Traffic Estimation in mobile ad-hoc networks

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1 Traffic Estimation in mobile ad-hoc networks SYED MUSHABBAR SADIQ RADIO COMMUNICATION SYSTEMS LABORATORY

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3 Traffic Estimation in mobile ad-hoc networks SYED MUSHABBAR SADIQ Master Thesis April 2004 TRITA S3 RST XXXX ISSN ISRN KTH/RST/R XX/XX SE RADIO COMMUNICATION SYSTEMS LABORATORY DEPARTMENT OF SIGNALS, SENSORS AND SYSTEMS

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5 Abstract Mobile Ad-hoc Networking (MANET) technology allows a set of mobile users equipped with radio interfaces to discover each other and dynamically form a communication network. It uses relaying in order to reach most other nodes in a network and can have different kinds of topology. Due to the mobility this topology can change very quickly. Change in topology results in changing traffic load rates over the links in the network. In a radio network the channel resources are one of the most limiting factors, it is therefore very important that this resource is used as efficiently as possible. The Medium Access Control (MAC) protocol is responsible for how this radio resource is divided between the nodes. Spatial Time Division Multiple Access (S-TDMA) is an example of MAC protocol. It allocates radio resource (time slot) to more than one nodes that are geographically separated from each other. Sharing of radio resource increases the overall capacity of the system. It is important to give the different nodes their fair share. In order to do this, precise knowledge on the traffic situation is needed. If the slots allocation is done with knowledge of the traffic load, more efficient allocation results than just assuming uniform traffic can be achieved. A very important issue is therefore to make estimations on traffic flows that each node handles. In this master thesis report we look into traffic estimation methods that are applicable in mobile ad-hoc networks. We study existing methods and then present a traffic load estimation method based on an exponential decrease function. Furthermore, we look into two parameters; window size T ws and gamma γ. We analyze and suggest fine tuning of these parameters for estimation of Poisson based traffic load. Finally, performance analysis on the basis of traffic load estimation error in percentage has been presented. This traffic estimation method based on exponential decrease function may also work for other traffic models if fine tuning of the above parameters have been made. V

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7 Acknowledgments I would like to pay a deep gratitude and appreciation to the persons who made it possible for me to complete this work through their contributions by providing required information, by giving their time and by their piece of mind and encouragement. First of all I would like to express my deep gratitude to my Examiner, Tim Giles <tim@radio.kth.se> and Supervisor/Advisor, Jimmi Grönkvist <jimgro@foi.se> for giving me the opportunity to work in this very interesting and challenging project work. I am also thankful for their continuous guidance in every step of this project work and the confidence they placed in me. Secondly I would like to thank people at FOI (The Swedish Defense Research Agency), especially to Ulf Sterner <ulfst@foi.se> for their contribution in terms of information and guidance. I thank them for their time and participation that made this thesis work possible. Sincere thanks are extended to all the students at RST Lab at S3, Wireless@KTH who co-operated from time to time to their best and provided not only the necessary help but also guided me to the extent to lead me to the completion of my project. I am obliged to my friends and colleagues who remained a constant source of help and encouragement to me to complete the project and to my daughter and son who would cheer me up at times of distress. I would also like to pay special thanks to my family for their support and especially to my wife whose critical discussions helped me to make my work better. Thank you all. Syed Mushabbar Sadiq, <icss-sym@dsv.su.se> VII

8 Dedicated to my mother, whose blessings and faith in my abilities has motivated me to pursue my dreams and without her support and encouragement I could not have achieved what I have accomplished today. VIII

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10 Contents ABSTRACT V ACKNOWLEDGMENTS... VII 1 INTRODUCTION BACKGROUND APPLICATIONS OF MOBILE AD-HOC NETWORKING (MANET) RADIO RESOURCE ALLOCATION AND TRAFFIC RATES Traffic sensitive S-TDMA scheduling AIM AND MOTIVATION OF THE THESIS PROJECT WORK OUTLINE OF THE THESIS REPORT TRAFFIC ESTIMATION METHODS TRAFFIC MATRIX OF THE LOAD ON EACH LINK BASED ON THE NUMBER OF ROUTING PATHS USING A LINK Illustration with example Improvement suggestion TRAFFIC ESTIMATION BASED ON NODE DEGREE LIMITATIONS OF EXISTING TRAFFIC LOAD ESTIMATION METHODS A PROPOSED TRAFFIC LOAD ESTIMATION METHOD Exponential decrease traffic load estimation function Time-dependent traffic load estimation IMPLEMENTATION AND EVALUATION ISSUES PERFORMANCE EVALUATION Correct Values (True Values) of traffic load on the relative scale Estimated Values of traffic load Relation between Method 1: Time Average and Method 2: Exponential Decrease Load Estimation Function Performance Evaluation Criteria Justification for Relative Load Error Difference (Percentage Error) SIMULATION ASSUMPTIONS AND CONSIDERATIONS Routing MAC Protocol Mobility Geographical area of the mobile ad-hoc network Average maximum radio connectivity distance between nodes SIMULATION RESULTS AND ANALYSIS OF TRAFFIC LOAD ESTIMATION TRAFFIC LOAD ESTIMATION FOR STATIC AD-HOC NETWORKS Optimum values of Gamma γ Optimum values of Window Size T ws TRAFFIC LOAD ESTIMATION FOR MOBILE AD-HOC NETWORKS Optimum values of Window Size T ws Analysis of Estimation Error for optimum window sizes

11 4.2.3 Optimum values of Gamma γ Analysis of Estimation Error for optimum gamma Explanation Comparison of Estimated and True traffic load CONCLUSIONS AND RECOMMENDATION FOR FUTURE WORK RECOMMENDATION FOR FUTURE WORK Analysis of more realistic packet data traffic models Average Network Throughput and Average Network Delay Take account of Queue Lengths APPENDIX A SUMMARY OF ANALYZED NETWORKS (NWS) A.1 STATIC NETWORKS (NWS) STUDIED A.2 MOBILE NWS STUDIED: APPENDIX B DETAILED PLOTS FOR TRAFFIC LOAD ANALYSIS OF MOBILE AD-HOC NETWORKS B.1 DETAILED PLOTS FOR ANALYSIS OF WINDOW SIZES T ws AND CORRESPONDING ESTIMATION ERRORS 58 B.2 DETAILED PLOTS OF TRAFFIC LOAD FOR 10 NODES MOBILE AD-HOC NETWORKS (RUNNING AT AVERAGE NODE SPEED FROM 2.5 METERS/SEC TO 25 METERS/SEC) APPENDIX C MOBILITY MODEL AND MAXIMUM RADIO TRANSMISSION RANGE (FOI) C.1 MOBILITY MODEL USED C.2 MAXIMUM RADIO TRANSMISSION RANGE APPENDIX D ROUTING AND TRAFFIC DATA STRUCTURE D.1 ROUTING DATA FORMAT D.1.1 Routing in Static Ad-hoc Networks D.1.2 Routing in Mobile Ad-hoc Networks D.2 TRAFFIC DATA CAPTURE (AT NODE) FILE FORMAT APPENDIX E MODELS FOR TRAFFIC LOAD GENERATION E.1 UNIFORM POISSON TRAFFIC MODEL E.1.1 Mean, Standard Deviation and Variance E.1.2 ON-OFF deterministic traffic based on Poisson process E.2 TRAFFIC ARRIVAL MODEL E.3 WWW TRAFFIC ARRIVAL MODEL REFERENCES

12 1 Introduction 1.1 Background Mobile Ad-hoc Networking (MANET) is one of the most important technologies that have gained interest due to recent advancements in both hardware and software techniques. MANET technology allows a set of mobile users equipped with radio interfaces (mobile nodes) to discover each other and dynamically form a communication network [1]. Other wireless communication systems tend to focus just on the mobility of user devices, not on the network itself. For example mobile phones and W-LAN (Wireless Local Area networks) terminals rely on some kind of fixed and pre-prepared infrastructure, whereas a mobile ad-hoc network is unplanned, self configurable and does not require any help from fixed/installed communication network infrastructure. MANET incorporates routing functionality into the mobile nodes so that they become capable of forwarding (relaying) packets on behalf of other nodes and thus effectively become the infrastructure. It can have different kinds of topology. Mobile nodes may be located on ships, trucks, cars, etc, and on very small portable devices. Due to the mobility the topology can change very quickly and unpredictably. Furthermore, new nodes can join and leave the network at any time. The network may get divided into sub-networks. A MANET can be envisioned to have dynamic, rapidly-changing, random, multi-hop topologies which are composed of relatively bandwidth-constrained wireless links. Source Destination Figure 1. Mobile Ad-hoc Network (MANET) 3

13 1.2 Applications of Mobile Ad-hoc Networking (MANET) MANETs are of interest because they do not require any prior investment of fixed infrastructure. When a fixed backbone is not available, a readily deployable MANET can be used. In rural areas and third world countries, where basic communication infrastructure is not well established, MANET may be readily deployable at low cost. MANET may allow person-to-person, person-to-machine and machine-to-machine communications. There may be wide range of commercial applications possible to deploy using MANET, for example: Business associates sharing information during job and meeting, Students using laptops may participate in an interactive lecture, Emergency disaster relief personnel coordinating efforts in natural disasters. For obvious reasons there has also been a great interest from military and defense research organizations in MANET and its applications. This master thesis project work is done in co-operation with The Swedish Defense Research Agency (FOI). 1.3 Radio resource allocation and traffic rates In a MANET, topology changes results in changing traffic rates over the links in the network. In a radio network the channel resources are one of the most limiting factors, it is therefore very important that this resource is used as efficiently as possible. The Medium Access Control (MAC) protocol is responsible for how this resource is divided between the nodes (or links). Two common MAC protocols used in mobile ad-hoc networks are Time Division Multiple Access (TDMA) and Spatial Time Division Multiple Access (S-TDMA). TDMA TDMA is a channel access scheme that divides the scarce radio resource into small time durations, known as time slots. These time slots are uniquely allocated to nodes such that only one node can transmit during its allocated time slots. 4

14 S-TDMA S-TDMA is a collision-free multi-hop channel access protocol. In S-TDMA the same time slot can be allocated to nodes that are sufficiently separated from each other. The sharing of time slots is done for nodes such that no (or small) interference is obtained. This increases the overall capacity of the system, in comparison with classical TDMA, as more than one node can transmit during same time slots. [2] TDMA is simple and easy to implement, but it is very inefficient from a resource utilization point of view. S-TDMA increases the overall capacity of the system, but it is important to design efficient time slot scheduling algorithms so that different nodes (or links) can get their fair share. In order to do this, precise knowledge on the traffic situation is needed. If the time slot allocation is done with precise knowledge of the traffic load, more efficient allocation results than just assuming uniform traffic can be achieved [3][4]. A very important issue is therefore to make accurate estimations of the traffic flows that each node handles Traffic sensitive S-TDMA scheduling There are a number of studies attempting to find good traffic sensitive S-TDMA schedules, based on slots allocation with knowledge of the traffic load. A critical description of some of these studies follows. In [3], Somarriba has described a traffic sensitive S-TDMA schedule, named Enhanced Schedule (ES). His novel systematic procedure to find transmission schedules in S- TDMA system is based on the traffic load in each link. The approach suggested in his work is a combination of the basic S-TDMA protocol proposed in [2], together with some extra slots allocated to the heavier loaded links. His work concludes that traffic-sensitive schedules show better performance in comparison to the classical S-TDMA. His simulation results show an improvement of up to 30% in comparison with the Basic Schedule in classical S-TDMA. Some other attempts have been made by Robertazzi and Shor. [4] They have presented a distributed traffic sensitive algorithm, called The Degree Algorithm. It uses node degree (the number of active, incident links to a node) as the basis for establishing priority during the process of generating schedules. The basic idea it uses is that the more incident links a node has, the more traffic it will carry and the more slots it should be assigned. It 5

15 has shown better performance than its counterpart non-traffic sensitive distributed algorithm of Ephremides and Truong both in terms of deficiency and surplus. [4] 1.4 Aim and motivation of the thesis project work The aforementioned research work makes it obvious that for good network performance, the nodes (or links) with heavy traffic loads need to access the channel more often than the nodes (or links) with small traffic loads. If time slot allocation is done on the basis of the time-dependent traffic loads on the nodes, then channel/resource utilization could be improved. How can these time-dependent traffic loads on the nodes or links be estimated? What traffic estimation methods have been used in earlier research work mentioned above? How good traffic estimates they produce? How to evaluate them to know how well they perform? There are many questions that need to be answered. This master thesis reports will answer the above listed questions. 1.5 Outline of the Thesis Report The short description of the forthcoming chapters, given below, will give a brief idea of how this report has been organized: Chapter 2 Chapter 2 is about traffic load estimation methods. We first present existing traffic load estimation methods. We then explain their limitations in live networks scenario and propose a traffic load estimation method based on an exponential decrease function that has been analyzed in this research project work. Chapter 3 Chapter 3 is about Implementation and Evaluation Issues. We present a method that could be used in performance analysis of the proposed traffic load estimation method. We describe how correct values (also called true values) of traffic load are calculated on the relative scale and present how estimations of traffic load are done, based on the proposed traffic load estimation method. We also highlight simulation assumptions and considerations. 6

16 Chapter 4 In chapter 4 we present the simulation results and analysis of estimated traffic load in ad-hoc networks. We have analyzed both static and mobile ad-hoc networks. Performance analysis results have been shown about how good, estimates are made by the proposed traffic load estimation method. We present fine tuning of the two parameters; Window Size T ws and gamma γ. Chapter 5 Chapter 5 is about conclusions and recommendations for further research work. Appendices This report has five appendices: Appendix A is about summary of analyzed networks (NWs). We list studied networks and provide their details. Appendix B contains detailed plots for traffic load analysis of mobile ad-hoc Networks. Appendix C describes the mobility model used and average maximum transmission distance in simulation of mobile ad-hoc networks at FOI. Appendix D is about routing and traffic data structure and formats. Appendix E describes models for traffic load generation. In the end, references are listed. 7

17 2 Traffic Estimation Methods We will first describe existing traffic load estimation and measurement methods that have been used in mobile ad-hoc networks research, in an attempt to find an optimum slot allocation algorithm. They are explained in sub-sections 2.1 and 2.2. We will then talk about their limitations that make them inefficient to use in live networks. Finally, in section 2.4, we will propose a new traffic load estimation method that has been analyzed during this research project work. 2.1 Traffic Matrix of the load on each link based on the number of routing paths using a link This method has been used at least in two research studies. [5][6] According to this method the traffic load that can be expected to flow in each link (i,j) is based on the number of routes (or paths) that use the link (i,j). This method probably works for all forms of routing (more or less). However it assumes that the traffic load on each route (or path) is equal. So, as long as different routes (or paths) carry exactly the same traffic, this method gives the correct values of traffic load on the relative scale. Although this might be true for uniform traffic load distribution, it is generally not true. Let λ ij be the traffic load on a link (i,j). Then ( using the link (, )) λ ij µ paths i j = equation 2-1 Where µ is the traffic load on each route (or path). Since traffic load distribution is uniform, so µ is given by (for a fully connected network): µ = λ NN ( 1) equation 2-2 Where λ is the total traffic load over the whole network and N is the total number of nodes in a mobile ad-hoc network. 8

18 Denote the number of paths that use the link (i,j) as λ λ = µ P = p NN ( 1) ij ij ij p ij. So equation 2-1 implies: equation 2-3 p ij depends on the routing protocols used and it is an undirected measure of the traffic load that can be expected to flow through the link (i,j). It is the measure of the traffic load on the relative scale. From the traffic sensitive S-TDMA slot allocation algorithm point of view it does not matter if we measure traffic load as λ ij or as p ij on the relative scale. It is preferred to use p ij as an undirected measure of the traffic load on the relative scale as network might not be fully connected and there might be packets loss. Let L ij be the relative traffic load flowing through the link (i,j). Then: L ij = P ij equation 2-4 This L ij are the correct values of traffic load flowing through the link (i,j)on the relative scale. (See section for the correct values of traffic load flowing through the node on the relative scale. I also call them True values of traffic load at a node.) The following research studies have been based on this method. Traffic Load Matrix based on Minimum Hop Routing (MHA), used by Somarriba. [3][5] Traffic Load Matrix based on Most Forward Routing (MFR), used by Robertazzi and Shor. [4][6] Illustration with example Consider a small mobile ad-hoc network example as shown in Figure 2. It consists of six (6) nodes that are numbered from node 1 to node 6. We will show how the relative traffic load Lij can be calculated based on the above described method. Note that uniform traffic load distribution is assumed, i.e. each route carries equal load. 9

19 Figure 2. Small 6-node mobile ad-hoc Network Topology Now consider the routing table as presented in Table 1. In this table, six nodes are also numbered from node 1 to node 6. Here the cell (i,j) means that node i has to transmit to node j via node k; where cell (i,j) has the value k. Node k is the next node en route to node j from node i. In this illustration i means row and j means column. For example the cell (1,3) has value 2. It means that node 1 has to transmit to node 3 via node 2. Note that (i,j)th entity is equal to -1 iff i = j as nodes can not transmit to themselves. Table 1 Sample Routing Table Nodes node 1 node 2 node 3 node 4 node 5 node 6 node node node node node node

20 Now we will proceed as follows: 1) If (i,j)th cell value is equal to j that means node i is transmitting to node j and node j is the final destination for current routing path. A relative load value of 1 will be added for the link (i,j) to the total relative load of this link. 2) If (i,j)th cell value is not equal to j that means node i is transmitting to node j via some intermediate node, say node k. In this case, a relative load value of 1 will be added for link (i,k) to the total relative load of this link. It also means that routing path has not yet ended and we need to follow the rest of the routing path until packet reaches its final destination j. A relative load value of 1 will be added for all the used links in this scenario. Above stated steps will be applied to all distinct source-destination pairs; starting from (node 0, node 0) to (node 6, node 6). As a result of this procedure, when routing paths between every distinct pair of nodes have been taken into account, we will get relative traffic load values for all the links as presented in Table 2. Table 2 Matrix of the relative traffic load L ij on each link (i,j) Nodes node 1 node 2 node 3 node 4 node 5 node 6 node node node node node node Note:- Here entity (i,j) represents the relative traffic load value L ij of link (i,j). Value of cell (i,j) is the relative traffic load at this link. For 11

21 example value of cell (2,1) is 2. So relative traffic load for link (2,1) is L21 = P21 = 2. Node based relative traffic load The traffic load matrix gives relative traffic load estimation for each link. However, if we want relative traffic load estimation for each node, then this can be calculated by summing up the load of all the outgoing links of that node. This gives an idea of the relative number of time slots that must be allocated to each node to satisfy the load. The node with the largest load value may be arbitrary allocated a number of slots and all other nodes receive a number of slots which is proportional to their load as compared with the largest one Improvement suggestion If we have Quality of Service (QoS) implemented in mobile ad-hoc network, then, we may be able to know how much traffic load each route (or path) generates. This may allow us to improve this method so that it will also work for non-uniform traffic load distribution. 2.2 Traffic Estimation based on Node Degree Another traffic load estimation method that can be used in mobile ad-hoc networks is based on node degree. Node degree is the number of active, incident links to a node. It is a simple method where each node can determine its individual degree by monitoring transmissions from neighboring nodes. In [4][6] Robertazzi and Shor describe how their Degree algorithm uses node degree to allocate time slots based on the relative traffic estimation of a node. Their degree algorithm uses node degree as the basis for establishing priority. It assumes that the more incident links a node has, the more traffic it may carry and the more time slots it must be assigned. 2.3 Limitations of existing traffic load estimation methods The above described methods (sub-sections 2.1, 2.2), have limitations that make them inefficient in a real live scenario. They assume equal (uniform) traffic load distribution on each path (or link). If the non-uniform traffic load distribution is unknown, then they do not work at all. In practical live networks we can not assume uniform traffic load 12

22 distribution, so we need better methods for traffic estimation that should be independent of the type of traffic load distribution. In the next section 2.4, we will suggest a new traffic load estimation method that is based on simple mathematical calculations, that works for both uniform and non-uniform traffic load distribution. In fact, it does not care about the type of traffic load. However, one important thing to notice is that the method explained in section 2.1, based on traffic matrix of the load, can be useful as a reference method as it gives correct values of traffic loads on the relative scale when uniform traffic load distribution is used. Section 3.1 will describe how it can be used for performance evaluation of other traffic estimation methods. 2.4 A proposed Traffic Load Estimation Method If we measure the inter-arrival time between two packets, say t seconds, and size of packet, say L bits. Then the traffic load through the node, say L est be give by: Inter-arrival time between two packets t bits L est L = t seconds NODE L Length of Packet Another way is to take time average over time, say T ws. This implies: L est 1 = n Tws packets seconds equation 2-5 Where L is the estimated traffic load through the node, n is the number of packets that est have arrived in the time T ws. A design parameter here is the time T ws. We will call it the window size. Simulation studies will help us to choose appropriate value of window size T ws. 13

23 2.4.1 Exponential decrease traffic load estimation function The problem with time average is that it gives equal importance to all packets that have been received in window size T ws. But the importance of traffic load measured at a link, decreases with time. For instance the packet that has arrived most recent, say at time t n, should be given more weight compared with packets that have been arrived earlier in time. See Figure 3. t 1 t n-2 t n-1 t n --- T ws = Window Size, Total Time for n packets to be received. Figure 3. T ws = Total Time for n packets to be received. This importance of packets can be controlled and evaluated via exponential decrease estimation function: n ( ti ) est = γ i ws i= i L c e t T equation 2-6 Where L est is the estimated traffic load and t is the time since arrival of the packet. i T ws and γ are the design parameters that will be decided during simulation studies. c is a constant and controls relative load factor. c is equal to relative load factor times γ. Relative load factor is a constant value for the whole network during the window size T ws. It is used to normalize estimated traffic load values so that reasonable comparison can be made. It is γ that controls how much more importance should be given to recent packet arrivals compared with packets that have been arrived earlier in time. Larger value of γ means to give more importance to recent packet arrivals. However, small γ means to give all 14

24 packets almost same preference. We need to choose an appropriate value of γ during simulation studies so that we can have best estimation of traffic load L Time-dependent traffic load estimation Node mobility causes changes in traffic loads. Therefore, it is also important that the number of time slots allocated to a node must be updated regularly. In order to do this we must know the time-dependent traffic loads of the nodes. For highly mobile networks the traffic load updates must be done more often than for less mobile networks. In ideal case we can say that we must do load update as soon as possible. est 15

25 3 Implementation and Evaluation Issues As explained in previous chapter, the limitations of existing traffic load estimation methods make them inefficient for use in practical live networks scenarios. Therefore, we have proposed a new traffic load estimation method. This chapter will look into implementation and evaluation issues. We will present how performance analysis of the proposed traffic load estimation method has been done. 3.1 Performance Evaluation We need to have some way to evaluate how good estimates the proposed traffic load estimation method will give. Our proposed method does not care about the type of traffic that flows through the links and it should work well for both uniform and non-uniform traffic load distribution. However, the relative traffic load estimation method described in section 2.1 can give correct values of traffic load on the relative scale if uniform traffic is generated through the simulated mobile ad-hoc network. The requirements of this method are to have precise information and status of routing protocol(s) used in the simulated environment. Not only we need to know about routing matrices, but we also need to know the precise time when new routing tables are generated or routing matrices are updated. In Appendix D we describe some of the details of routing matrices that have been used during simulation. So, for the evaluation purposes, we can populate the simulated network with a uniform Poisson based traffic load distribution such that the method described in section 2.1 gives correct values of the traffic load on the relative scale. These correct values can then be compared with results obtained from our traffic estimation modules (implemented via the exponential decrease traffic load estimation function). This will help us to evaluate the accuracy of the estimates they give Correct Values (True Values) of traffic load on the relative scale As said, Correct Values of traffic load are based on routing information as well as the type of input traffic. In this case it is uniformly distributed Poisson data, which means the traffic load on each route (or path) is equal. 16

26 From this point on we call Correct Values of traffic load as the True values of traffic load. Say L True (i), are the true values of relative traffic load on each node i, which are calculated as the sum of relative traffic load on all the outgoing links (i,j) of the node i. Consider the Figure 2 and Table 2. L ij is the relative traffic load on the outgoing link (i,j) of the node i (See equation 2-4), then, true values of relative traffic load, for node i are give by: L ( i) = n True L ij j = 1 where n is the total number of outgoing links from node i. equation 3-1 Table 3 L True (i) for nodes of Figure 2 Node i L True (i) Estimated Values of traffic load Estimated Values of traffic load, say L est (i), in packets per second are estimated as described in sub-section 2.4 for each node i. We have used both methods as they are inter-linked with each other. Time Average is a special case of Exponential Decrease Load Estimation Function when same importance has been given to all packets, i.e. when γ is equal to zero: 17

27 Method 1: Time Average This method is a special case of method 2, when γ is equal to zero. It is just time average over time T ws (Window Size). See equation 2-5 at page 13. Method 2: Exponential Decrease Load Estimation Function This is a general function that we have used for traffic load estimation. It controls importance given to each packet via parameter γ. See equation 2-6 at page Relation between Method 1: Time Average and Method 2: Exponential Decrease Load Estimation Function equation 2-6 implies: L est [ ( ) ( ) ( ) ( )] γt t t n t e 1 γ 2 γ γ + e e + e n 1 = c Time average is a special case of exponential decrease load estimation function when same importance has been given to all packets, i.e. when γ = 0 and c = (1/T ws ), i.e.: 1 Lest = e e... e e T ws 1 Lest = [ ] T (0) (0) (0) (0) ws equation 3-2 which is the time average i.e. the number of packets that have arrived in the time T ws (Window Size). equation 3-2 is equivalent to equation Performance Evaluation Criteria Let L est (i) be the relative estimated values of the traffic load and L True (i) be the relative true values of the traffic load for node i. Then, the absolute error difference between the true and estimated values of traffic load for node i is given by: ε () i = L () i L () i for node i. True est 18 equation 3-3

28 MSE (Mean Square Error) and Relative Traffic Load Error Difference (Percentage Error) are the two obvious choices for error analysis methods/techniques. They are described below. However, we will make traffic load estimation decisions on the basis of only Relative Load Error Difference (percentage error). Justification for this choice is presented in section MSE (Mean Square Error) MSE (Mean Square Error) is given by: ε () i MSE ( ()) i = ε 2 for node i. i.e. 2 MSE () i ( LTrue() i Lest ()) i for node i. ε = We need to choose design parameters (Window Size T ws and γ) so that ε MSE gets minimum for all nodes, i.e. ε MSE () i should be minimum. i Relative Traffic Load Error Difference (Percentage Error) Relative traffic load error, ε (i) for node i is given by: rel ε rel ( i) = L True ( i) L L ( i) True est ( i) Most often percentage error is used and relative traffic load percentage error, ε ( i) is given by: per _ rel ε per LTrue( i) Lest ( i) _ rel ( i) = 100 L ( i) True for node i. equation

29 In this case we need to choose design parameters (Window Size T ws and γ) so that ( i) ε per _ rel ( i) should be minimum. ε gets minimum for all nodes i.e. per _ rel We will use this as the basis of most of the decisions to choose design parameters Justification for Relative Load Error Difference (Percentage Error) The whole purpose of this research work is to estimate traffic load so that the time slots allocation schedule performs as well as possible. It is not necessary that it will perform well in all cases when MSE (Mean Square Error) gets minimum. In other words for a time slots allocation schedule to perform well it is not necessary that estimated load L est (i) should be as close to true load values L True (i) as possible. We need to focus on relative load error difference or percentage error. An example: Consider two nodes; node 1 and node 2. Suppose for node 1, relative true traffic load L True(1) is 50 and for node 2, relative true traffic load L True(2) is 2. A good traffic sensitive time slots schedule should give node 1 many more time slots than node 2. The best should be to allocate 25 times more time slots to node 1 compared with node 2. MSE (Mean Square Error): Now suppose that we have an error in the estimated traffic load, with MSE both of these nodes are equally bad. Let s say error ε ( i) = LTrue ( i) Lest ( i) = 5, so our estimated traffic load looks like: Estimated traffic load at Node 1: L est (1) = 55 [error +5]. Estimated traffic load at Node 2: L est (2) = 7 [error +5]. MSE will give equal importance to estimated traffic load error in both cases; node 1 and node 2. A good traffic sensitive time slots allocation algorithm based on above estimated traffic load will now only assign 8 times more time slots to node 1 compared with node 2. This might be too few time slots allocation for node 1 and too much for node i

30 Relative Load Percentage Error: Relative Load Percentage Error in this case will be: For Node 1: ε For Node 2: ε per _ rel per _ rel LTrue(1) Lest (1) 5 (1) = 100 = 100 = 10% L (1) 50 True LTrue(2) Lest (2) 5 (2) = 100 = 100 = 250% L (2) 2 True This means that Relative Load Percentage Error will not give equal importance to both cases; node 1 and node 2. It tells us that there is a big difference in error in these two cases. So, better decisions can be made on this basis. 3.2 Simulation assumptions and considerations This research work has been done in co-operation with FOI (The Swedish Defense Research Agency). [7] Simulation studies for this research work have been performed in two parts. The first part, done at FOI, simulates mobile ad-hoc networks, generate traffic load data, populate the simulated network with the generated data and capture the raw traffic data at each node. The required data with routing information is then bundled in CDs and shipped to the author to perform 2 nd part of simulation. The simulation software used at FOI is named aquarius. It has been used to simulate networks and generate Poisson distributed uniform traffic load as described in Appendix A. Each simulation run from FOI consists of 12 hours, i.e. 12*60*60 = seconds. Three instances of traffic load have been generated for all analyzed networks, with increasing values of overall network load: 1 st instance: Poisson parameter, λ = overall network load = 20 packets/seconds. 2 nd instance: 21

31 Poisson parameter, λ = overall network load = 40 packets/seconds. 3 rd instance: Poisson parameter, λ = overall network load = 60 packets/seconds. aquarius provides routing tables and traffic data flow in each node in a network as described in Appendix D. It provides packets arrival times and transmission times for each node in the network during a simulation run. For the 2 nd part of simulation, Traffic Estimation Modules/Routines have been written in MATLAB that implement traffic estimation method as described in section 2.4. This is the focus point of this research work. MATLAB modules/routines that have been coded can be requested from author Routing Minimum Hop Routing has been used. In Minimum Hop Routing, the route with minimum number of hops has been used when a packet has to be transferred from source to destination. The shortest path is not necessary the best possible path. Routing paths are generally stored in routing matrices at nodes. It is the routing matrices that will give us true values of the traffic load as described in section 2.1. See Appendix D for details of routing data structure in simulation environment MAC Protocol Only plain TDMA (Time Division Multiple Access) has been used as the Medium Access Control (MAC) protocol. In TDMA time is divided into small time durations, known as time slots. These time slots are allocated to mobile ad-hoc network nodes, so that only the node that has been allocated the present time slot may transmit. S-TDMA (Spatial Time Division Multiple Access) has not been used during this research work. As discussed earlier, in S-TDMA, the same time slots can be allocated to more than one nodes that are geographically separated so that are no transmission conflicts arising from neighboring nodes. The reasons for using TDMA are that it is simple and easy to implement. Moreover from a traffic estimation point of view it does not matter if we use TDMA or S-TDMA. This 22

32 research work focuses on traffic load estimation. Any MAC protocol can take advantage of traffic load estimation if feedback between MAC and traffic load estimation modules has been designed and used Mobility We have also considered node mobility as the node which once may carry heavy traffic load, when it changes its position, it may then carry low traffic load (or nothing) and vice versa. It is therefore important that the number of time slots allocated to a node (or link) must be updated regularly. In order to do so we must know the time-dependent traffic loads of the nodes. First step; load analysis of static ad-hoc networks As a first step, static ad-hoc networks have been analyzed with no mobility. In Appendix A we have given a list of analyzed static ad-hoc networks. In static networks, the topology does not change during the simulation period (in this case of 12 hours) as nodes do not move. That means there are no changes in a routing table(s). Infact, routing table remains un-changed during the simulation period of analyzed networks. This leads to a constant load throughout the life time (in this case of 12 hours) of the simulated network as we are generating uniform Poisson based traffic load. Traffic load analysis of static ad-hoc networks will help us in making general conclusions. For example, how long time it takes to get appropriate values of estimated load. Static ad-hoc networks may help us in verifying if we are proceeding in a right direction and analyzing in a proper way. They may tell us if our implementation of traffic load estimation modules is correct. Traffic load estimation of static ad-hoc networks is assumed to be simple and close to true values as we are generating uniformly distributed Poisson based traffic load. Second step; load analysis of mobile ad-hoc networks In step two, mobile ad-hoc networks have been analyzed. Please refer to Appendix A for a list of analyzed mobile ad-hoc networks. In order to generate movement of mobile ad-hoc network nodes, a simple 2-dimensional random walk mobility model has been used. Please look in Appendix C about how this mobility model has been implemented. 23

33 This is the major part of analysis work. Analysis of static ad-hoc networks is a step to proceed towards analysis of mobile ad-hoc networks Geographical area of the mobile ad-hoc network The mobile ad-hoc network nodes movement is bounded in a square and the length of the square is 1000 meter (1 Km) for all analyzed networks. This is supposed to give reasonable scenario which is close to real military case where 10 to 20 mobile nodes are scattered within 1000 meter square boundary. From the traffic load estimation point of view what matter is the number of packets received at a node and radio connectivity between nodes, not the area of the network Average maximum radio connectivity distance between nodes The radio connectivity between mobile nodes is chosen such that in each network scenario, at least 95% of all node pairs can communicate by single- or multi-hop connections. That means the transmitter power is chosen to get the connectivity that allows at least 95% of all node pairs to communicate. The average maximum transmission range has been estimated at FOI. It is approximately same for the different network scenarios when they are bounded within a 1000 meter square boundary if the simulation time is large. We refer to appendix C.2 for average maximum transmission range (in meters) for networks with 2 to 24 mobile nodes moving around for 12 hours in a 1000 square meter area. 24

34 4 Simulation results and analysis of traffic load estimation 4.1 Traffic Load Estimation for Static Ad-hoc Networks The following design parameters will be optimized to get the estimated traffic load values for static ad-hoc networks so that the relative load estimation error gets minimum: Gamma γ It controls the importance given to most recent packets arrival. Window Size T ws It answers for how long time we need to count packets arrival at a particular node to get the best possible results in terms of minimum relative load estimation error. Our simulation results indicate that the best results can be achieved, in terms of minimum traffic load estimation error, when gamma γ is zero and when window size T ws is maximum. This is what should be expected for Poisson distributed traffic load. When the window size becomes large, the number of packets that have been received during this time becomes large. If n is the number of packets that have been received during window size T and λ is equal to mean arrival rate then: ws n λ = E ( Poisson distributed load ) = Tws Optimum values of Gamma γ packets seconds equation 4-1 We refer to exponential decrease traffic load estimation function [equation 2-6] as described in section During simulation studies, we need to choose a value of γ so that our estimated traffic load matches true values of traffic load or provides us with the best possible traffic load estimation. 25

35 In Figure 4, we plot traffic load estimation error in percentage verses packets λ seconds λ ( packets). γ 1 seconds γ Traffic load estimation error, say ε per _ rel ε per _ rel, has been calculated as: s n 1 1 nodes LTrue() i Lest () i = 100 s samples= 1 n i= 1 LTrue() i equation 4-2 Where s means total number of samples and n nodes means total number of nodes. This plot shows that estimation error increases as γ increases and vice versa. Best estimation can be made when γ is as small as possible (i.e. when γ is close to zero). Gamma γ equal to zero means to give equal importance to all packets. This is what was expected for uniform Poisson distributed traffic load. The plot also indicates that estimation error decreases as we have more packets to analyze. This plot is for three instances of twenty nodes static ad-hoc network with overall network traffic load λ = 60 packets/sec, 40 packets/sec and 20 packets/sec. The ideal plot of twenty nodes, with overall network traffic load λ = 60 packets/sec has also been shown. In ideal case there is no packet loss and we know exact value of traffic load λ for whole network, which is 60 packets/sec. This gives an idea of how the curve should look like for a single node in ideal case for Poisson based traffic load distribution. However, the analyzed networks are far from ideal situation. First, there is packet loss of about 5%, so we do not know precise value of overall network traffic load λ, neither precise value of traffic load at individual nodes. Second, different nodes of the static ad-hoc networks have different traffic load and there is a wide difference on the relative scale. Third, in our analyzed networks relayed traffic does not follow Poisson characteristics. Still we can see that the traffic load estimation error in analyzed static ad-hoc networks follows the ideal cure and slope of y = 1 2 x on the log scale. It means that ε per _ rel 1 packets 26

36 Figure 4. Analysis of Gamma γ values when Window Size is constant plot of Traffic Load Estimation Error verses Lambda / Gamma According to Sheldon M. Ross, the probability that the sample mean of estimation error values differs from true value by more than 1.96 is approximately 5%. [8] s σ ε σε Here s means total number of samples and s of estimation error values. It is given by: is the standard deviation of sample mean 27

37 1 s σ ε samples= 1 s = s ( ) 2 ε per _ rel ε samples per _ rel s equation 4-3 Note that σ ε is the standard deviation of individual sample. ε per _ rel is called sample mean and is given by: ε s 1 = ( ε ) _ per _ rel per rel s samples= 1 samples equation 4-4 σε Standard deviation of sample mean of estimation error values has also been plotted s in Figure 4 for these three instances of twenty nodes static ad-hoc network with overall traffic load λ = 60 packets/sec, 40 packets/sec and 20 packets/sec. Since, the values of σ are too small, you can not see them in Figure 4. It s mean value is approximately - ε s 0.7 db Optimum values of Window Size T ws We need to find the optimum value of window size T ws, so that we can get minimum estimation error. In the side figure, T ws is shown. We will analyze packets that have arrived during T ws. We will use γ equal to zero for best estimation. See equation 3-2, exponential decrease traffic load estimation function will become the time average for window size T ws. In Figure 5, we plot traffic load estimation error t T ws = Window Size t n-2 t n-1 t n Tp = Time Period to Re-Compute Load. T ws = Window Size Tp = Time Period to Re-Compute Load. 28

38 verses T ws ( seconds ) Tws λ λ ( packets) packets seconds. For each T ws, traffic load estimation error ε per _ rel, has been calculated according to equation 4-2. This plot is for three instances of twenty nodes static ad-hoc network with overall network traffic load λ = 60 packets/sec, 40 packets/sec and 20 packets/sec. The plot shows that estimation error decreases as T ws increases and vice versa. Best estimation is made when T ws becomes large as expected for Poisson distributed traffic load. The plot also indicates that estimation error decreases as we have more packets to analyze. The ideal plot of twenty nodes, with overall network traffic load λ = 20 packets/sec has also been shown in this case. As said earlier, in ideal case there is no packet loss and we know exact value of overall network traffic load λ, which is 20 packets/sec. This gives an idea of how the curve should look like for a single node in ideal case for Poisson based traffic load distribution. However as stated earlier the analyzed networks are far from ideal situation. First, there is packet loss of about 5%, so we do not know precise value of overall traffic load λ. Second, different nodes of the static ad-hoc networks have different traffic load and there is a wide difference on the relative scale. Third, in our analyzed networks relayed traffic does not follow Poisson characteristics. In this case, also, traffic load estimation error follows the slope of ideal cure i.e. y = 1 2 x on the log scale. 29

39 Figure 5. Analysis of Window Size when Gamma γ is zero plot of Traffic Load Estimation Error verses Window Size times Lambda This plot also indicates that we do not have to take very long time averages for acceptable estimation error. It depends on what is the acceptable estimation error, but in general time averages with 1000 packets (or more) achieve estimation error below 5%. Standard deviation σε s of sample mean of estimation error values has also been plotted in Figure 5 by using equation 4-3. Since, the values of them in Figure 5. It s mean value is approximately -1 db. σε s Traffic estimations get better for high traffic loads are too small, you can not see Figure 5 also indicates that traffic load estimations get better for high traffic loads when Tws is constant. For high traffic loads, λ gets higher and this gives more packets to analyze within a window size. As a result estimation gets better. The blue curve in Figure 5 is for high traffic loads (λ = 60 packets/sec). 30

40 In general, traffic load estimation error decreases as packets to be analyzed increases. Packets to be analyzed will increase whenever Tws or λ (which is packets per time unit) will increase (or both). This is what we were expecting as when λ increases we have more data packets to analyze per time unit. When we have more data (i.e. high traffic loads) our load estimates get closer to true values. 31

41 4.2 Traffic Load Estimation for Mobile Ad-hoc Networks In this section, for mobile ad-hoc networks, we will also attempt to find the optimum values of window sizes T ws to count number of packets that have arrived during this time and optimum values of gamma γ that controls the importance given to packets so that best estimation can be made. Similar to traffic load analysis for static ad-hoc networks, simulation results indicate that the best results can be achieved in terms of minimum percentage error, when γ is close to zero. However γ is not exactly equal to zero for optimum results. Optimum value of γ increases as network nodes mobility increases that reduces the effective window sizes T. ws Furthermore, in contrast with static ad-hoc networks, we can not use maximum window sizes T ws (time duration) to get best results. In fact, the optimum value of T ws depends upon the speed of the network nodes Optimum values of Window Size T ws We need to find the optimum value of window size T ws, to count for packets that have arrived in that time duration so that we can get minimum relative load estimation error. In case of static networks, where topology of networks does not change as nodes do not move, there is static non-changing routing matrix. (Refer to section 4.1.2) In those cases the longer the T ws, the better the results are. However, in case of mobile ad-hoc networks where nodes are moving and topology of network depends on the movement of nodes, we often have changes in routing matrices that depends on the speed of the nodes. In these scenarios we can not achieve better results by simply counting number of packets for longer T ws. Figure 6 presents analysis of optimum values of T ws when γ is equal to zero. Optimum window size T opt has been calculated so that estimation error gets minimum for whole network. First for each window size T ws, estimation error ε ws has been calculated by: ε ws n 1 nodes L () i L () i = n L i True est 100 i= 1 True() for each window size T ws 32

42 equation 4-5 Then, a sample of optimum window size minimum i.e.: T opt has been chosen for which ε s ws is T opt s n nodes 1 LTrue() i Lest () i min 100 T ws n i= 1 LTrue() i Finally, the optimum window size T opt that is plotted along the y-axis in Figure 6 has been calculated as the sample mean, i.e. T opt s 1 = s samples= 1 ( Topt ) s equation 4-6 Figure 6. Optimum Window Size verses Nodes Mobility for 10 nodes mobile ad-hoc networks 33

43 σt opt Standard deviation of sample mean of optimum window sizes T opt, say has also s been plotted for three instances of ten nodes mobile ad-hoc networks with overall traffic load λ = 60 packets/sec, 40 packets/sec and 20 packets/sec. Here, σ is the standard deviation of individual sample and is given by: Topt σ s 1 = ( T T ) 2 Topt optsamples opt s samples= 1 equation 4-7 where s means total number of samples and T opt is called sample mean of T opt, it is given by: T s 1 = ( T ) opt opt samples s samples= 1 equation 4-8 We can see that optimum values of window size T opt depend on network nodes mobility. For less mobile network, rather longer window size produces better results, where as a rather small window size produces better results for highly mobile networks. For example, we could see in Figure 6 that window sizes of seconds produces better results for networks with average node speed of 2.5 meter per seconds., window sizes of 7-10 seconds produces better results for networks with average node speed of 10 meter per seconds and window sizes of about 4-6 seconds produces better results for networks with average node speed of 25 meter per seconds. This behavior was expected as changes in network topology and hence routing tables cause nodes, which once carry heavy traffic loads, to carry low traffic loads or no traffic at all and vice versa. There is high probability for fast moving network nodes to have many such changes compared with slow moving network nodes. Many such changes cause to use small window size to count for number of packets when estimating traffic load for best possible results in terms of minimum percentage error of traffic load estimation. In general, window size decreases as network nodes mobility increases. 34

44 1 Relative _ Speed packets Figure 7. Analysis of Optimum Window Size Figure 6 also indicates that T opt depends on traffic load. Figure 7 is an attempt to present analysis of T opt independent of traffic load and network nodes speed. On the y-axis it plots ( seconds T opt 1 packets ) λ( seconds ) 1 ( ) packets and on the x-axis it plots meters speed seconds 1 Relative _ Speed packets packets RadioRange( meters ) λ seconds Figure 8 plots the same on the log scale. From figure, it can be seen that the curve follows 2 the slope of y = x. That means that: 3 35

45 1 T λ opt ( Relative _ Speed ) T opt Relative _ Speed 2 3 Note: T opt 1 γ opt RadioRange is the average maximum radio transmission range (in meters) that has been estimated at FOI by considering the simulated network at discreet points (every second) and ignoring what happens in between the discreet points. We refer to appendix C.2 for estimation of average maximum transmission range when simulated mobile nodes moved around for 12 hours in a 1000 square meter area. 1 Relative _ Speed packets Figure 8. Log plot: Analysis of Optimum Window Size 36

46 4.2.2 Analysis of Estimation Error for optimum window sizes In Figure 9, we plot traffic load estimation error for optimum window sizes verses mobile ad-hoc network nodes mobility (node speed in meter/seconds). Estimation error has been calculated for optimum window sizes T opt using equation 4-2. Optimum window sizes, T opt has been calculated using equation 4-6. Standard deviation of estimation error values has also been plotted. It has been calculated using equation 4-3 and equation 4-4. Figure 9. Estimation Error for Optimum Window Size verses nodes mobility We can see that estimation error increases as nodes mobility increases. This is because T opt decreases as network nodes mobility increases. When we have small T opt, it means that we have less packets to analyze. According to the Poisson based traffic load the best estimation can be made when we have large T opt. When nodes mobility increases, T opt decreases and as a result estimation error increases. 37

47 In order to get independence from network nodes mobility, we plot estimation error 1 verses Relative _ Speed in Figure 10. Figure 11 plots the same on log scale. packets We can see that estimation error is proportional to number of packets. Estimation error 1 decreases as we have more packets to analyze or when Relative _ Speed packets decreases. 1 Relative _ Speed packets Figure 10. Analysis of Estimation Error for Optimum Window Sizes 1 Figure 11 shows that estimation error approximately follows the slope of y = x on the 3 log scale. That means estimation error, say ε approximately satisfies: per _ rel ε ( ) 1 3 per _ rel Relative _ Speed 38

48 1 Relative _ Speed packets Figure 11. Log Plot - Analysis of Estimation Error for Optimum Window Sizes We refer to Appendix B for detailed plot of 10 nodes mobile ad-hoc networks when mobility ranges from 2.5 meter per seconds to 25 meter per seconds with a gap of 2.5 meter per seconds. In those plots relation between T opt and estimation error can be analyzed in a single sub-plot Optimum values of Gamma γ We refer again to exponential decrease traffic load estimation function as described in section During simulation studies, we need to choose γ, that controls how much more importance should be given to recent packet arrivals, so that our estimated traffic load matches true values or provides us the best possible traffic load estimation. In Figure 12, we plot optimum values of γ verses nodes mobility (in meter/seconds). Optimum values of γ, say γ opt, have been calculated for large window size T ws. γ opt has 39

49 been chosen so that estimation error gets minimum for whole network. For each gamma value, estimation error ε γ has been calculated by: ε γ n 1 nodes L () i L () i = n L i True est 100 i= 1 True() for each γ. equation 4-9 Then, a sample of optimum gamma, γ opt s γ opt has been chosen for which ε s γ is minimum i.e.: n nodes 1 LTrue() i Lest () i min 100 γ n i= 1 LTrue() i Finally, the optimum gamma γ opt that is plotted along the y-axis in Figure 12 has been calculated as the sample mean, i.e. γ opt s 1 = s samples= 1 ( γ ) opt s equation 4-10 Figure 12 shows that optimum value of γ in mobile ad-hoc networks increases as nodes mobility increases. When nodes mobility increases, we expect more changes in network topology and hence more changes in routing tables. Many such changes cause to use high value of γ that gives more important to the most recent packet arrivals and hence effective window sizes decreases. 40

50 Figure 12. Optimum values of Gamma γ verses Nodes Mobility [Large Window Size has been used] opt Standard deviation of sample mean of optimum gamma γ opt, say has also been s plotted for three instances of ten nodes mobile ad-hoc networks with overall traffic load λ = 60 packets/sec, 40 packets/sec and 20 packets/sec. Here, σ γ is the standard deviation opt of individual sample and is given by: s 1 σγ = opt γ γ samples s samples= 1 ( ) 2 opt opt σ γ equation 4-11 where s means total number of samples and γ opt is called sample mean of γ opt, it is given by: 41

51 γ opt s 1 = s samples= 1 ( γ ) opt samples equation 4-12 Figure 12 also indicates that γ opt depends on traffic load. Figure 13 presents an attempt for analysis of γ opt independent of traffic load and network nodes speed. Figure 14 plots the same on the log scale. 1 Relative _ Speed packets Figure 13. Analysis of Optimum values of Gamma 42

52 On the y-axis it plots 1 seconds 1 packets packets λ seconds γ opt and on the x-axis it plots meters speed seconds 1 Relative _ Speed packets packets RadioRange( meters ) λ seconds 1 Relative _ Speed packets Figure 14. Log plot: Analysis of Optimum values of Gamma 43

53 From figure, it can be seen that the curve follows the slope of γ opt λ ( Relative _ Speed ) 2 3 ( _ ) 2 3 γ opt Relative Speed Note: γ opt 2 y = x. That means that: 3 1 T opt Analysis of Estimation Error for optimum gamma In Figure 15, we plot traffic load estimation error for optimum gamma verses mobile adhoc network nodes mobility (node speed in meter/seconds). Estimation error has been calculated for optimum gamma γ opt using equation 4-2. Optimum gamma γ opt has been calculated using equation Standard deviation of estimation error values has also been plotted. It has been calculated using equation 4-3 and equation

54 Figure 15. Estimation Error for Optimum Gamma verses Nodes Mobility We can see that estimation error for optimum gamma γ opt increases as nodes mobility increases. This is because γ opt increases as network nodes mobility increases. Higher value of γ opt means we are giving more weight to more recent packet arrivals and effective window size becomes small. In order to get independence from network nodes mobility, we plot estimation error 1 verses Relative _ Speed in Figure 16. Figure 17 plots the same on log scale. packets Similar to section 4.2.2, we can see that estimation error is proportional to number of packets. Estimation error decreases as we have more packets to analyze or when 1 Relative _ Speed packets decreases. 1 Relative _ Speed packets Figure 16. Analysis of Estimation Error for Optimum Gamma 45

55 1 Figure 17 shows that estimation error approximately follows the slope of y = x on the 3 log scale. So, just like earlier results presented in section of estimation error for optimum window sizes, estimation error for optimum gamma, say approximately satisfies: ε per _ rel ε ( ) 1 3 per _ rel Relative _ Speed 1 Relative _ Speed packets Figure 17. Log Plot - Analysis of Estimation Error for Optimum Gamma Comparing Figure 11 and Figure 17, we can also conclude that both traffic load estimation methods (see section 3.1.2) i.e. simple time average with optimum window sizes and exponential decrease estimation function with optimum gamma give almost same estimation error. 46

56 4.2.5 Explanation If window size is relatively large, then we expect that Large Window Size our estimated traffic load will slowly converge to the true value of traffic load. On the other hand, for relatively small window size, our estimated traffic load will quickly converge to the true value of traffic load. True Load Small Window Size However, in the later case estimation error will be higher. If ε per _ rel is the estimation error, then, for optimum window size T opt, we can write: 1 ε per _ rel Topt Relative _ Speed + Topt K2 ε per _ rel = K1 Topt Relative _ Speed + Topt By differentiating with respect to T opt and equating to zero: equation 4-13 dε 1 = 0 = K1 Relative _ Speed K2 T dt 2 ( ) 3 opt per _ rel 2 opt 1 K1 Relative _ Speed = K2 T opt 2 Relative Speed T ( ) 3 2 _ opt ( ) 3 1 T 2 opt Relative _ Speed 1 T opt Relative _ Speed ( )

57 However, T opt 1 γ, so we can also write: opt 1 1 γ opt Relative _ Speed 2 3 ( γ ) ( _ ) 2 3 opt Relative Speed Using above equations: Relative _ Speed 1 ε per _ rel ( Relative _ Speed ) ( Relative _ Speed ) ( ) 1 1 ε 3 per _ rel Relative _ Speed Relative _ Speed 1 1 ( ) 3 ( ) 3 ε per _ rel Relative _ Speed + Relative _ Speed ( ) 1 3 ε per rel Relative Speed 48

58 4.2.6 Comparison of Estimated and True traffic load In case of mobile ad-hoc networks, topology of network changes and hence loads at nodes change too. So we need to have periodic estimation of traffic load. The ideal thing is; of course, to do load estimation as often as possible. Detailed comparison of Estimated and True traffic load values for thirty instances of 10 nodes mobile ad-hoc networks has been presented in section B.2 of Appendix B. In this section a plot has been presented in Figure 18. It presents Estimated and True values of traffic load verses time for 10 nodes mobile ad-hoc network; nodes mobility is 10 meters/second, Poisson parameter lambda λ is equal to 20 packets per second and load update time is 5 seconds. This plot is only for two nodes; each sub-plot on left column is for node 0 and each sub-plot on right column is for node 1. It demonstrates the effect of window size T ws as it changes. The optimum value of window size T opt is seconds. The plot shows that how estimated traffic load differs from true values of traffic load below and above T opt. 49

59 Figure 18. Effect of window size T ws on Estimated Traffic Load, (Gamma γ = 0) 50

60 5 Conclusions and Recommendation for Future Work The proposed exponential decrease traffic load estimation method is a general traffic estimation method. It is intended for any kind of traffic load distribution. It depends on selection and optimization of following parameters: Gamma γ It controls weight-age given to each packet. Larger value of γ means to give more weight-age to recent packet arrivals. However, small γ means to reduce weight-age and γ = 0 means all packets should be given same weight-age. When γ is equal to zero, exponential decrease traffic load estimation function becomes the time average for window size T ws (See equation 3-2). Window Size T ws For how long time we should count number of packets arriving at a particular node. For static (or less mobile) ad-hoc networks larger time will be preferred. And for highly mobile networks small time is preferable. In this research work only Poisson based, uniformly distributed traffic load, has been estimated and analyzed. It is important to realize that true values of traffic load in our simulation only changes when routing changes due to changes in network topology as a result of mobility. Above parameters have been analyzed only for Poisson based traffic load and our results and conclusions are valid only for uniformly distributed Poisson based traffic load. However, the proposed traffic load estimation method based on exponential decrease function may also work fine for other traffic models if fine tuning of the above parameters have been made. The following conclusions can be drawn: 1) Estimation of traffic load in static ad-hoc networks is much better compared with estimation of traffic load in mobile ad-hoc networks. When large window size (that gives more than 1000 packets to analyze) is used estimation error gets below 5% in static ad-hoc networks (See Figure 4 and Figure 5). On the other hand in case of mobile ad-hoc networks the best result gives 51

61 estimation error about 10% for low mobile network (See Figure 9 and Figure 11). Estimated load percentage error rate in mobile ad-hoc networks increases with increase in mobility. 2) Traffic load estimation error in both static and mobile ad-hoc networks depends on traffic load. For high traffic load we have got better load estimation than low traffic load. This is because we have more packets per time unit available for traffic analysis in case of high traffic load (For static ad-hoc networks, see Figure 4 and Figure 5. For mobile ad-hoc networks, see Figure 11). 3) For static ad-hoc networks, the larger the window size T ws, the better the estimation (See Figure 5). For mobile ad-hoc networks, the optimum value of window size T ws depends on nodes mobility as well as traffic load. It decreases as nodes mobility increases. It also decreases as traffic load increases (See Figure 6). We have found that: T opt 1 Relative _ Speed 2 3 4) For static ad-hoc networks, the best value for γ is 0 (See Figure 4). For mobile ad-hoc networks, the optimum value of γ depends on nodes mobility as well as traffic load. It increases as nodes mobility increases. It also increases as traffic load increases (See Figure 12). When nodes mobility increases, changes in network topology increases and we face more changes in routing tables. Many such changes cause to use high value of γ so that it gives more important to the most recent packet arrivals and hence effective window sizes decreases. We also have found that: γ ( _ ) 2 3 opt Relative Speed 52

62 5) Traffic load estimation error in mobile ad-hoc networks also depends on nodes mobility (See Figure 9 and Figure 15). When tried to get independence from network nodes mobility and traffic load, we found that estimation error is Relative _ Speed proportional to ( ) ). (See Figure 11 and Figure 6) In case of mobile ad-hoc networks, both traffic load estimation methods (see section 3.1.2) i.e. simple time average with optimum window sizes and exponential decrease estimation function with optimum gamma give almost same estimation error (See Figure 11 and Figure 17). The above conclusions suggest that traffic load estimation is feasible in ad-hoc networks, but, fine tuning of above described parameters is needed for optimum performance. 5.1 Recommendation for Future Work Analysis of more realistic packet data traffic models A number of traffic studies have shown that Poisson process is not very well suited for packet data traffic models as packet inter-arrivals are not exponentially distributed. [10] Also packet data traffic is bursty, statistically self-similar and fractal in nature. So other data traffic models, such as Traffic Arrival Model and/or WWW Traffic Arrival Model should be analyzed and parameters for proposed exponential decrease traffic load estimation method should be analyzed in this scenario. See Appendix E Models for Traffic Load Generation Average Network Throughput and Average Network Delay To further analyze proposed exponential decrease traffic load estimation method, feedback should be designed and implemented between traffic sensitive MAC algorithm(s-tdma) and exponential decrease load estimation function. Traffic sensitive MAC algorithm(s-tdma) can then get estimated load from feedback function and can assign slots based on estimated load. Then we may be able to analyze 53

63 how much over all performance of the network has been improved. The performance measures will then be Average Throughput and Average Network Delay Take account of Queue Lengths When allocating time slots, queue lengths of the active as well as neighboring nodes may also be considered in future research work. Consider the queue model as shown in Figure 19. λ l is packet arrival rate originated from local node. λ r is packet arrival rate due to relayed traffic originated from other nodes. L is the queue length at current node. When MAC algorithm (e.g. S-TDMA) allocates time slots, more weight or high priority may be given to longer queue for better results. For example when Queue Length, L = 0, that means there exists no packets (traffic) in corresponding link that need to be transmitted. As a result no (or less) time-slots should be allocated for that link even if it had a heavy load a moment ago. λ l = rate of packet arrival originated from local node. λ r = rate of packet arrival due to relayed traffic originated from other nodes. L = Length of Queue Figure 19. Queue Model Neighboring Queues can also be considered when prioritizing or allocation time slots. 54

64 Appendix A SUMMARY OF ANALYZED NETWORKS (NWS) This research work has been done in co-operation with FOI. [7] During traffic load estimation study we got raw simulated data from FOI for both static and mobile ad-hoc networks. Following networks have been simulated at FOI using aquarius simulation environment. A.1 Static Networks (NWs) studied 6 Nodes networks: Three instances of simulated network, each of 12 hours (12*60*60 = seconds) duration: Overall traffic load (Poisson parameter) λ = 20 packets/seconds Overall traffic load (Poisson parameter) λ = 40 packets/seconds Overall traffic load (Poisson parameter) λ = 60 packets/seconds 20 Nodes networks: Three instances of simulated network, each of 12 hours (12*60*60 = seconds) duration: Overall traffic load (Poisson parameter) λ = 20 packets/seconds Overall traffic load (Poisson parameter) λ = 40 packets/seconds Overall traffic load (Poisson parameter) λ = 60 packets/seconds A.2 Mobile NWs studied: 6 Nodes networks (mobility: 20 meter/seconds, area: 1000 meters): Three instances of simulated network, each of 12 hours (12*60*60 = seconds) duration: Overall traffic load (Poisson parameter) λ = 20 packets/seconds Overall traffic load (Poisson parameter) λ = 40 packets/seconds Overall traffic load (Poisson parameter) λ = 60 packets/seconds 55

65 20 Nodes networks (mobility: 20 meter/seconds, area: 1000 meters): Three instances of simulated network, each of 12 hours (12*60*60 = seconds) duration: Overall traffic load (Poisson parameter) λ = 20 packets/seconds Overall traffic load (Poisson parameter) λ = 40 packets/seconds Overall traffic load (Poisson parameter) λ = 60 packets/seconds 10 Nodes networks (area: 1000 meters): Thirty instances of simulated network, each of 12 hours (12*60*60 = seconds) duration. Mobility rate from 2.5 meter/seconds to 25 meter/seconds as shown below: NW Instances Time Duration Mobility Speed 56 traffic load (Poisson parameter) ג 3 12 hours 2.5 meter/sec 20 packets/seconds 40 packets/seconds 60 packets/seconds 3 12 hours 5.0 meter/sec 20 packets/seconds 40 packets/seconds 60 packets/seconds 3 12 hours 7.5 meter/sec 20 packets/seconds 40 packets/seconds 60 packets/seconds 3 12 hours 10 meter/sec 20 packets/seconds 40 packets/seconds 60 packets/seconds 3 12 hours 12.5 meter/sec 20 packets/seconds 40 packets/seconds 60 packets/seconds 3 12 hours 15 meter/sec 20 packets/seconds 40 packets/seconds 60 packets/seconds

66 3 12 hours 17.5 meter/sec 20 packets/seconds 40 packets/seconds 60 packets/seconds 3 12 hours 20 meter/sec 20 packets/seconds 40 packets/seconds 60 packets/seconds 3 12 hours 22.5 meter/sec 20 packets/seconds 40 packets/seconds 60 packets/seconds 3 12 hours 25 meter/sec 20 packets/seconds 40 packets/seconds 60 packets/seconds 57

67 Appendix B DETAILED PLOTS FOR TRAFFIC LOAD ANALYSIS OF MOBILE AD-HOC NETWORKS B.1 Detailed plots for analysis of window sizes T ws and corresponding estimation errors In Figure 20 and Figure 21, we plot traffic load estimation error verses window sizes T ws. Estimation error has been calculated using equation 4-2. Analysis of thirty instances of 10 nodes mobile ad-hoc networks has been pictured in these plots. Figure 20 presents analysis of first 5 nodes; nodes 0, 1, 2, 3 and 4. Figure 21 presents analysis of last 5 nodes; nodes 5, 6, 7, 8 and 9. Each instance of simulated network data consists of 12 hours (43200 seconds) and was captured at FOI in there local simulation environment. Each row represents three instances of 10 nodes mobile ad-hoc networks running at same speed and with three different loads. The load is generated via Poisson distribution with Poisson parameter, lambda λ, equals to 20 packets per seconds, 40 packets per seconds and 60 packets per seconds. Note that Poisson parameter, lambda λ, here represents overall ad-hoc network traffic load distribution. The speed/mobility ranges from 2.5 meters per second to 25 meters per seconds with a gap of 2.5 meters per second. Note that gamma γ is constant, which is zero. It means that equal importance (in terms of weight-age) has been given to all packets that have been received during the window size T. ws 58

68 Figure 20. Nodes 0, 1, 2, 3, 4: Estimation Error verses Window Sizes 59

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70 Figure 21. Nodes 5, 6, 7, 8, 9: Estimation Error verses Window Sizes B.2 Detailed plots of Traffic Load for 10 nodes mobile ad-hoc networks (running at average node speed from 2.5 meters/sec to 25 meters/sec) These plots illustrate the effect of mobility on traffic load estimation. From these plots it can be seen that as mobility (in terms of nodes speed as implemented according to section Appendix C) increases, the traffic load estimation error increases too. In these plots, ws T stands for window sizes and Tp stands for load estimation update time. Nodes are numbered from 0 to 9. Each subplot represents traffic load at one node, starting with node 0 and ending with node 9. 61

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83 Appendix C MOBILITY MODEL AND MAXIMUM RADIO TRANSMISSION RANGE (FOI) C.1 Mobility model used To generate mobile ad-hoc network nodes movement, a simple 2-dimensional random walk mobility model has been used. It has been assumed that all nodes in the mobility model moves independent of each other. Furthermore, all nodes move according to the same mobility model and use the same values for the constants that have to be defined in the model. To avoid that the nodes diffuse away from each other, we limit the nodes coordinates to be in a square, or more precisely ( x ( t), y( y) ) Ω = {[ 0, l] [ 0, l] } where l is the side of the square. If a node hits the boundary of the square, it will reflect back like a ball. We assume that the reflection is in-elastic. The speed v of a node is assumed to be constant, while the direction of a node s movement θ (t) is assumed to be given by ω ( t) = αω( t) + βµ ( t) ω ( 0) = 0 θ ( t) = ω( t) θ θ( 0) = U(0,2π ) where α and β are constants, µ θ (t) is a white Gaussian process with mean 0 and variance 1, and U is a uniform distribution. The coordinates of a node are then given by x ( t) = υ cos( θ ( t)) x( 0) U(0, l) y( t) = υ sin( θ ( t)) y( 0) U(0, l) In the Figure 22, below, an example of paths generated by this mobility model has been presented: 74

84 Figure 22. Path of three nodes generated by the random walk mobility model with α π 2 = 1 [1/s], [ rad / s ] β = and v = 20 [m/s]. 30 C.2 Maximum radio transmission range During simulation of mobile ad-hoc networks at FOI, the transmitter power is chosen to get the radio connectivity between mobile nodes so that in each network scenario, at least 95% of all node pairs can communicate by single- or multi-hop connections. The average maximum transmission range is approximately same for the different network scenarios if the simulation time is large. 75

85 The average maximum transmission range (in meters) for networks with 2 to 24 mobile nodes has been estimated at FOI. The nodes were moving around for 12 hours in a 1000 square meter area. The distance is calculated for a connectivity of at least 95% and a speed of 20 meter/seconds. Maximum Radio Range = r_max = [ ]. 76

86 Appendix D ROUTING AND TRAFFIC DATA STRUCTURE D.1 Routing Data Format The data.mat file comes with each instant of simulated network data, from FOI. It contains routing information. The routing tables are structured differently for static and mobile ad-hoc networks. D.1.1 Routing in Static Ad-hoc Networks For static ad-hoc network, variable routing_table contains routing information of the network. It is a single static routing table used for the whole life time of the network. For example the routing table of one of the 20 nodes static/fixed networks is: routing_table =

87 D.1.2 Routing in Mobile Ad-hoc Networks In the case of mobile ad-hoc networks routing matrix changes as soon as the topology of the network changes. It changes as quickly as nodes of the network are moving. The table below presents number of changes in routing matrices and nodes mobility for analyzed mobile ad-hoc networks. Number of Network Nodes 6 3 Number of Traffic Load Instances ג = 20 pckts/secs ג = 40 pckts/secs Time Duration 12 hours Mobility Speed 20 meter/sec Number of changes in Routing Matrix Coverage Area meters ג = 60 pckts/secs 20 3 ג = 20 pckts/secs ג = 40 pckts/secs 12 hours 20 meter/sec 1000 meters ג = 60 pckts/secs 10 3 ג = 20 pckts/secs ג = 40 pckts/secs 12 hours 2.5 meter/sec meters ג = 60 pckts/secs 10 3 ג = 20 pckts/secs ג = 40 pckts/secs 12 hours 5.0 meter/sec meters ג = 60 pckts/secs 10 3 ג = 20 pckts/secs ג = 40 pckts/secs 12 hours 7.5 meter/sec meters ג = 60 pckts/secs 10 3 ג = 20 pckts/secs ג = 40 pckts/secs 12 hours 10 meter/sec meters ג = 60 pckts/secs 10 3 ג = 20 pckts/secs ג = 40 pckts/secs 12 hours 12.5 meter/sec meters ג = 60 pckts/secs 10 3 ג = 20 pckts/secs ג = 40 pckts/secs 12 hours 15 meter/sec meters 78

88 ג = 60 pckts/secs 10 3 ג = 20 pckts/secs ג = 40 pckts/secs 12 hours 17.5 meter/sec meters ג = 60 pckts/secs 10 3 ג = 20 pckts/secs ג = 40 pckts/secs 12 hours 20 meter/sec meters ג = 60 pckts/secs 10 3 ג = 20 pckts/secs ג = 40 pckts/secs 12 hours 22.5 meter/sec meters ג = 60 pckts/secs 10 3 ג = 20 pckts/secs ג = 40 pckts/secs 12 hours 25 meter/sec meters ג = 60 pckts/secs Due to large number of routing matrices, routing matrices are presented in variables routes_n* in file, named data.mat. Where number of variables routes_n* are listed in nof_route_m. Each routing table in variables routes_n* is listed in one row as for example in one of the 10 nodes network: >> routes_n0(1, :) ans = Columns 1 through Columns 20 through Columns 39 through Columns 58 through Columns 77 through Columns 96 through

89 This has to be converted in proper routing matrix form. Following logic will do the trick: % Code extracted from m_true_load.m. Ask author to see m_true_load.m for full picture. % Loading Initial Data + Routing Table(s) % load('f:\sms_manet\cd1\data.mat'); load('f:\sms_manet\v1\data.mat'); r_10000 = nof_route_m; str_r_10000 = sprintf('%d',r_10000); c_nof_rt = 1; % Counter for Total number of Routing Table(s) in_rt_row = 10; in_rt_column = 10; max_node_number = in_rt_row - 1; % since node numbers start from '0' to '1 less than no. of rows' tmp_final_time_n = eval(['time_n', str_r_10000]); tmp = 2; while tmp_final_time_n(tmp+1) ~= 0 tmp = tmp+1; end nof_routes = r_10000* tmp; times = zeros(nof_routes, 1); routes = zeros(10, 10, nof_routes); nof_r = 1; ro = 0; while ro <= r_10000 route_row = eval(['routes_n', sprintf('%d',ro)]); if (ro == r_10000) counter_end = tmp; else counter_end = 10000; end for counter = 1:counter_end c = 1; 80

90 end for r_part =1:10:100 routes(:, c, nof_r) = route_row(counter, r_part:r_part+9); c = c + 1; end nof_r = nof_r + 1; end ro = ro + 1; The above routing table converted into proper routing matrix: >> routes(:, :, 1) D.2 Traffic Data Capture (at node) File format Traffic Data Capture File is named, e.g. tdma_node_11_rec_1.csv, where 11 means node number and 1 means (Poisson parameter, lambda = 20 packets per seconds). There are only three cases of Poisson parameters, they are: Poisson parameter, lambda = 20 packets per seconds Poisson parameter, lambda = 40 packets per seconds Poisson parameter, lambda = 60 packets per seconds [rec_1] [rec_2] [rec_3] The format of these files consists of 5 columns and it is as follows:

91 File format (5 columns): [start node, end node, session (not used for this application), creation time for the packet, arrival time to the queue] 82

92 Appendix E MODELS FOR TRAFFIC LOAD GENERATION This appendix describes different traffic models that could be used for packet data traffic generation purposes in simulation studies. The first sub-section describes the traffic model that is configured and implemented in the used simulation software at FOI, named aquarius. It is based on uniform distribution Poisson process. Poisson process [9] was earlier proposed for modeling of packet data traffic. Poisson processes are often used to model network arrivals for simplicity reasons. But a number of traffic studies have shown that packet inter-arrivals are not exponentially distributed. Also packet data traffic is bursty, statistically self-similar and fractal in nature. Also these models do not capture the duration of the ON and/or OFF periods that are found to be heavy-tail distributed which does not exhibit the memory-less property of exponential distribution [10]. Two of the most popular packet data applications on the Internet are and WWW browsing and it may also be the case in mobile ad hoc networks [In fact it depends on the type and usage of network]. Therefore and WWW traffic models have been suggested to use in future research work. They are described in sub-sections E.2 and E.3. E.1 Uniform Poisson Traffic Model Of course in most cases packet traffic does not obey Poisson distribution. However, it is still most widely used traffic model. Most of the present mobile ad-hoc network research uses Poisson distribution based traffic models. So this model has been used at FOI, in aquarius, for traffic generation purposes. In case of Poisson(λt) distribution, the number of arrivals N(t) in a finite time t is given by: (λt) n P{N(t) = n} = e -λt n! Where λ = mean arrival rate N(t) = number of arrivals in the interval (0, t) 83

93 Figure 23. Shape and probabilities of the Poisson distribution with λ = 10 The inter-arrival times are independent and obey the Exp(-λ) distribution: P{interarrival time > t} = e -λt λ = mean arrival rate t E.1.1 Mean, Standard Deviation and Variance If X is a Poisson random variable and λ is it s parameter, then: Expected Value of X = E[X] = λ = Weighted Average Value. Variance of X = Var[X] = λ = E[X]. Standard Deviation of X = std[x] = sqrt(var[x]) = sqrt(λ). 84

94 E.1.2 ON-OFF deterministic traffic based on Poisson process One of the traffic types that aquarius simulation software supports is the generation of "ON-OFF" traffic patterns from deterministic source. It creates deterministic sessions between two random nodes according to a Poisson process. Once a session is initiated it will give a fixed packet rate. It may be a good model for voice traffic. E.2 Traffic Arrival Model In [11], it is demonstrated that the arrival of messages to the mailbox can be approximated by a Poisson process. Individual user generates the ON/OFF traffic patterns in the downlink during an session as shown in Figure 24. An ON period represents the duration of a message download. The OFF period is the interval between the end and the beginning of two consecutive messages download. It may represent user reading time. ON OFF ON OFF ON... message download ends. User begins reading message. message download begins. Figure 24. Traffic Arrivals within a User Session E.3 WWW Traffic Arrival Model Each user s selectable link in a web page may involve one or more Universal Resource Locator (URL) requests. When a user submits an URL request, the WWW server executes a client program that generates response to the user. Depending on the content of the web page, additional requests may be generated by the client program. For example, the client program may initiate a separate request for each inline image. Each of 85

95 these requests establishes a new TCP connection that may overlap each other or be in sequential order. When all the requests related to the URL are complete, it will take the user some time to read the information before initiating the next request. Thus, we may capture the WWW traffic by a model which consists of active and inactive periods. The active period corresponds to the duration from the submission of request to service completion. It consists of the transmission time of the individual files and the active OFF time. The active OFF time is the relatively short time interval between two file receptions when the node is processing the received Web page component. The inactive OFF time is the time interval when the user is reading the received information. It is the duration between the completion of a service request and the beginning of the next service request. Figure 25 shows the WWW traffic arrival pattern. Active ON Active OFF Inactive OFF... User Click Active period Service Complete User Click Figure 25. WWW Traffic Arrivals within a User Session There are a number of studies [12] which investigate the distribution of ON and OFF periods. The ON time is a function of the file size and the available downlink bandwidth. 86

96 6 References [1] IETF MANET Working Group, MANET Charter, [2] Nelson, R., Kleinrock, L., Spatial- TDMA, A collision free multihop channel access protocol, IEEE Trans Comm., vol. COM-33, no. 9, Sept [3] Somarriba O., "Multihop Multi-hop Radio Networks in Rough Terrain: Some Traffic Sensitive MAC Algorithms", Dept. of Digital Systems and Telecommunications, Faculty of Electrical and Computer Engineering, National University of Engineering (UNI), Managua, Nicaragua, [4] Robertazzi, T., Shor, J., Traffic Sensitive Algorithms and Performance Measures for the generation of Self-Organizing Radio Network Schedules, IEEE Trans Comm, vol. COM-41, No. 1, Jan [5] Somarriba O., "Multihop Packet Radio Systems in Rough Terrain", Licentiate Thesis, Radio Communications Systems, Department of Signals, Sensors and Systems, Royal Institute of Technology, Stockholm, Sweden, October [6] Robertazzi, T., Shor, J., Traffic Sensitive Algorithms for Generating Self Organizing Network Schedules, Dept. of Electrical Engineering, SUNY at Stony Brook, Stony Brook, NY [7] The Swedish Defense Research Agency, [8] Sheldon M. Ross, Simulation, 2nd Edition, Statistical Modeling and Decision Science. [9] L. Kleinrock, Queueing Systems, Volume I: Theory, John Wiley & Sons, [10] V. Paxson and S. Floyd, Wide Area Traffic: The Failure of Poisson Modeling, IEEE/ACM Trans. on Networking, Vol. 3, No. 3, June [11] Y. Zhu, J. Ho and L. Beauchamp, Traffic Modeling at the Access Link, Nortel Networks Technical Report, [12] P. Barford and M. Crovella, Generating Representative Web Workloads for Network and Server Performance Evaluation, Proc. ACM Sigmetrics 98,

97 [13] D. Stiliadis, Traffic Scheduling in Packet Switched Networks: Analysis, Design, and Implementation, Ph.D. Thesis, University of California, Santa Cruz, June [14] H. Heffes and D. M. Lucantoni, A Markov Modulated characterization of Packetized Voice and Data Traffic and Related Statistical Multiplexer Performance, IEEE JSAC, Vol. SAC-4, No. 6, pp , Sept [15] B. Shrader, M. S anchez, and T.C. Giles, "Throughput-delay Analysis of Conflictfree Scheduling in Multihop Ad-hoc Networks", Radio Communication Systems Lab., Department of Signals, Sensors and Systems, KTH, [16] M. S. Taqqu, W. Willinger, and R. Sherman, Proof of a Fundamental Result in Self-Similar Traffic Modeling, Proc. ACM SIGCOMM. 88

98 Review Report Traffic Estimation in mobile ad-hoc networks (MANET) by SYED MUSHABBAR SADIQ Markus Sjöberg Radio Communication Systems Laboratory Department of Signals, Sensors and Systems 24th May Introduction The thesis is an evaluation of a traffic load estimator for ad-hoc networks. The idea is to make an estimation of how much resource, number of slots in a TDMA systems, to be spent for each node. Since the routing of an ad-hoc network makes different links carry different load, the performance of the network must improve, adjusting the resource allocation accordingly. The thesis introduces a traffic estimator which makes calculations based on previously sent packets. It further discusses optimization of two parameters, which defines the memory of the algorithm. The network under study has poisson-distributed load and different mobility. 2 Problem formulation In chapter 1.4 no limitations are stated: Will the results apply for other than poisson distributed traffic? The proposed algorithm, equation 2-6, does not consider lengths of packets. If sent packets are of different lengths, method described in extended by exponential decrease averaging over T ws should give better estimates. 3 Performance measure In section estimation error definitions are discussed. For each node a load is estimated, L est (i), and compared with True load, L T rue (i). The error measure of node i must then be some function of ɛ(i) = L T rue (i) L est (i). A strange definition of Mean Square Error is made, where t and T are unknown parameters. These parameters are not present in the relative error method, making them difficult to compare. 1

99 The choices might be split into two questions: For each node, should we use absolute error, ɛ(i), or relative error, ɛ rel (i), as in equation 3-4? Second, the total error measure. Either plain sum or MSE? ɛ(i) or i (ɛ(i)) 2 i To choose a method does not seem to be obvious. In section an example is given to motivate the use of relative error measure. The example is telling how resources are shared when the estimated loads are in error. But since the MAC protocol is only aware of the estimate and not of the error, it will perform the same, no matter how error is measured. The motivation of using relative error measure is difficult to capture from the text. We would like to do more efficient allocation, based on estimated load for each node. Parameters will be adjusted such that the estimator gives nodes recourses in proportion to their load. So, while adjusting these parameters, will the result be different if absolute or relative error measure is minimized? How? 4 Results In figure 7, true and estimated loads are shown as a function of time. The plot makes the impression that the estimate is biased. Has the estimate average been studied for longer time periods to verify if it is biased or not? If so, What can be done to minimize this? The optimization of the two parameters has been done separately. Optimum T ws is searched for while γ is set to zero etc. It might be to deep into details, but if this algorithm is going to be implemented, there must be a table combining γ and T ws for a certain mobility? Probably there will exist pairs of (γ, T ws ) where γ 0 and T ws. Would it not be of value to optimize the parameters together? What is supposed to be viewed in figure 9, 10, 15 and 16? What are the conclusions to draw from those graphs? In the comments of figure 19 it says that estimation error is almost the same as in figure 13. The conclusion that must be drawn is that the introduction of exponential decrease and parameter γ, is of no, or very little, impact of the estimator performance, compared to plain averageing over T ws. 5 Conclusions The proposed algorithm measures previous load, and it might thus be implemented for nonpoisson traffic systems. On the other hand this thesis is based on poisson traffic. Assume you are implementing an ad-hoc network, where you know the traffic is poisson distributed. Wouldn t it be better to use the theoretical model of True values, counting the number of routes which are passing each node and update at each instant routing table is changed? 2

100 6 Structure of the report The report is well structured, although some parts are not very clear and some are repetitive. 7 Minor comments In equation 2-3 P ij is used, while p ij is used in the text. It is confusing. Line 5, page 12, is saying that the dominant node may be allocated arbitrarily... Why not try to give each node a percentage of the total slots corresponding to the percentage of the relative load, such that all slots are allocated. In equation 2-6 i will start by 1? L est = c n i=1 e γti In section the phrase arrival of packets is used, whereas the estimator is used to calculate the load for all outgoing links of a node. Easy to mix things up while reading. In figure 8, unit of y-axis must be seconds and in y-axis in figure 11 %? 3

101 Comparison of Estimated and True traffic load [STATIC Ad-hoc Networks] Figure 1 plots True (Blue color) and Estimated (Red color) traffic load verses time for window sizes T ws equal to 5 seconds when gamma γ is zero. Each line in sub-plot represents true and estimated traffic load at a particular node. Figure 1. Normalized True (Blue color) and Estimated (Red color) traffic load 1

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