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Int. J. Space-Based and Situated Computing, Vol. 3, No. 1, 2013
Performance evaluation of mixed-bias scheduling schemes for wireless mesh networks Jason B. Ernst* and Joseph Alexander Brown School of Computer Science, University of Guelph, Guelph, Ontario, N1G 2W1, Canada E-mail:
[email protected] E-mail:
[email protected] *Corresponding author Abstract: Typically, peripheral nodes in a multi-hop wireless network experience poor performance from starvation, congestion, queue build-up and contention along the path towards internet gateways. We propose three adaptive methods for scheduling based on mixed-bias scheduling which aim to prioritise mesh routers near the gateways to ensure they can handle their own traffic and peripheral traffic. We also give an overview of the mixed-bias approach for scheduling. We then evaluate the performance of each technique in comparison with each other and the IEEE 802.11 distributed coordination function. Each solution is evaluated based on average packet delivery ratio and average end-to-end delay. Two experiments were performed to examine the performance. First, we studied the effect of varying the inter-arrival rate of the packets. Second we examined the effect of changing the number of sources. In all experiments, the proposed approaches perform at least as well or better than IEEE 802.11 DCF. Keywords: IEEE 802.11 DCF; co-existence; parameter computation; feedback; scheduling; evolutionary algorithms; evolutionary programming; mixed bias; wireless mesh network; Tabu search; adaptive. Reference to this paper should be made as follows: Ernst, J.B. and Brown, J.A. (2013) ‘Performance evaluation of mixed-bias scheduling schemes for wireless mesh networks’, Int. J. Space-Based and Situated Computing, Vol. 3, No. 1, pp.22–34. Biographical notes: Jason B. Ernst received his MSc in Computer Science from the University of Guelph, Guelph, Ontario, Canada and BSc (Hons) in Computer Science with a minor in Physics from Wilfrid Laurier University, Waterloo, Ontario, Canada in 2007 and 2009, respectively. He is currently completing his PhD at the University of Guelph, Guelph, Ontario, Canada in Computer Science. His research interests are next-generation networking and seamless communication. Joseph Alexander Brown received his MSc and BSc (Hons) in Computer Science from Brock University, St. Catharines, Ontario, Canada in 2009 and 2007, respectively. He is currently working on his PhD in Computer Science at the University of Guelph, Guelph, Ontario, Canada. His research interests include bioinformatics and applications of evolutionary algorithms.
1
Introduction
Wireless communication is becoming more pervasive and ubiquitous all the time. The typical home has only single-hop communication using technology such as Wi-Fi (IEEE 802.11 Wireless LAN). Larger networks such as those located within corporations and university campuses, as well as those provided by municipalities and cities make use of wireless multi-hop networks such as wireless mesh networks. These networks are often based on IEEE 802.11 access technology, but are further distributed such that not every access point has a direct connection to the internet. Access points which do have a direct connection to the internet are called gateways, the rest are called mesh routers. Mesh clients are those which connect through the mesh router infrastructure, i.e., the end users with devices
Copyright © 2013 Inderscience Enterprises Ltd.
such as laptops, mobile phones and tablets. Typically traffic in these types of networks flows from the mesh clients towards the internet, through the gateways. One large problem affecting the scalability and performance of multi-hop wireless networks is the distance, or number of hops between the client and the gateway. Generally, the farther the client, the more times it must contend for the medium along the path making it less and less likely that a successful transmission will occur. While distance and hops are not necessarily the same since the routing path may change, for the purpose of this work we will consider static paths. Furthermore, mesh routers closer to the gateway are overwhelmed because they must handle their own traffic in addition to that at the peripheral of the network. Traditional approaches give equal scheduling resources to all mesh
Performance evaluation of mixed-bias scheduling schemes for wireless mesh networks routers regardless of their distance from the gateways they are routing to. In all of the proposed approaches presented in this paper, we propose to give priority to those nodes which are closer to the gateways. The motivation is that the mesh routers closer to the gateway may better handle the traffic load of their own traffic and peripheral traffic when they are prioritised in the scheduling. The rest of the paper is organised as follows. First, in Section 2, the background and related work is presented to give an understanding of similar approaches and previous work. Next, in Section 3 an in-depth overview of mixed-bias scheduling and the proposed adaptive approaches are given. In Section 4, the performance of each approach is evaluated in comparison with the IEEE 802.11 distributed coordination function (DCF) approach. Finally, the conclusions and future work conclude the article.
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Background and related work
In this section a background on techniques similar to those which we propose will be presented. This includes the traditional mixed-bias technique, other competing scheduling schemes and those related to our proposed adaptive schemes – Tabu search (TS) and evolutionary programming (EP). There is much motivation to make use of adaptive techniques for scheduling in wireless mesh networks, or more generally multi-hop wireless networks. Due to the unpredictable and changing nature of environmental conditions which may affect wireless networks, adaptive techniques are quite useful to allow the network to adapt and to prevent instability. Many other resource allocation and scheduling techniques such as Pham et al. (2012) require system stability so that queues do not increase towards infinity. In the paper by Pham et al. (2012), the authors assume that links have fixed capacities during schedule generation, however in the presence of interference the capacities may change when the link adjusts to a lower rate to avoid errors. Until the next scheduling round, if the assumption is not valid the result could be system instability because nodes will not be able to transmit at the rate the system requires to maintain stability. This could be mitigated by introducing tolerances along with the capacity or by using an adaptive scheduling scheme.
2.1 Mixed-bias scheduling for wireless mesh networks Mixed bias scheduling was first proposed in Singh et al. (2008). The original work focused on analysis of the technique mathematically. The authors also showed that in theory, mixed-bias scheduling should perform better than proportional and max-min techniques. A thorough classification of scheduling techniques such as proportional, max-min and others based on fairness in presented in Ernst and Denko (2011). Since the original work by Singh et al, further work has been done to compare the performance of
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mixed-bias scheduling to other techniques. In Ernst and Denko (2010), the original mixed-bias approach by Singh et al. (2008) was extended to include biasing against link quality and queue size in addition to the distance from the gateway. The extension work also confirmed that the performance of mixed-bias scheduling performs well compared to existing schemes. Two adaptive approaches based on mixed-bias scheduling were proposed as well. In Ernst and Nkwe (2010), a TS algorithm was used to adapt the mixed-bias parameters while Ernst and Brown (2011, 2012) used EP to adapt the parameters. These approaches apply a probabilistic scheduling scheme which will be explained in detail in the following sections.
R=
1 cβ
(1)
For context, equation (1) shows how resources are assigned in a proportional scheduling technique. As the value of R grows towards one, the more likely a node will receive resources in the schedule. Conversely, as R approaches zero, the node becomes more likely not to receive resources in the schedule. The parameter, c, is the characteristic one wishes to bias proportionally against. β controls how strongly to bias against this characteristic. In the case of this paper, c represents the distance from the GW, but it could also represent other quantities we wish to bias against such as available queue size, link quality and so forth. R=
α c β1
+
1−α c β2
(2)
Equation (2) shows the equation used to determine the resource allocation for nodes within the mesh network. c is the characteristic one wishes to bias against. β1 and β2 control how strongly the characteristic is biased against. α controls the mix between the strong and weak bias. In Figure 1, the probability of resources being assigned to nodes using proportional and mixed-bias is compared. One the one extreme is proportional fairness with a weak bias [β = 2, equation (1)]. In some cases, it may desirable to bias more strongly against nodes which are far away, for instance when the network is extremely congested – more emphasis may need to be given to closer nodes. On the other extreme is a strong bias [β = 5, equation (1)]. As the bias grows larger, nodes toward the periphery become less likely to receive scheduling resources. Notice how the stronger proportional fairness curve converges toward zero very quickly. This means nodes more than one or two hops from the gateway become very unlikely to receive scheduling resources. On the other hand, the weak proportional technique still has higher probability for five or six hops away. The figure also shows how using the mixed bias technique allows us to assign resources somewhere between these extremes [β1 = 2, β2 = 5, α = 0.5, equation (2)]. Depending on how α is set, the curve can fluctuate between these two extremes. Despite being able to become both strong or weak, the mixed-bias curve is also midway between being too steep and too gradual.
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Figure 2 illustrates how controlling the α parameter allows the resource allocation from sliding between very strongly biased to very weakly biased. As α moves closer to zero, the emphasis moves towards the strong bias curve. Conversely, as α moves towards one, the emphasis moves towards weak bias. This tuning is what we wish to control in this paper using the adaptive techniques we will present, including TS and EP.
As the previous figures show, it is possible to tune the mixed-bias functions so that the subtle shifts in scheduling priorities can occur as network conditions change. For instance, when the network is lightly loaded, it is best to shift towards a weak bias so that nodes towards the edge of the network receive more resources. When the network is congested, it is be best to give priority to nodes closer to the gateway.
Figure 1
Strong and weak proportional vs. mixed bias resource probabilities (see online version for colours)
Figure 2
Various mixed bias resource probabilities (see online version for colours)
Performance evaluation of mixed-bias scheduling schemes for wireless mesh networks
2.2 TS algorithms TS is often used for local search techniques and has several mechanisms that are helpful in avoiding local optima. The main idea of TS is to avoid repeating the same exploration of the search space by making parts of the search space Tabu for a period of time. There is an idea of a Tabu neighbourhood, which is the set of potential states for the system. A change in state from one to another is called a move. After a move has been made, it is set to be Tabu for a period of time, which is called a Tabu tenure. Once the move is Tabu, it is now called a Tabu move. After enough moves, the Tabu tenure of a Tabu move expires, allowing the system to reexplore this area of space again. This is particularly useful for online adaptive approaches because it allows the system to return to a good state after some external event causes the system to temporarily require adaptation. Related to this idea is the idea of aspiration criteria. This allows the Tabu system to escape a local area and move farther across the search space. There are many ways this can be accomplished. For example, the best known state can be remembered and returned to periodically to avoid venturing into a bad part of the search space for too long. Another technique is to jump randomly to unexplored areas of the search space to help diversify the search. TS has been successfully applied to more generic offline job scheduling problems. Previously, for example Gao and Tang (2008) which uses offline TS to schedule colouring of steel in the manufacturing process. However, it is used less frequently for online scheduling problems. Another offline approach, used to help assign channels and place gateways within a wireless mesh network was proposed by Beljadid et al. (2008). The earliest known online example is for power-plant scheduling in 1999 by Kamiya et al. (1997) where TS was used online in combination with genetic algorithms (GAs) to help with local search. In the economics domain, online TS is used by Tippayachai et al. (2003) to help decrease the cost of power generation.
2.3 Evolutionary algorithms Evolutionary algorithms (EAs) are bioinspired models of in slico evolution. The primary guidance coming from the Neo-Darwinian ideas of natural selection, also called survival of the fittest, as well as models of natural mutation and crossover in genetic materials. The models may work at a genotypic level, modifying the instructions to build a solution, or a phenotypic level, modifying the solution directly. Four major models form the basis for modern research: GAs (Holland, 1975), genetic programming (GP) (Koza, 1992), EP (Fogel et al., 1966; Fogel and Chellapilla, 1998), and evolutionary strategies (ES) (Rechenbreg, 1965, 1973; Schwefel, 1975, 1977). The majority of these approaches used for networking are offline evolutions, that is the current generation is not actively making changes to a running system but are creating a fixed controller. However, EP allows for a online evolution, were the system is
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concurrently using an evolved agent as well as evolving new and hopefully better agents for future predictions. EP works by the modification of finite state machines (FSMs) at a phenotypic level with only a mutation operator. FSMs are simple transducers that can allow for the modelling of complex behaviours despite their simplicity. A number of states with transitions between states based on an input are defined. Outputs can be either on the state itself, a Moore (1956) machine, or on the transitions, a Mealy (1955) machine. This study uses Mealy machines as they require a smaller number of states for the same level of representational power as the transitions between states provide output. Further, they are more commonly used in evolutionary studies than Moore machines. Use of FSM for prediction problems have included bioinformatics. Polymerase chain reaction primers are used in the amplification of DNA sequences for diverse applications such as sequencing and disease detection. Finding good primers allows for a reduction in spurious results and increases the yield of DNA produced. FSM created via EA have been used for both the sequencing of zea mays, more commonly known as corn, and in mice (Ashlock et al., 2002; Yadav and Corns, 2010). These predictors have a fitness which is calculated as an incremental reward; each correct predictive state, these were Moore machines, rewards fitness. Conversely, an incorrect prediction removed fitness. Secondly, there is the introduction of an ‘I don’t know’ state into these machines – we call this a quiescence state. This state while not contributing to fitness, does not penalise, and allows a machine to move through transitory states where a prediction cannot be made. A quiescence state in a control structure would be once which makes no changes to current settings thus allowing the system to reach and maintain a setting. Co-evolutionary EA is where a number of populations or population members evaluate their fitness based on each other. The co-evolution of FSM is commonly used for models in game theory. As this study looks at the evolution of FSM for the purposes of cooperation between routers, these findings become directly applicable to the choice of pre-presentation. Fogel (1993) used EP as a method to evolve FSM to play Iterated Prisoner’s Dilemma (IPD). IPD is an interesting problem in evolutionary game theory as it shows that cooperation can be reached as a emergent behaviour in species. Further studies into EA on IPD using the representation of FSM where applied by Ashlock and Ashlock (2006). This study looked at deep time evolution, running the evolution on a time scale much larger than previous studies of IPD agents. Interesting properties were found in the resultant agents such as handshaking. Brown (2011) used a spatially structured EA in order to both sort a set of common and uncommon agents from the literature. This system showed there existed an agent called Trifecta which was able to play optimally with the common agents of always cooperate, always defect, and tit-for-tat. This agent and other properties seen in evolving agents were further elaborated upon in Brown and Ashlock (2011). It
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showed that general agent behaviours can be classified into sets of optimal agents when playing another agent. These findings do not hold to the theory of evolutionary stable strategies (ESS) presented by Maynard-Smith (1982). The issue being that EA normally models a finite sized population and ESS have been found not to hold (Ficici and Pollack, 2000). Studies by have also verified that ESS findings are not seen in other co-evolutions of games such as Hawk and Dove (Fogel et al., 1997). This means that there is no one good play strategy for any co-evolved game and the system should be seen as constantly in flux. Hence, evolution of new players at different time periods dependant upon the state of the system is required. The choice of representation of a game playing agent as a data structure is important dependant upon application. FSM were found to have high levels of cooperation in evolved populations, whereas Neural Networks were unable to reach cooperation (Ashlock et al., 2006). Seeing as how both have the same set of space of representation, that is all finite languages, FSM are a better representation to evolve when one is seeking cooperation. In this application the network as a whole must be guided to produce better results and therefore FSM are a good choice for the evolving agent. Finally, the choice of algorithm which is used in this study is an online method, were predictions are made during the evolution without simulation. In comparison with other techniques such as GAs, EP was used because it may be performed in an online manner. Approaches such as Xhafa et al. (2012), for example, have been used in an offline manner for applications such as ground station scheduling for space equipment which is computed ahead of the actual transmissions. These types of applications do not have the same types of rapidly changing conditions such as interference and environmental affects since the frequencies are usually reserved. So often the communication may occur without unexpected events affecting the schedule and once a good offline solution has been computed, it will likely succeed. The aim of our approach is meant for rapidly changing networks and aims to react to these changing conditions quickly.
2.4 Adaptive Scheduling techniques There are also many other competing scheduling schemes that try to address resource allocation in multi-hop wireless networks. While this work tries to address fairness with the objective of increasing performance, other approaches have multiple goals. For instance, Bai and Xue (2011) try to balance the performance fairness with the price that users are willing to pay for access to the network. In addition to adaptive scheduling techniques, there are also many other adaptive techniques in wireless networks that try to control parameters within the system for different problems such as routing.
3
Proposed approaches
In this section we give details on the proposed adaptive mixed bias techniques. First we discuss the traditional mixed-bias technique, then we follow with the adaptive approaches such as TS, evolutionary and evolutionary with quiescence.
3.1 Mixed-bias technique The mixed-bias scheduling technique is used to give priority to mesh routers which are closer to the gateway. This follows the idea that mesh routers which are closer must handle their own traffic in addition to the traffic from the periphery. In other words, we would like to bias against the nodes which are far away from the gateway. This could be accomplished using existing techniques such as proportional fairness or max-min. However, there are some reasons for using mixed-bias instead. Max-min may cause node starvation, which is undesirable – particularly in networks where users are paying and expect at least some service. Conversely, proportional fairness may not bias strongly enough against nodes which are far away from the gateway. The solution is mixed-bias scheduling. It is similar to proportional fairness – except it allows both a strong and a weak bias. This provides a balance from being too strong – similar to max-min and too weak – similar to proportional. The formula for computing the resource allocation is given in equation (2). Alpha controls the weight between strong and weak bias. β1 is the weak bias, and is less than β2 which is the strong bias. The higher these numbers, the more likely the approach will starve a mesh router. On the other hand, the smaller they are, the more likely they will give each mesh router an equal time slice. In the traditional mixed-bias approach, these values are fixed entirely. The values found by Singh et al. (2008) to be analytically optimal in typical network conditions were α = 0.5, β1 = 2, β22 = 5. These results were also confirmed to perform well in simulation by Ernst and Denko (2010). However, it may be possible to achieve even better performance if these fixed values are allowed to fluctuate dynamically. This is the purpose of the next three techniques – the TS, evolutionary and evolutionary with quiescence techniques. The idea with these approaches is that certain scenarios may require abandoning this hard policy to give priority to nodes which are near to the gateway. For instance, perhaps this approach is only useful when the network is congested. When the network only receives traffic form a few users at the periphery of the network, it may be best to abandon this strategy and aim for something that gives equal time slices to all. This is where the adaptive approach comes it. It allows control of the amount of strong and weak biasing to apply and how strong or weak to make it. It lets the behaviour of the scheduling switch smoothly between a proportional and max-min type of approach and everywhere between.
Performance evaluation of mixed-bias scheduling schemes for wireless mesh networks The mixed-bias technique is implemented by modifying the IEEE 802.11 DCF mechanism. When the resource allocation is computed by the formula given in 2, it returns a result between zero and one. This is the probability that the packet will be forwarded by the router or delayed. This is implemented at the queuing mechanism in the IEEE 802.11 DCF. The same technique is used for all of the dynamic approaches to follow as well. The difference is in the computation on whether or not to delay the packet. The hope is that delaying the packet will allow nodes which receive more priority a chance to send their data into the network by decreasing the contention. At the nodes where the packets have been delayed, their MAC layer does not think they have anything to deliver yet, so they do not request access to the medium, allowing other nodes to send. It is also possible to specify a maximum number of delays allowed so that nodes are not starved completely in the event that they have a very high delay probability. Once the counter reaches this maximum, the packet is delivered regardless.
3.2 TS mixed-bias technique This section provides details on the TS algorithm used in the experiments. The algorithm is split into several subsections including initial conditions, utility, neighbourhood, Tabu moves and aspiration criteria. Algorithm 1
TS for mixed-bias parameters
if packetCount > TABUMOVE then packetCount = 0 current.utility = computeUtility() if currentUtility > best:utility then best = current end if while !isTabu(current) do current = generateTabuMove() end while tabuList.add(current) tabuList.expireOldTabuMoves() else if packetCount > TABURESET then current = best end if
Algorithm 1 shows the general idea of how the TS approach can be applied to mixed-bias scheduling. The ‘TABUMOVE’ parameter is the number of iterations before a new move is attempted on the network. This allows control over the ‘resolution’ of the approach. Lowering this number would make the algorithm more able to change the parameters rapidly, however may be more prone to oscillations or over-corrections. Making this number too high would cause the algorithm to react to slowly. In short, the algorithm evaluates the current solution by computing the utility. If the current state has a higher utility than the best known solution, make this solution the best known
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solution. The ‘TABURESET’ parameter controls how long before a reset back to the current known best solution. This is so that there is an exploratory phase and a phase where the network performs as best as it can. The utility used in Algorithm 1 is shown in more detail in Algorithm 2. Algorithm 2
computeUtility for TS
if currentDelay > maxDelay then maxDelay = currentDelay end if delayUtility = (oldDelay – currentDelay) / maxDelay PDRUtilty = currentPDR – oldPDR utility = delayUtility + PDRUtility oldDelay = currentDelay oldPDR = currentPDR return utility;
3.2.1 Initial conditions The initial conditions in a TS algorithm define the starting state of the system before the algorithm is run. In this case, the algorithm is used to attempt to find better values of α, β1 and β2 at a given time in the simulation. One possible starting state would be to set α = 0, β1 = 1, β2 = 1, since these are low bounds on the values, however since previous research indicates that α = 0.5, β1 = 2, β2 = 5 achieves good performance this will be used as the initial conditions for the algorithm.
3.2.2 Utility In order for the TS algorithm to operate, it must be able to evaluate whether the last configuration of mixed-bias parameters performed better or worse than the currently known best configuration. This is what the utility function is for – it puts a value on a particular configuration. Two things we are interested in improving with this approach are end-to-end delay and packet delivery ratio. At each mesh router running the algorithm, we can keep track of running totals of these values and compare the difference between the old value and the new value to see what the effect of a change was. This makes the TS algorithm an online approach. Compared with other techniques which try to simulate the effects of a change in the parameter, then make the change, this technique does the change immediately and compares how the network performance changes. The downside to the offline approach is that by the time the result is computed, the network conditions may have changed making the result useless. The online approach allows for fast reaction. The utility computation is specified in Algorithm 2. As can be seen, a high utility means the network is performing better than the previous iteration. The function will increase with higher PDR or lower delay compared with the previous network conditions. Alternatively, if one parameter increases and the other decreases, the utility will remain relatively unchanged
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unless the difference between the two parameters is great. In this case, the utility depends on which parameter has changed more.
3.2.3 Neighbourhood Since TS relies on restricting unique values from being used again, it is necessary to restrict the possible values of α, β1 and β2. In other words, we cannot let each of them take on values from the real numbers, instead it is necessary to impose a quantisation on the values so that they are discrete. This reduces the search area significantly and may make it impossible to find an exact optimal solution, however it is a necessary trade-off in order to improve the efficiency. The resolution of this can also be controlled and experimented with in order to yield better results.
3.2.4 Tabu moves A Tabu move in the mixed-bias scheduling is defined as the triple: (α, β1, β2). Any unique set of values for these three parameters is considered a move. In order to prevent moving back towards the exact same set of values in subsequent moves, once a move is tried it is added to the Tabu list. While a move is on this list, it is not possible for a later iteration to select the same values. Note: all three values together cannot be selected, but two out of three values can be the same. It is also possible to restrict individual values, but for this work we do not consider this since it may be too restrictive. Algorithm 3 shows the technique used for making Tabu moves in the proposed approach. Algorithm 3
αScale = uniformVariable(1, 5) β1Scale = uniformVariable(1, 5) β2Scale = uniformVariable(1, 5) if direction < 0.45 then current.α = current.α + 0.05 * αScale current.β1 = current.β1 + 0.1 * β1Scale current.β2 = current.β2 + 0.1 * β2Scale else if direction < 0.9 then current.α = current.α –0.05 * αScale current.β1 = current.β1 –0.1 * β1Scale current.β2 = current.β2 –0.1 * β2Scale else current.α = uniformVariable(0, 1) current.β1 = uniformVariable(2, 7) current.β2 = uniformVariable(2, 7) return current;
The aspiration criteria in used to avoid getting stuck at local optima. In this case, to achieve this goal, we propose to reset back to the best known solution after a certain number of Tabu moves. We chose to use twenty, however this could be adjusted to achieve different results. A low number would result in little exploration while a large number would allow much exploration but perhaps an inability to react quickly enough to rapidly changing conditions. After some experimentation, it appears that twenty allows for a good mixture of both properties. The reset condition is illustrated in Algorithm 1 where the packetCount reaches the TABU RESET threshold.
3.3 Evolutionary mixed-bias technique This section looks at the EA used in the study. It gives an overview of the EP using Mealy FSMs.
3.3.1 Finite state machines The type of FSM used is known as a Mealy (1955) machine. It is defined as a hextuple, 〈Q, I, Z, δ, ω, q〉 with the following: •
Q is a finite set of states
•
I is a finite set of input symbols which are taken from calculations made by the system
•
Z is a finite set of output symbols which is the manipulation to be made to the system
•
δ is the state transition function, such that δ: I × Q → Q. It maps the current state and the input to the next state
•
ω is the output function, such that ω: I × Q → Z. It maps each state transition to an output symbol in Z
•
q is an initial state such that q ∈ Q.
generateTabuMoves for TS
direction = uniformVariable(0, 1);
end if
3.2.5 Aspiration criteria
FSM are uniquely defined therefore by giving a state diagram with the initial state clearly marked or by a transition table showing the outputs of each of the state transition and output functions with the initial state. Figure 3 gives an example machine used in this study. Its set of input symbols is {+, −} for the measurement from the system which the sign of the calculation of fitness on the node The output set is {+, −} which decides if the α value in the MB will be increased or lowered by a set amount. Based upon the findings in PCR Primer studies (Ashlock et al., 2002; Yadav and Corns, 2010) a quiescent output response is examined. This system extends the output set to {+, −, ?} where ? is used as the make no change response, or keep α at its current value. Figure 4 is the same example machine structure with a few outputs changed to the quiescent transition.
Performance evaluation of mixed-bias scheduling schemes for wireless mesh networks Figure 3
Mealy FSM state diagram and transition table
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a larger search space in general. Thus, this increase in representational space might create a less directed evolution via the selection process. Naturally, a machine must possess at least one state for prediction to occur and actions which would remove all the states during an evolutionary process are avoided.
3.3.2 Evolutionary programming
Notes: State diagram read as input from the set {+, −} to output from the set {+, −}. Transition table read as output symbol and transition to state. Figure 4
Mealy FSM state diagram and transition table with quiescent transitions
EP was developed in the 1960s by Fogel et al. (1966) as a method of evolution of FSM for string prediction problems. This type of EA was originally used in an online fashion. That is the evolution occurs while prediction is being made. This allows for responsive predictions while still providing a capacity for learning. The EP accomplishes an online evolutionary search via the following process: a population of FSM is first randomly initialised, where one is randomly selected to be the current machine making a prediction. When a new prediction is called for each machine saves its response and the current prediction machine returns its response as the action to be made by the system. After a window of predictions has been made, each of the machines is evaluated and given a fitness based upon how well their response matched actual result. The population is sorted by fitness, the most fit machines are copied with small changes, known as mutation, over the least fit members of the population. The machine with the highest fitness now becomes the current predictor for the next window, where the cycle of prediction, fitness evaluation, and mutation continues. Algorithm 4
Evolutionary programme
for all FSM in the population do calculate fitness on previous window; end for for top half in fitness of the population do mutate these FSM via genetic operators; replace bottom half of population; end for if current window full then Notes: State diagram read as input from the set {+; −} to output from the set {+, −, ?}. Transition table read as output symbol and transition to state.
Note that there exists a large number of isomorphic FSM for any given size. The FSM in the study are allowed to vary in size, however, the value of Qmax is used as a limit on the maximum number of states a machine will be allowed to possess during an evolutionary process, i.e., |Q| ≤ Qmax. Giving a larger maximum number of states increases the representational ability of a FSM. However, a router has a limited amount of memory and processing which must be taken into account during the final implementation of such an evolutionary system, this value can be set to optimise to the hardware available. Secondly, and perhaps of more importance, the increase in states allows for more isomorphic, therefore equally fit, machines to be created and
for all FSM in the population do calculate fitness on current window; end for prediction machine ← most fit in population; previous window ← current window; end if return prediction from the current prediction machine;
The original studies into EP saved all inputs and was only seeking to predict the next input, that is the machine was reactive and had no influence on the system. In order to make the predictions based on current system behaviour and to limit the runtime and memory requirements, only a window of predictions is evaluated. This window is evolved upon for a number of prediction rounds equal to the size of
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the window before being updated by the actions of the current machine. A rolling window is not used for two reasons. First, the evolution requires some time to converge if there has been a new change to the system, a rolling window would not allow for a burn-in period. Secondly, as FSM are started at a set initial state, constant change of the window would be a large disruption to current structures.
3.3.3 Genetic operators The mutations to FSMs which can be selected in this system are: change an action, change a transition, change the current initial state, adding a state, or removing a state. Mutation operators are selected uniformly at random. In the event that a FSM has Qmax states the addition action was excluded, if it has one state then the deletion is excluded. These mutation operators are described as follows:
packet delivery ratio is maintained over time as well as delay. Fitness is determined by combined utility balanced between both of these measures using Algorithm 2 defined previously for the TS approach. Over the prediction period, if the utility increases, good feedback is passed to the prediction engine, otherwise negative feedback is provided. For this experiment, the packet delivery ratio and the delay were given equal weight in the fitness, however this may be altered depending on the application of the network. In EPs the largest cost in runtime comes not from the genetic operations made upon the FSM but the evaluation of fitness. Simulation is commonly used in offline approaches to EAs, however it is not a suitable method of evaluation for this problem for the following reasons: 1
each node would require a large coprocessor to run simulations of network state
1
Change an action: An output action is randomly changed on a randomly selected state.
2
each node would require knowledge of the network topology and the state of other nodes on the network
2
Change a transition: A random transition in the machine is redirected at random to another state in the machine.
3
the speed of simulations is slower than reality making any results acquired from simulations long out of date when a prediction is required immediately.
3
Change the initial state: The initial state is changed at random.
4
Adding a state: A new state is created and its outbound transitions are assigned randomly. A randomly selected currently existing state then has a transition broken and changed to become the new state. This is to encourage the new state to take part in the determination of fitness.
5
Removing a state: A state is selected to be removed at random. All incoming links to the state are randomly reassigned among the remaining states. If the removed state was the initial state, then the initial state is reassigned randomly.
This reasoning means that in order to use an evolutionary approach some heuristic assumptions are required in the fitness evaluation. The main heuristic is that if the current prediction machines choice increased the fitness, then the opposite choice would lead to a directly corresponding drop in fitness, and vice versa. The parameters could be in a state where performance decreases independently due to a confounding factor and there is no way to discover that without costly simulation. For quiescent states this same model of fitness is used. That is if the current prediction machines choice was correct/incorrect, then the other outputs are incorrect and correct respectively. This of course is an assumption which can lead to mistakes. Take for example if the current machine keeps the parameter the same, however performance will improve if it is increased. Then machines which select an increase in the parameter will suffer the same drawbacks as those which selected to reduce the parameter. Again, this is unavoidable as we can only know the results of the current prediction machine without resorting to simulation.
Each of these operators has a varying degree of disruption to the underlying logic of the FSM. Changes to transitions or output actions make little changes in the behaviour, and sometimes no change at all such as changing the output transition on a state with no incoming transitions. These null mutations, on which has no effect on the fitness of a machine, are not discouraged. Their detection would be computationally expensive, the mutation might be an intermediary step in a chain of mutations leading to greater fitness, and during evolution it is often helpful to have a level of inheritance when fitness is relatively higher for a machine as it promotes exploitation. Conversely, their exist operations which will cause drastic disruption to current logic in the FSM, addition and deletion of states. Having both types of operators allows the EP to exploit current areas of the search space and explore new areas of the search space.
3.3.4 Fitness evaluation Fitness of a FSM is calculated by feedback from the mesh network known to each node. At each mesh router, the
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Performance evaluation
4.1 Simulation environment and methodology The simulation environment for the experiments was the NS3.13 simulation tool which is the successor the well known NS2 simulation environment. We used the mesh model which implements a wireless mesh network using IEEE 802.11 (Wi-Fi). Traffic was modelled as constant bit rate with the server representing the gateway the traffic is being forwarded to. Client traffic was generated at uniformly distributed points from around the network. There were two experiments which were
Performance evaluation of mixed-bias scheduling schemes for wireless mesh networks performed in order to evaluate the performance of the various mixed-bias implementations. First, the number of sources in the network. The size of network was set to 100 mesh routers. The inter-arrival rate was held at 0.01. The second experiment examined the inter-arrival rate of the packets (or the network load). Again the size of the network was held constant at 100 mesh routers. In both cases, sources were uniform and random from around the network, and all routed towards a single gateway in the upper left corner.
4.2 Results First we evaluate the proposed approaches with respect to varying sources. For this experiment, the network size is fixed at 10 × 10 mesh routers (or 100 mesh routers total). Sources are selected randomly and route towards a single gateway which is fixed in the upper left corner of the network. The network interarrival rate is held at 0.01. Figure 5 shows the average packet delivery ratio as the number of sources increase. In most cases, the PDR of all of the proposed approaches performs at least as good or very
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close to IEEE 802.11 DCF. In most cases however the adaptive techniques (MB-Tabu, MB-EP and MB-EP-Q) all perform slightly worse than the static MB in terms of packet delivery ratio. However, this difference is within 5%. Similarly, in Figure 6, almost all of the proposed approaches perform similarly. The delay for MB-EP-Q is better as the number of sources is high, but this is likely due to fewer packets being successfully delivered when compared in conjunction with Figure 5. Together, these results show that while the dynamic approaches are better than IEEE 802.11 DCF, they do not significantly outperform the static approach. The trend is also that while the performance improves in all cases as the number of sources increases, there is a limit to how many sources the mixed-bias approach can be helpful for. With more than 30 sources transmitting from around the network, the performance starts to converge back towards the IEEE 802.11 DCF approach, and in some cases, the mixed-bias approaches begin to perform worse with up to 40 sources.
Figure 5
Average packet delivery ratio with varying sources (see online version for colours)
Figure 6
Average end-to-end delay with varying sources (see online version for colours)
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In Figure 7, the average packet delivery ratio is evaluated as the load of the network is varied. This experiment was conducted with a network size of 10 × 10 (or 100 mesh routers). The number of sources remained constant, but randomly distributed around the network, routing towards a single gateway in the upper left corner. In this case, the packet delivery ratio is very similar in all cases, with some results showing that the dynamic approaches outperform IEEE 802.11 DCF slightly. Finally, in Figure 8, the average end-to-end delay is shown as the network load is varied. In this case, the MBEP-Q approach performs best in most of the cases. The exception is when the network has too much load, it becomes difficult for the MB-EP-Q approach to perform well. This may be related to the amount of time the packet are delayed within the MB-EP-Q approach. In the implementation this was a fixed maximum delay time, and once the load gets high, perhaps this time should also be decreased to prevent this effect. On the other hand, as the load begins to ease, the MB-EP-Q approach seems to be able to better select the correct packets to deliver immediately and which ones to delay since the packet
delivery ratio remains high while the delay is the lowest of all of the approaches.
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Conclusions and future work
In this paper we provided an overview of mixed-bias scheduling techniques for wireless mesh networks. First we presented the static traditional approach. We then give details on three different adaptive approaches – TS, evolutionary, and evolutionary with quiescence. For each technique an in-depth survey and background similar techniques was provided. Experimental results comparing each of the techniques was presented using simulation tools. The results were evaluated with respect to packet delivery ratio and end-to-end delay. The various mixed-bias approaches were compared against the standard IEEE 802.11 DCF. All three proposed approaches performed at least as well or better than IEEE 802.11 DCF in terms of average packet delivery ratio and average end-to-end delay. In particular, the MB-EP-Q approach performed best with varying network loads in terms of average end-to-end delay while retaining a high packet delivery ratio.
Figure 7
Average packet delivery ratio with varying load (see online version for colours)
Figure 8
Average end-to-end delay with varying load (see online version for colours)
Performance evaluation of mixed-bias scheduling schemes for wireless mesh networks A wider study of the parameters used in the evolution and TS would be of importance. Current settings are based upon empirical experimentation and not a overview of the parameter space. If the method were introduced into hardware these parameter settings would be limited by existing hardware and software, so finding good settings which limit the required runtime and memory used in a prediction would be necessary. We leave this to future works to give such an overview. The EP could be improved by looking at the trajectories of the evolution for differing network types. Most likely there is a number of machines which are used more often than others due their stability or ability to rapidly change based on the current network. If these machines occur often enough then there could be an argument made for a evolutionary process which makes them into immortal ancestors for the population. This would allow both to have a preset group of generally good machines preset into a router, limiting the need for a early training period, cutting down on memory resources and training, and still allowing for an evolutionary process to improve upon existing structures.
Acknowledgements The second author wishes to thank the Natural Sciences and Engineering Research Council of Canada (NSERC) for their support of this work.
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