based mesh networks. The performance of an based mesh network can be much superior. The studies on multihop networks are [8], [9], [23], [34], [35] and [39]. In [39] a simple heuristic scheduling and a Tree routing algorithm are proposed to achieve efficient channel utilization. [8] and [23] provide fair access to all nodes and also efficient utilization of resources. In [35] also routing and scheduling algorithms are provided which are efficient for the overall system but spatial reuse of the channels is not allowed (because the standard at that time did not allow spatial reuse). In [34] also channel spatial reuse is not allowed but within this limitation this study provides QoS to individual TCP and real time connections. The QoS guarantee to individual flows has not been provided in any other multihop wireless network study that we are aware of (all the other studies mentioned above provide scheduling and routing for the aggregate traffic generated at different nodes which as we will see is not

11 Chapter 1. Introduction 5 sufficient to guarantee QoS to individual connections). In [9] the authors study the distributed scheduling. 1.4 Our Contribution In this report, we present algorithms for centralized scheduling of real and non-real time traffic with the objective of providing QoS within the framework of the IEEE mesh mode. Our algorithms use the network resources efficiently and fairly and can be used in real time by the MBS. In literature, there are many papers which deal with interference aware optimal tree routing structure. We develop a new metric for constructing an interferenceaware optimal tree routing structure, whose performance is better than the previous algorithms. We also extend our scheme of providing QoS to individual data and real application to multi-channel, multi-radio fixed mesh networks. Furthermore, e scenarios of limited mobility support is also considered. Finally, we also consider the scenario where an end user is connected to an IEEE based WLAN. The Access point of the WLAN is connected to the Internet via a WiMax network. We demonstrate that our ideas to provide QoS can be extended to such a setup. 1.5 Organization of report The organization of the report is as follows. Chapter 2 describes the system model. We obtain an optimal and fair routing and link scheduling algorithm for the aggregate traffic in Chapter 3. We also obtain an approximate algorithm to allocate slots to various links, satisfying the given interference constraints. In Chapter 4 we provide scheduling schemes for flows within an aggregate to provide QoS to individual flows. In Chapter 5, we consider the multi hop scenario where the infrastructure modes are fixed but some clients can be mobile. Chapter 6 develops algorithms to provide QoS in an WLAN-WiMax interconnected network. Section 7 concludes the report

12 Chapter 1. Introduction 6 and suggests future directions.

13 Chapter 2 System Model 2.1 Introduction In this chapter we briefly explain the PHY and MAC layers of the IEEE standard. Then we outline our QoS architecture for an based network. The rest of the report will develop these ideas PHY and MAC An IEEE network consists of a Base Station (BS) and multiple Subscriber Stations (SSs). The BS serves as a gateway for the SSs to the external network, and each SS acts as an access point that aggregates traffic from end users in a certain geographical area. IEEE support two modes of operation: Point-to-Multipoint (PMP) mode and mesh mode. In PMP each SS directly communicates with the BS through a single-hop link, which requires all SSs to be within clear LOS transmission range of the BS. In contrast, in the mesh mode, the SSs can communicate with the mesh BS and with each other through multi-hop routes via other SSs. The mesh topology not only extends the network coverage and increases capacity in non-los environments, but it also provides higher network reliability and availability when node or link failures occur, or when channel conditions are poor. IEEE operates at GHz for Line-of-Sight (LOS), and 2-11 GHz for non-los connection. In this report we consider 7

14 Chapter 2. System Model 8 the mesh mode. The mesh mode supports two different physical layers, WirelessMAN- OFDM and WirelessHUMAN. Both of these use 256 point FFT OFDM TDMA/TDM for channel access and operate in a frequency band below 11GHz. The first operates in the licensed band but the second uses the unlicensed band. The standards also support adaptive modulation and coding where the burst profile of a link (i.e., modulation scheme and the coding rate) and hence the link rate is changed depending upon the channel conditions. The IEEE mesh mode uses Time Division Multiple Access (TDMA) for channel access among the mesh BS and SS nodes, where a radio channel is divided into frames. Each frame is further divided into time slots that can be assigned to the BS or different SS nodes. A frame consists of a control subframe and a data subframe. Each frame is further divided into 256 minislots for transmission of user data and control messages. In the control subframe, transmission opportunities, which typically consist of multiple minislots, are used to carry signalling messages for network configuration and scheduling of data subframe minislot allocation. There are two types of control subframes: network control subframe and scheduling control subframe. A network control subframe follows after every NS scheduling control subframes, where NS is a configurable network parameter. In the network control subframes, Mesh Network Configuration (MSH- NCFG) and Mesh Network Entry (MSH-NENT) messages are transmitted for creation and maintenance of the network configuration. A scheduling tree rooted at the mesh BS is established for the routing path between each SS and the mesh BS. Active nodes within the mesh network periodically advertise MSH-NCFG messages which contain a Network Descriptor that includes the network configuration information. A new node that wishes to join the mesh network scans for active networks by listening to MSH-NCFG messages. Upon receiving the MSH-NCFG message, the new node establishes synchronization with the mesh network. From among all the possible neighbor

15 Chapter 2. System Model 9 nodes that advertise MSH-NCFG, the new node select one as its sponsor node. Then the new node sends a MSH-NENT message with registration information to the mesh BS through the sponsor node. Upon receipt of the registration message, the mesh BS adds the new node as the child of the sponsor node in the scheduling tree, and then broadcasts the updated network configuration to all SSs. In the IEEE mesh mode, both centralized scheduling and distributed scheduling are supported. Mesh Centralized Schedule (MSH-CSCH) and Mesh Distributed Schedule (MSHDSCH) messages are exchanged in the scheduling control subframe to assign the data minislots to different stations. The number of transmission opportunities for MSH-CSCH and MSH-DSCH in each scheduling control subframe are network parameters that can be configured. Centralized scheduling is mainly used to transfer data between the mesh BS and the SSs, which corresponds to external traffic from the Internet; while distributed scheduling targets data delivery between two SSs in the same WiMax mesh network, which corresponds to intranet traffic. In the standard, the data subframe is partitioned into two parts for the two scheduling mechanisms respectively. The centralized scheduling handles both the uplink, where the traffic goes from the SSs to the mesh BS, and downlink, where the traffic goes from the mesh BS to the SSs. In the mesh mode, Time Division Duplex (TDD) is used to share the channel between the uplink and the downlink. In distributed scheduling, all SSs are peers and they compete for transmission opportunities based on a pseudo-random election algorithm. A three-way handshaking procedure is employed to reserve minislots for transmitting data between neighboring SSs. In centralized scheduling, the mesh BS acts as the centralized scheduler and determines the allocation of the minislots dedicated to centralized scheduling among all the stations. The time period for centralized scheduling is called scheduling period, which is typically a couple of frames in length. There are two stages in each

16 Chapter 2. System Model 10 scheduling period. In the first stage, the SSs send bandwidth requests using the MSH- CSCH:Request message to their sponsor nodes, which are routed to the mesh BS along the scheduling tree. Each SS not only sends its own bandwidth request but also relays that of all its descendants in the scheduling tree. The SSs transmit MSH-CSCH:Request messages in such an order that the sponsor nodes always transmit after all their children. In this way, the mesh BS collects bandwidth requests from all the SSs. In the second stage, the mesh BS calculates and distributes the schedule by broadcasting the MSH-CSCH:Grant message, which is propagated to all the SSs along the scheduling tree. 2.3 System Model We consider the following scenario. Consider a Mesh network with M MSSs labeled 1,2,...,M. The MBS is labeled 0. We consider Uplink and Downlink Centralized Scheduling of the MSSs, which, according to the standards uses TDMA with spectral reuse. Also the data is directed either to or from the MBS. We assume that each node transmits at the maximum allowed power, if needed. (Although power control is also an important issue in performance of a mesh network, the standard currently does not emphasis it and hence we donot address this in this Chapter). As the channel condition on a link changes, the data rate is also changed so as to meet the desired BER. Let r ij denote the rate and E[r ij ] the average rate of the channel from node i to node j. Resource allocation is done by the MBS in units of (mini) time slots. One time slot consists of multiple OFDM symbols. Each allocation is valid for K frames consisting of N time slots (for simplicity of notation we will take K=1).

17 Chapter 2. System Model Our approach to QoS IEEE supports real and nonreal time applications. The real time applications, e.g., IP telephony and video conferencing, use UDP while data applications use TCP. Real time applications and interactive data (file transfer and web browsing) require QoS. To provide QoS to these applications will require careful routing and scheduling of traffic through the mesh network. We will consider these problems for both types of traffic. Since UDP traffic and real time QoS requirements are very different from TCP traffic and interactive data QoS requirements, we will consider these problems separately and then show how to integrate them in the same system. To provide the QoS, we will generally follow the QoS-architecture developed in [34] since this seems to be the only architecture available for mesh networks which guarantees end-to-end per flow QoS. However, due to mesh requirements at that time [34] did not consider spectral spatial reuse. This can be a serious limitation because spectral-reuse can provide significant capacity improvement. Thus, in our current proposal we will remove this restriction. We will use a two step approach. In the first step we will provide routing and scheduling for the aggregate traffic for each source-destination pair of MSSs (one of these MSSs will be the MBS). The aggregate traffic will be the mean total traffic of all the real and data applications between different source-destination pairs. This ofcourse does not guarantee the QoS to individual flows. In the second step we develop scheduling algorithms to share the long-term throughput guaranteed in step one between real and data applications of each source-destination pair to guarantee QoS to individual flows. We will justify the two step approach and will provide simulation results to verify the claims on QoS guarantees. Chapter 3 provides the routing and scheduling for step 1 to satisfy the aggregate demands of source-destination pairs. In Chapter 4, we detail our step 2 to

18 Chapter 2. System Model 12 ensure the end-to-end QoS to individual real and interactive data applications. Chapter 5 extends our approach to include mobility support for some nodes. Chapter 6 will show how we can indeed further extend our approach to accommodate a wifi network at the last mile.

19 Chapter 3 Routing and Scheduling in Mesh Networks 3.1 Introduction In this chapter we consider the problem of routing and scheduling in a wireless mesh network to satisfy certain aggregate traffic requirements. The algorithms developed will form the first stage of our architecture to provide end-to-end QoS to individual flows in an based mesh network. This problem has been addressed in numerous other recent studies. We will first address the the general problem which can be useful in other mesh networks also (e.g., in based mesh networks). Later on we will also consider a tree-based routing and scheduling problem which has been studied particularly in the context of WiMax mesh networks. This chapter is organized as follows. In section 3.2, we state and explain the optimization problem, to obtain optimal and fair routing and scheduling for the aggregate traffic requirements of various source destination pairs. The computational complexity of this problem is very high. Thus, section 3.3, provides the simpler solutions which do our task at less complexity and guarantees a solution. In section 3.4, we develop an approximate algorithm which uses the solution obtained in section

20 Chapter 3. Routing and Scheduling in Mesh Networks 14 to allocate slots to various links which satisfies the given transmission and traffic constraints. In Section 3.5, we consider the problem of optimal Tree routing and scheduling, instead of multi-path routing obtained in the previous sections. A Tree-structure is particularly considered in the WiMax networks. In section 3.6, we extended single channel multi-hop networks to multi-channel multi-radio multi-hop mesh networks, with finite number of orthogonal channels. 3.2 Optimization problem The algorithms developed in this chapter can be used for uplink as well as downlink simultaneously. Let λ(s, d) be the mean number of bits per slot to be transmitted from MSS s to MSS d. This is the sum of mean throughput required by all the real time and data connections transmitting from MSS s to MSS d. The calculation of mean throughput requirements for TCP connections is shown in Section 4.3. For the CBR connections, it is the traffic they generate per slot. For a VBR connection it equals the equivalent bandwidth. For downlink, MSS s(source) will always be the MBS and for uplink MSS d(destination) will be the MBS. We develop algorithms in this chapter which will decide the routes that λ(s, d) will follow and also the slots in which each link will transmit. We develop algorithms which provide routes and schedules that will be functions of λ(s, d) and the mean link rates E[r(i, j)] but otherwise would not vary with time. By exploiting the current queue lengths at different links and the channel states one could vary the routes and the schedules to obtain better performance ([33], [34]) but we will not do this. This is because frequently varying routes and schedules in real time is computationally more complex and can also cause loops in the path traversed by a packet and resequencing problem at the receiver. Furthermore, our QoS architecture requires reservation of resources at intermediate MSSs along a route. Thus frequent route variation is not desirable. In addition, in case of spectral

21 Chapter 3. Routing and Scheduling in Mesh Networks 15 spatial reuse, changing the routes and schedules is more complicated. Thus we will change the routes and schedules of link transmissions only when some of the λ(s, d) and/or E[r(i, j)] change drastically and/or some links/nodes fail. These algorithms will be run at the MBS and then the schedules broadcast to different nodes via Mesh Centralized Schedule messages. The algorithms we develop will satisfy the traffic requirements λ(s, d) of each source-destination pair (s, d) if possible. If not, then we will provide a fair solution which is also efficient. When it is possible to satisfy certain (fair) traffic requirements of all source-destination pairs, we will provide routing and scheduling which optimizes a cost function. In this chapter we use the approach developed in [31] which in turn was partly motivated by [24]. In [34], where spatial reuse is not allowed it was shown that the routing and scheduling problems can be decoupled and that a Tree structure can be optimal for routing. In the present general scenario this may not be true (although the standard seems to prefer the Tree structure ([8], [39])). The cost function to optimize will be a sum of the link cost functions f(γ(i, j)n(i, j)) where Γ(i, j) is the total mean traffic rate per slot and n(i, j) is the fraction of slots assigned to link (i, j). Better cost functions can be obtained as a function of higher moments of traffic arriving at link (i, j) but higher moments are difficult to obtain and handle. Thus it is desirable to use only the first moments. But even then f will often be a nonlinear function. For example, using Kleinrock s independence assumption ([38]) or approximating the queues at each link by an M/M/1 queue, we get f(γ(i, j),n(i, j)) = Γ(i, j) n(i, j)e[r(i, j)] Γ(i, j) (3.1) as the mean queue length at the link (i, j) and [n(i, j)e[r(i, j)] Γ(i, j)] 1 as the mean

22 Chapter 3. Routing and Scheduling in Mesh Networks 16 delay. Similarly we can consider packet loss probability if the buffer lengths are small. Using Lagrange multipliers one can accommodate constrained optimization (see [31] for more details). The cost functions provided above may not be very good approximations of mean delay and queue lengths. Better approximations are provided in [31]. However it is an important direction for future research. We consider the following joint routing and scheduling problem: Find n(i, j) and α p (s, d) that minimizes f(γ(i, j),n(i, j)) (3.2) (i,j) L subject to Γ(i, j) = (s,d) α p (s, d)λ(s, d) n(i, j)e[r(i, j)], (3.3) p:(i,j)is on p 0 α p (s, d) for each p, (s, d) (3.4) and α p (s, d) =1 for each (s, d) (3.5) p where α p (s, d) is the fraction of (s, d) traffic on route p, L is the set of links and the inner summation in (3.18) is over all possible routes for (s, d). The condition (3.18) is required to satisfy the stability condition at each link (i, j) Transmission Constraints In addition to (3.18)-(3.5) the network should also satisfy some transmission constraints. These constraints occur due to the wireless nature of the links. In the standard these are given by stating that two links can be scheduled for transmission in the same slot if they are 1, 3 or 7 hops away from each other. However in a practical system it may or may not be possible to schedule two links in a slot depending upon the power of transmission, the distance between the receiving nodes and other

23 Chapter 3. Routing and Scheduling in Mesh Networks 17 geographical factors. This can be decided in a particular scenario by actually taking measurements and finding the SINR (Signal to Interference and Noise Ratio) at different nodes. In the following we will assume that this has been done for the network under consideration. Sometimes we can write these constraints as necessary and/or sufficient inequality constraints. For example, if no spatial channel reuse is allowed (as was done in the standard in 2004 or if in the current standard we choose the option that spatial reuse is allowed only with a hop distance of 7, in which case it may effectively be no spatial reuse) then necessary and sufficient conditions are n(i, j) 1. (3.6) (i,j) It is shown in [31] that if our transmission constraints are such that a node can receive successfully if and only if one of its neighbouring nodes transmits in a slot and that a node can transmit only on one of its links at a time, then the necessary and sufficient conditions are n(i, j) 1 for all i j:(i,j) L and i=(i,j) L n(i, j) 1 for all j. (3.7) If we put the constraint that only one incoming or outgoing link at a node can be active at a time, then it is shown in [8] that necessary and sufficient conditions, in the context of WiMax mesh networks are n(i, j)+ n(i, j) 1 for all nodes i. (3.8) j:(i,j) L j:(i,j) L It is argued in [8] that by using directional antennas and careful placement of nodes, these constraints can be quite realistic in the WiMax.

24 Chapter 3. Routing and Scheduling in Mesh Networks 18 In a mesh network formed from nodes, RTS-CTS-DATA-ACK model, for a successful transmissions, neighbours of the transmitter as well as the receiver have to refrain from transmission at that time. Thus, for link (i, j), ifn(i) are the neighbouring nodes i and E(i) is the set of links incident on it, The transmission constraints are : n(l) 1 for each link(i, j) (3.9) i N(i) l E(i) Our general setup can work with transmission constraints of the type along with the optimization problem considered above. The problem of transmission constraints has also been studied in [5], [17] and [25]. Sometimes corresponding to these constraints, one may only be able to get only sufficient inequality constraints. In the following we will assume the transmission contraints have been put as linear inequality constraints and call them (T ). To be specific, in our examples in this report we will use the following scenario: Consider a link (i, j), where i is the transmitting node and j is the receiving node. When a link (i, j) is active, for successful transmission, node i can transmit only at link (i, j) and node j can receive only at (i, j), i.e, n(e ) 1 (i, j) E (3.10) e E(i)) E(j)) E in (N(i))) E out(n(j))) Where E(i) are adjucent links to node i, E(j) are adjucent links to node j, E in (N(i)) are incoming links on node i, E in (N(i)) are outgoing links on node j 3.3 Approximate Solution and Algorithms Obtaining the optimal solution for (3.2)-(3.5),(T )(transmission constraint) can be very time consuming because of the nonlinear cost function. Infact, one needs from n(i, j) an integral number of slots with in the scheduling frame. Also, if it is not

25 Chapter 3. Routing and Scheduling in Mesh Networks 19 possible to satisfy the λ(s, d) requirements of each (s, d), the above optimization problem may not provide any solution. Thus in the following we first develop algorithms which will check for feasibility of the demands λ(s, d). If these are not feasible, then we provide a solution which may be fair to all (s, d) pairs. Finally we obtain a solution which is fair to all (s, d) pairs and optimizes the nonlinear cost function. Consider the following optimization problem: maxλ such that (3.11) α p (s, d) λ for all (s, d) (3.12) p and (3.18), (3.4) and (T ) are satisfied where the summation in (3.12) is over all possible paths p in the network. A solution to the above optimization problem can be considered fair and efficient. This is because if there is a routing and scheduling algorithm which satisfies all the traffic requirements λ(s, d) then λ will be 1. If not, it provides the largest fraction of traffic that can be satisfied for each (s, d). This concept of fairness has also been considered in [25], [34] and [36]. Furthermore unlike (3.2)-(3.5), this problem is a linear program (LP) and hence can be solved much faster than the nonlinear problem (3.2)-(3.5). As mentioned above, a solution n(i, j) and α p (s, d) satisfying (3.18), (3.4), (3.11), (3.12) and (T ) will be considered efficient and fair. However observe that the service provider will frequently need to run an algorithm in real time to obtain a solution and hence complexity of the algorithm will be an important issue. In general the scheduling problem is NP hard because the n(i, j) need to be integer valued (should be the number of slots in a frame assigned to link (i, j)). However if we ignore the integrality of n(i, j) and consider them as non-negative fractions as considered above, (3.18), (3.4), (3.11), (3.12), (T ) becomes an LP problem which is computationally much more tractable.

26 Chapter 3. Routing and Scheduling in Mesh Networks 20 If the number of nodes in the mesh is large, then complexity of the above LP can also be of concern because the number of variables α p (s, d) can be exponential in number of nodes. However in that case this LP can be reformulated in term of link flows ([5], [3]) and this problem can be taken care of. Another way to handle it, in terms of α p (s, d) itself is by solving the dual problem as discussed in [24]. If λ obtained from the above optimization problem is 1 then there is a route and schedule for all (s, d) pairs and links which can satisfy the traffic requirements of all users. If λ<1then, λ is the largest fraction of traffic requirements of all (s, d) pairs that can be satisfied by the network. Our solution of the above problem can also provide λ>1. When this happens, the network has more BW/throughput than needed to satisfy the current QOS requirements of all the users. Then the above solution allocates the extra resources to different (s, d) pairs in a fair way. The extra resources can be used by the TCP connections usefully because in our QoS requirements we have only specified the minimum mean throughput a TCP desires. One can further improve the efficiency of the system if the optimal λ in (3.11) is less than 1. In [31] a method is suggested where the fraction of demands satisfied for some of the (s, d) pairs can be increased without decreasing the fraction for other (s, d) pairs below the optimal λ obtained above. The routing and scheduling provided above will ensure that the slot assignment n(i, j) for link (i, j) is such that its average rate n(i, j)e[r(i, j)] is sufficient to carry the overall traffic passing through it. However, it will not ensure that the throughput (rate) seen by traffic of a pair (s, d) will indeed get its required share of throughput. This may partly happen because the TCP connections passing through fewer hops tend to get more throughput than the other TCP connections sharing links with it (see [7], [34]). Thus to ensure that the traffic of some (s, d) pairs does not hog most of the throughput at a link, we will store the traffic of different (s, d) pairs in different queues at each link and provide the required throughput to each queue via

27 Chapter 3. Routing and Scheduling in Mesh Networks 21 WRR (Weighted Round Robin). This will ensure that traffic of each (s, d) pair will get its share of throughput at each link on its routes. In next subsection, we will improve upon the above solution to take into account the cost function Algorithms for optimal solutions Once we have verified via LP in Section 3.3 above the feasibility of traffic demands of different (s, d) pairs, either we can satisfy the full demand (λ =1)orwe have restricted the demand of different (s, d) pairs in a fair way via multiple stages of LP in Section 3.3. In either case we now know that the traffic demands of different (s, d) pairs can be met. The next step is to obtain certain routing and scheduling that can optimize a system cost function For illustration purposes we fix it to be the sum of mean queue lengths at each queue: Γ(i, j) n(i, j)e[r(i, j)] Γ(i, j) (3.13) is the mean queue length at link (i, j) when mean traffic Γ(i, j) is flowing through it and n(i, j) fraction of a slot is assigned to it. As mentioned before, (3.13) is the mean queue length when we approximate the queue at link (i, j) by an M/M/1 queue. The cost function (3.13) is not a linear or convex function of its variables n(i, j) and α p (s,d). Thus it is not easy to compute the global minimum of the sum of (3.13). In the following we explore some algorithms to compute the minimizer of sum of (3.13). Dinkelbach s algorithm This algorithm provides an efficient solution of optimization problem: Max x S f(x) g(x). (3.14)

28 Chapter 3. Routing and Scheduling in Mesh Networks 22 where f,g are continuous functions from R n to R It has been shown that x solves the above Fractional Programming Problem if and only if it solves the global optimization problem, Max x S (f(x) λg(x)) (3.15) with constant λ = f(x ). This fact can be used to obtain an efficient algorithm for (3.14) g(x ) if there is an efficient solution of the global optimization problem (3.15). The global optimum is easy to obtain if f and g are linear or convex functions. Dinkelbach s original iterative algorithm is based on the above result and can be described as follows. 1. Select some x (0) S. Set λ (0) = f(x(0) ) and k =0. g(x (0) ) 2. Solve the constrained global optimization problem to get the optimal point x (k+1). 3. If λ (k) f(x (k+1) ) g(x (k+1) )=0, then set x = x (k+1) and λ = λ (k), and stop. 4. If λ (k) f(x (k+1) ) g(x (k+1) ) > 0, then set λ (k+1) = f(x(k+1) ), k = k +1and go to step g(x (k+1) ) 2. We use MATLAB to implement this iterative algorithm. Sum of Fractions As mentioned above, Dinkelbach algorithm provides a global optimum for function f g if f and g are linear or convex. In our case the link cost for each link is a linear function of the variables but we need to optimize a sum of such functions. The overall function does not satisfy these requirements. Thus, our cost function being a non-linear function without some nice features which can be exploited with the current state-of-the-art will fetch us only a local minimum. The current methods for sum of fractions, use SQP (Sequential Quadratic Programming) method. The other popular ones are Interior-reflective Newton method, Complex method, Zoutendijk s method,

29 Chapter 3. Routing and Scheduling in Mesh Networks 23 Rosen s Gradient Projection method, interior and exterior penalty function method. We will use SQP. Min-max algorithm Instead of minimizing the sum of link cost functions, one could consider minimizing the maximum of link cost functions. For the cost function (3.13) one advantage of doing this is that instead of using a non-linear optimization algorithm, one can use LP. This as we know provides a huge computational advantage. The cost function will be, min max (i,j) Γ(i, j) n(i, j)e[r(i, j)] Γ(i, j) (3.16) Example In this subsection we provide an example to demonstrate the above algorithms for routing and scheduling. Consider the 5 node example shown in Figure 3.1. The transmission constraints for this graph when each node can transmit and receive on one link at a time are: n(1, 2) + n(1, 5) 1 n(2, 3) + n(2, 5) 1 n(3, 4) 1 n(4, 1) 1 n(5, 4) + n(5, 3) 1 n(2, 5) + n(1, 5) 1 n(2, 3) + n(5, 3) 1 n(5, 4) + n(3, 4) 1

30 Chapter 3. Routing and Scheduling in Mesh Networks 24 Figure 3.1: A sample network We have seen earlier that these are necessary and sufficient conditions for our network model. Now consider the traffic demands: E[λ(2, 1)] =3, E[λ(2, 4)] =3, E[λ(3, 4)] =1. After running the LP once, at the end of stage one we obtain λ = Thus it is not possible to satisfy the traffic of all the users by more than 75% of their demands simultaneously. Also we get n(3, 4) = 0.25 and n(5, 4) = Thus, node 4 cannot receive any more traffic. For stage 2 to see any possible improvement in efficiency, we need to remove links (3, 4) and (5, 4). Then, one sees that we cannot transmit any more data from any of the sources. Thus we cannot improve the efficiency any more. Next we run the three optimization algorithms: Dinkelbach, Sum of fractions, min-max(lp). Each of the algorithms provide us with the following routings: α ( ) (2, 1) =1, α (2 5 4) (2, 4) =1,α (3 4) (3, 4) = 1. Also all the three algorithms provide n(2, 5) =1, n(5, 4) = 0.75, n(3, 4) = 0.25, n(4, 1) = 1. One can check with exhaustive search that we cannot improve over this result in terms of fairness, as well as getting maximum

31 Chapter 3. Routing and Scheduling in Mesh Networks 25 throughput. With traffic demands E[λ(1, 4)] =4, E[λ(2, 1)] =3, E[λ(5, 2)] =3, the LP in the first stage provides λ = 0.5. Now running the sum of fractions algorithm with 50% load we get the routes as α (1 5 4) (1, 4) =1,α ( ) (2, 1) =1,α ( ) (5, 2) = 1. Then we observe that the link (4, 1) is fully loaded. Thus traffic λ(5, 2) and λ(2, 1) can no longer be sent. Hence, now in second stage we transmit only traffic (1, 4). The second stage provides λ 2 = 0.5 and hence we can further transmit 1 unit of λ(1, 4) traffic. Observe that now the link (5, 4) is fully loaded. Now we rerun the sum of fractions algorithm with total load E[λ(1, 4)] =3,E[λ(2, 1)] = 1.5 and E[λ(5, 2)] = 1.5 and obtain that all the traffic of λ(1, 4) follows the path (1 5 4), ofλ(2, 1) follows path ( ) and of λ(5, 2) follows the path ( ). Also n(1, 2) = 0.5, n(1, 5) = 0.5, n(2, 5) = 0.5, n(5, 4) =1,n(4, 1) =1,n(2, 3) = 0.5, n(3, 4) = 0 and n(5, 3) =0. Again this can be shown to be a globally optimal solution from fairness and cost point of view. Observe that although link (2, 3) is not being used, we do get n(2, 3) = 0.5. But this does not increase the cost of the solution. If we apply the Dinkelbach algorithm after stage 1 and then stage 2 of the LP, the total routed traffic obtained is E[λ(1, 4)] = 2.99, E[λ(2, 1)] = 1.5 and E[λ(5, 2)] = 1.5. One sees that this algorithm is sending slightly less traffic for λ(1, 4) than the sum of fractions. But this loss of traffic is insignificant and could be attributed to computational errors. This method also routes all the three traffic streams almost entirely along the same paths as the sum-of-fractions algorithm (there are some differences in the fourth decimal place). Also, due to slightly less load carried in this solution, the n(i, j) are also almost same as the above solution except for n(2, 3) (which is not relevant) and n(2, 5) = Next we ran the min-max algorithm. We just summarize the results for this. Since stage 1 λ does not depend on the non-linear algorithm, λ = 0.5, but λ 2 = The traffic for the three streams is still carried entirely by the three routes given above.

32 Chapter 3. Routing and Scheduling in Mesh Networks 26 The n(1, 2) = 0.5, (we are rounding off to two decimal places) n(1, 5) = 0.5, n(2, 3) = 0.47, n(2, 5) =0,n(3, 4) =1,n(4, 1) =0,n(5, 4) =1. The total cost of the three solutions above are 6751, 6453, Slot Assignment Problem The computation of feasible scheduling space is NP-hard. In addition, the link scheduling problem is also NP-hard [43]. Our approach to the problem is quite flexible and is a promising method to handle more sophisticated interference conditions, multiple channels and multiple antennas. LP, discussed in section 3.3 with interference constraint ( ) will give an optimal routing and scheduling, α p (s, d) and n(i, j) respectively. Let T be the number of slots per scheduling frame in Then n(i, j)t number of slots are to be allocated to each link (i, j) per scheduling frame. But, the n(i, j)t may not be a integer valued. We will take n(i,j)t slots for assignment. This ofcourse reduces the total capacity of the link (i, j). But this can be taken care of by solving the LP with the constraints (3.18) i.e, Γ(i, j) = (s,d) p:(i,j)is on p α p (s, d)λ(s, d) n(i, j)e[r(i, j)] (3.17) replaced by Γ(i, j) = (s,d) p:(i,j)is on p α p (s, d)λ(s, d) (1 ɛ) n(i, j)e[r(i, j)] (3.18) where ɛ is small fraction (say 0.05) After each n(i, j)t is truncated to its integer value, the actual allocation of slots to different links still requires a careful algorithm. We present one in the following section Algorithm Step 1

33 Chapter 3. Routing and Scheduling in Mesh Networks 27 Construct a constraint graph (CG) for the give graph G(V,E) as follows. The number of nodes in constraint graph CG is equal to number links in graph G. Two nodes in the constraint graph are connected by a link, if they are interfering links in the graph G. S : The set of nodes in the graph v : A node in the set S N(v) : Adjacent node set of v d(v) : Degree of node v B : A set of links which can be active simultaneously. n(v) : Number of slots to be allocated to link in G(V,E); which corresponds to node v in CG. Step 2 B S S while S choose v such that d(v) =min(d(w)),w S and in case of more than one node with minimum degree take one with maximum slots yet to be allocated. B B v S S {v N(v)} Step 3 Allocate min(d(w)),w Bslots to setb, and remove nodes v from the set S such that d(v) =min(d(w)),w S,v S. go to step 2,ifS is nonempty.

34 Chapter 3. Routing and Scheduling in Mesh Networks Interference-Aware tree structure routing and scheduling In [34], it was shown that a tree can provide an optimal (and desired) routing structure for However in [34] channel spatial reuse was not allowed. In previous sections of this chapter we considered joint routing and scheduling with channel reuse. The optimal routes obtained do not necessarily provide a tree structure. Infact we will see that often the traffic of a source destination pair is split along two or more paths. However, tree routing in WiMax mesh networks seems to be a preferred structure([8],[39]). Even though the standard does not mandate a Tree, the procedure prescribed in the standard for a new node to join the mesh would lead to a tree if the routes are not changed with time. Thus, in this chapter we will obtain an optimal tree structure with spatial channel reuse. We will compare its performance with the optimal solution obtained in section 3.3. We will also compare its performance with other tree routing solutions obtained in literature([39]) Tree routing structure To achieve efficient spectral utilization and high throughput in mesh networks, the route construction within the mesh network is crucial. To this end, we propose an interference-aware route construction algorithm that considers the interference condition in the mesh network. For link (u, v) we define the blocking value, B(u, v) = E[r(i, j)] N(u, v) E[r(u, v)]) (i,j) (3.19) where N(u,v) is the set of links interfering with link(u,v). Depending upon different interference models we may obtain different N(u,v) sets for the link (u,v). Our interference-aware tree routing construction algorithm is similar to that in [39]), different except for the blocking value of the link. The blocking value of a route is the sum

35 Chapter 3. Routing and Scheduling in Mesh Networks 29 of blocking values of the links on it. In the interference-aware route construction scheme, the blocking metric information is incorporated into the Network Descriptor of a MSH-NCFG message. When a new node is scanning for active network during the network entry process, the new node chooses the potential Sponsoring Node based on the blocking metric information (i.e blocking value of the route)to reduce the interference of the multi-hop route and hence to improve the throughput Interference-aware tree route construction Algorithm S {0} N s {1, 2,...,n} p(i),i {1, 2,...,n} Do if N s m arg max i (Ns neighbour(s)) σ(i) // node m with high σ(m) value joins first C(m) =Neighbour(m) // all nodes with in transmission distanceof node m W (m) C(m) S // candidate parent nodes of node m p(m) argmin i W (m) B(i) // select the node with minimum blocking Add mtos Remove mfromn s END So far we consider the minimal interference along the path but after an SS enters the network, the interference value on the path of other SSs in the network chang. Therefore, the entry order of different nodes impacts the construction of the routing tree. Thus, the routing tree can be reconstructed periodically.