Ant-based Load Balancing Algorithm in Structured P2P Systems

Ant-based Load Balancing Algorithm in Structured P2P Systems

1

Wei Mi,

Chunhong Zhang,

Xiaofeng Qiu

Beijing University of Posts and Telecommunications, Beijing 100876, China,

{miwei1985, zhangch.bupt.001, qiuxiaofeng}@gmail.com

Abstract

Dynamic load balancing is one key adaptation mechanism often deployed in networking and computing systems. Numerous proposals exist for load balancing in P2P networks. All of them will enhance the availability of P2P system to some extent. However, their convergence rate is still low, and the load collection overhead and load transfer overhead are high. In this paper, we propose an ant-based load balancing algorithm, and design a candidate nodes discovery mechanism and a target nodes selection mechanism. Two types of agents are cooperating to realize these mechanisms: Search ant and Guide ant. Performance evaluation shows that, to achieve some specific load balancing effect, compared to the classical algorithms, the convergence rate, the load collection overhead and load transfer overhead of our proposed algorithm are significantly reduced; In addition, this paper analysis how system and algorithm parameters affect the performance of proposed algorithm in depth.

Keywords

1. Introduction

Decentralized structured overlays and distributed hash tables (DHT) proffer a unique vision of computing: a collection of computing and communication resources shared by active users. However, nodes are heterogeneous, workload assigned to system may be heavy-tailed, node availability and churn rates may change over time. Load balancing is a key step towards adapting to these characteristics and ensuring the reliability and availability of the systems.

There is a large body of literature on load balancing schemes of DHT system. The basic idea of all algorithms is based on the real-time load condition of some part or all DHT system, to design the load re-assign or load transfer algorithm. Therefore, the evaluation index of load balancing algorithms include: load balancing effect, load balancing overhead. Here, load balancing overhead can be divided into load information collection overhead and load transfer overhead, the speed of load information collection and load transfer reflect the convergence rate indirectly.

According to the different entity which is responsible for collecting real-time load conditions and generating load re-assign or load transfer algorithm, the DHT load balancing can be divided into two categories: centralized and decentralized dynamic load balancing algorithm.

Centralized load balancing algorithm [1-6] can be divided into all-centralized and semi-centralized load balancing. In all-centralized load balancing scheme, a central node is responsible for collecting real-time load conditions and generating load re-assign or load transfer algorithm for global system; in the semi-centralized load balancing scheme, multi-central nodes are respectively responsible for collecting real-time load conditions and generating load re-assign or load transfer algorithm for local system. In the centralized model, although the load collection and redistribution centers can provide efficient global or local optimal allocation strategy, these centers can easily cause single point failure and the system performance bottleneck in large-scale dynamic systems, because the overhead of load information collection and load distribution strategy implementation is huge.

In the decentralized load balancing schemes [1-2, 7-10], the load transfer nodes need to detect the load distribution of the system, then based on the detected load conditions, to achieving load balancing effect, they need to change their ID or transfer their some part load. In this model, decentralized load balancing scheme can avoid the single point failure, but its convergence rate is higher caused by the blindness of the load detection. The load effect is much closer to global or local optimal one, the load information collection overhead is much greater.

In this paper, based on the analysis of advantages and disadvantages in centralized and decentralized load balancing algorithm, we propose an Ant-based load balancing in Structured P2P network,

This work is supported by China-Finland Cooperation Project (No. 2010DFA12780), National Key Program (No.

2011ZX03005-abbreviation ANT-algorithm. ANT-algorithm makes a compromise between the load balancing effect and balancing cost, and is greatly improved in scalability, adaptability and robustness. Such advantages of ANT-algorithm are as following:

1) algorithm relies on all nodes in the system, so it can avoid a single point failure; ANT-algorithm introduce the parameters of load balancing effect and balancing overhead into the load transfer nodes selection, it is a fundamental tradeoff between the load balancing effect and balancing overhead. So, this algorithm is more suitable for the actual system requirements.

2) Based on ant colony optimization, a load transfer nodes selection technique is proposed in

ANT-algorithm. This is a non-direct cooperation way, it can avoid the blind search and

improve system convergence rate, which is greatly improved in extensibility. Compared to the proposed centralized and decentralized load balancing schemes, the load information collection overhead of ANT-algorithm is significantly reduced.

3) During the process of load transfer node selection, ANT-algorithm not only consider the load state of node, but also introduce a delay in the link between nodes which can avoid the load transfer on the large link delay between nodes, so ANT-algorithm can reduce the load transfer costs;

4) ANT-algorithm selects the available load of nodes as pheromone whose update is complete with the DHT routing table update. It does not need any additional structures to collect load information which enhance the system robustness, and it can solve the slow convergence problem which is caused by no significant differences of pheromone in the initial ant colony optimization.

The rest of this paper is structured as follows. The related work is presented in Section 2. Section 3 describes the ANT- algorithm. We evaluate performance of the proposed load balancing algorithm in Section 4. Finally, we conclude and present future work in Section 5.

2. Related work

As previous description, the basic idea of DHT load balancing algorithm is design the load re-assign or the load transfer algorithm based on the real-time load state collection of the whole or partial system. According to the different entity which is responsible for collecting real-time load conditions and generating load re-assign or load transfer algorithm, the DHT load balancing can be divided into two categories: centralized and decentralized load balancing algorithm. The difference of these methods is the specific load information collection and load re-assign or load transfer program.

In centralized dynamic load balancing model, reference [1, 2] provides one or more directory nodes which are responsible for collecting the load information and generating the load transfer schemes. A directory node periodically calculates load information of random nodes in the system and achieves load balancing through transferring virtual servers. Reference [3] builds a structure on top of the P2P: k-ary tree, which is responsible for the collection and the release of node information, as well as the transfer strategy of virtual server. Reference [4] the system is divided into several rings, each ring represents a region. To begin with, it balances the load in each ring. If not fully balanced, it will balance the load among the rings. There is a super-node in each ring which is responsible for the load state collection and the load re-assign.

In decentralized dynamic load balancing model, reference [1, 7] clones a node into multiple virtual servers, the number of virtual servers is proportional to some performance parameters, such as computing power; each virtual server acts as a node in the logical space and responsible for the corresponding space; the capacity of node is stronger, the number of its virtual servers is more, the proportion of its shared resource space is greater, so it will gain more request load. Reference [9] provides two methods to adjust the node mapping space: first, a node has multiple virtual servers, but only one of them become active at any time, it can connect to other nodes randomly and split the load space of the heavy-loaded nodes to balancing the load; second, to achieve the load balancing, it change the ID of the light-load node which make it share the load of the heavy-load node. Reference [10] also uses the similar method.

In this paper, the proposed algorithm is based on Ant colony optimization (ACO). ACO is a novel evolutionary algorithm, which has the characteristics such as positive feedback, distributing computing and the use of a constructive heuristic etc. And these features quite match the demands of network

optimization, some ant-based algorithms have been proposed for many application[12-13], such as mobile

3. Ant-based Load Balancing in DHT Systems

This paper adopts ant colony optimization to design the ANT-algorithm. It includes the candidate nodes discovery mechanism and target nodes selection mechanism. Specially, two types of agents cooperate to realize these mechanisms: Search ant and Guide ant. Search ant simulates the food-seeking behavior of ants that searches for light-nodes. Guide ant is responsible for managing a candidate light-load node list, instructing source node to select target nodes. In this section, the related definition, data structure of search and guide ants, candidate light-load nodes discovery mechanism, target node selection mechanism and overall process of load balancing algorithm will be presented.

3.1. Related Definitions

Definition 1 Node Capacity (C)

The factors that affect the load capacity of the node, such as CPU speed, storage capacity, delay, bandwidth, and so on, are unified as one resource.

C=P CPU( ) * 1w +P Space( ) * 2w +P Memory( ) * 3w +P IO( ) * 4w +P BandWidth( ) * 5w (1)

Where wi represents the weight of each factor; P(x) represents the value of factor x’s capacity.

Different application systems have different weight of each factor.

Definition 2 Node Load (L).

In DHT network, the load of nodes is the demand for capacity.

L=L(CPU) * 1 L(w + Space) * 2w +L(Memory) * 3w +L(IO) * 4w +L(BandWidth) * 5w (2)

Where wi represents the weight of each factor; L(x) represents the value of factor x’s load.

Definition 3 Utilization Rate (μ/m)

Node utilization rate μ refers to the ratio of load of node L to its largest carrying capacity C, that is,

μ=L/C. Node utilization rate describes the situation of the current node load.

System utilization rate mrefers to the ratio of all the nodes’ load in the system to the largest

carrying capacity, which represents the total load situation of network. It can be described as i=1 i=1 = ( ) / ( ) N N L i C i m

_å

_å

Definition 4 Load Deviation Rate (e)

It can be described as the difference between utilization rate of node and system utilization rate.

e=m-m

(4)

Definition 5 Physical Distance (D)

In this paper, we adopt the delay(a,b) as the physical distance between node a and b. It can be achieved

by network coordinates or actual network measure. In this paper, the physical distance of the simulation uses the real data of the delay measure: P2PSim data sets.

3.2. Data Structure of the Search and Guide ants

Based on the different tasks performed by the ants, there are two types: Search ant and Guide ant. Search ant simulates the food-seeking behavior of an ant that searches for light-nodes. Guide ant is responsible for managing a candidate light-load node list, instructing source node to select target nodes.

Search ant is generated by the source node whose e reach some setting threshold, that find

candidate light-load nodes in the DHT. Each search ant has a tabu list to record the visited nodes which

prevent repeat visit nodes and a maximal survival time TTL. Guide ant generated by candidate

light-load node or node whose search ant’s TTL is 0. Guide ant is responsible for managing a candidate

light-load node list that consists of pheromone and physical distance (delay).

Table 1. Structure table of search ant

Ant Id Restricted

condition

Source Node

Taboo list Delay list Pheromone

list

Survival time

AntID res(m) s.t FN tabu list Ds list Info list TTL Table 2. Structure table of guide ant

Ant Id Source Node Candidate nodes

list

Delay list Pheromone

list

AntID FN Candi list Ds list Info list

3.3. Candidate Light-load Nodes Discovery Mechanism

In DHT systems, the specific circumstance of node’s load is unknown, and nodes are heterogeneity. Adopting ant colony optimization algorithm, we can find candidate light-load nodes in the unknown load distribution system, and choose the suitable one or more nodes to data migration. In this section, we will elaborate the candidate node discovery mechanism from the following aspects: the generation and update of the pheromone, the routing mechanism and life-span control policy of Search ant.

3.3.1. Generation and Updating of Pheromone

Pheromone plays an important role in the candidate node discovery mechanism. It guides the route direction of search ant. Therefore, pheromone must fully reflect the node load. This paper defines

the pheromone ph(i) as the available capacity of node i , that is, ph(i)=C(i)-L(i).

How to generate and update pheromone is a key. For faster speed and lower cost, updating of pheromone is complete with DHT node routing table update process. The specific process is:

(1) Source node S sends route table update message;

(2) On receiving routing table update message, node i reply message with available capacity ph(i);

(3) On receiving a reply message, node S records nodes’ information in the routing table entry. This generation and update mode does not need any additional structures to collect load information. It solves slow convergence problem caused by no significant differences of pheromone in the initial.

3.3.2. Routing Mechanism of Search Ant

Pheromone is the core of the solution based ant colony optimization, which represents some prior knowledge, and its size represents the load balancing effect. Delay is also introduced in routing selection as a heuristic factor, which guaranteeing the load transfer overhead. Therefore, both pheromone and heuristic must be considered in DHT routing. Suppose that node i receives search ant k,

node i will select the neighbor node j as next hop by forward probability pk(i, j).

( ) ( ) *(1/ ( )) ( ) *(1/ ( )) k , ( ) 0 & & ( ) ( ) p (i 0, u routingTable i ph j delay j

ph u delay j ph j j routingTable i tabu k

others a b a b Î ì _{> Î} -ï å í ï î , j ) = (5)

Where, ph(j) represents the phenomenon value of node j; delay(j) represents the heuristic value of

node j; α and βis the relative important factor of pheromone and heuristic; routingTable(i) identifies

the routing table entry of node i; tabu(k )is the taboo list of search ant k.

3.3.3. Life-span Control Policy

In this algorithm, the survival time of search ant is controlled by life-span control policy. To

generate the Search ant, TTL will be set an initial value and minus one with every hop forward. When

a node receives a search ant, the control of its life cycle as follows:

(1) If the current node meets the restrictions, it should generate guide ant, update the TTL of search

ant to 0 by force, and end forward search ant.

(2) If its all neighbor nodes are in tabu list of search ant, this node should generate guide ant, update

(3) If neither the current node meets the constraints, nor all neighbors are in tabu list of search ant,

then it should update search ant TTL to TTL=TTL-1; and according to the formula (5), this node

chooses neighbor node whose forward probability is largest as the next hop, and forwards search ant.

In the first case, search is ended as long as candidate node is found. In the other case, if TTL is

0, target transfer nodes should require two or more candidate light-nodes to share the overloaded load.

3.4. Target Node Selection Mechanism

Source node takes the candidate light-load nodes from guide ant as a node list M, and chooses the optimal set of one or more light-load nodes from list M. The metrics should consider two factors: 1) load balancing effect, here, may be expressed in the standard deviation of e. 2) load migration overhead, here, may be expressed in the bandwidth consumption for transfer load.

The objective function (obF) for target node selected and the constraints (s.t.) as follows. 2 2 1 1 1 _ ( m ) _ 1 * ( ) ( ) * * ( ) M M m M Load transfer Load transfer m A e m e s B rep m + = = + å å obF= (6) 1 _ ( ) * ( ( ) ( )) . . ( ) _ ( ) ( ) * _ (m) _ M m

Load transfer C s e s threshold e

s t m M L m Load transfer m C m

Load transfer Load transfer

m = ì ü ï _{³ -} ï ï ï ï ï " Î + £ í ý ï ï ï ³ ï ï ï î

å

The selected target nodes (lists) are the candidate nodes who meet s.t. and their obF is largest. In

formula (6,7), where A and B are the weight of load deviation rate and service reputation;

Load_transfer is total load which source node transfers out; Load_transfer(m) is the load of node m receives. The constraints are as follows: lode deviation rate of overloaded node can drop

below threshold(e), lode deviation rate of light node can’t exceed 0.

3.5. Overall Process of Load Balancing Algorithm

Once source node FN’s load deviation rate e reach threshold(e), the flow is as follows:

(1) Node FN generates kth (k is initialized to 1) Search ant, and sets ant ID, constraints, node FN’s

information (address, physical distance etc) and TTL;

(2) According to the formula (5), node FN chooses the neighbor whose forward probability is

kth largest as the next hop, and forwards search ant k;

(3) On receiving ant k, node DN puts its ID, pheromones and delay into the data structure of ant k.

According to s.t., node DN judges whether it is a valid candidate node;

a. If node DN meets the s.t., it should generate guide ant which return to node FN directly, update

the TTL to 0 by force, and end forward search ant k.

b. If node DN does not meet the s.t., and all neighbors are in tabu lists, it should generate guide ant

which return to node FN directly, update the TTL to 0 by force, and end forward search ant k.

c. If neither node DN meets the s.t., nor all neighbors are in tabu list of search ant, it should update

TTL to TTL=TTL-1; If TTL=0, node DN generates guide ant which return to node FN directly,

otherwise, according to the formula (5), node DN chooses the neighbor whose forward probability is largest as the next hop, and forwards search ant, then go to step (3).

(4) On receiving guide ant, source node FN should make all candidate node forms list, and selects target nodes who meet formula( 7) and the value of formula (6) is largest, then doing data migration.

(5) Source node FN calculates the new load deviation rate e, if e>threshold(e), then k=k+1, go to

step (1); Otherwise the algorithm is end.

4. Performance Evaluation

In this section, we set some goal for load balancing effect using a list of threshold(e). For each

information overhead and load transfer overhead among ANT-algorithm-algorithm , O2O-algorithm [2]

(classic decentralized load balancing) and M2M-algorithm [2] (classic centralized load balancing) in

Chord context, and evaluates how system and algorithm parameters affect the performance of ANT-algorithm-algorithm. Parameters used in this section are listed in Table 3 and Table 4.

Table 3. Basic experiment parameters

Parameters Description Value

N node number [21,216] Load System load 106

C node’s capacity _{[0.5 C ,2 C ]} delay(a,b) the delay between

node a and b

m Node utilization rate

[0,1]

Table 4. Balancing algorithm parameters

Parameters Description Value

threshold(e) the threshold of e [0,1] TTL maximal survival time log2N

α the relative importance factor of pheromone

[0,1]

β the relative importance factor of heuristic

[0,1] dNum directory nodes number log2N

4.1. Performance comparison and analysis with the classical algorithm

In ANT-algorithm, once node’s e>threshold(e), it should execute to search for suitable light-load

nodes to data migration; In O2O-algorithm, light-load nodes, whose μ< m, should random detect node

periodically, if the node’s e>threshold(e), light-load node will do data migration from this node; In

M2M-algorithm, the assignment of loads is typically performed by one or more directory nodes, a directory node periodically receives nodes’ load information and executes the load balancing algorithm.

4.1.1. Load Balancing Effect

To evaluate load balancing effect, we compare the load distribution in ANT-algorithm, O2O, M2M

algorithms and without load balancing. Load distribution is also compared among different threshold(e)

(0.1, 0.2, 0.3, 0.4), N=210, m=0.4. And the simulation runs under different capacity settings.

-0.50 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.2 0.4 0.6 0.8 1

Load deviation rate e

F (e) threshold(e)=0.1 -0.50 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.2 0.4 0.6 0.8 1

Load deviation rate e

F (e) threshold(e)=0.2 -0.50 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.2 0.4 0.6 0.8 1

Load deviation rate e

F (e) threshold(e)=0.3 -0.50 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.2 0.4 0.6 0.8 1

Load deviation rate e

F (e) threshold(e)=0.4 No load-balancing ANT-algorithm O2O-algorithm M2M-algorithm No load-balancing ANT-algorithm O2O-algorithm M2M-algorithm No load-balancing ANT-algorithm O2O-algorithm M2M-algorithm No load-balancing ANT-algorithm O2O-algorithm M2M-algorithm

Figure 1. Cumulative Distribution Function of e. N=210

Fig. 1 shows the empirical CDF of e. As shown, maximum e is reduced a lot when using load

balancing algorithm, and three algorithms can balance the nodes load below threshold(e). However,

minimum e of M2M-algorithm is slightly bigger than the other two algorithms; in O2O-algorithm, the

proportion of nodes whose e>0 is obviously lower than the other two algorithms, and it is equal in the

other two algorithms. It means that compared with classical decentralized load balancing algorithms, algorithm is more efficient; compared with classical centralized load balancing algorithms, ANT-algorithm share many characters in common, and differ in relatively minor characters.

For balancing system load, all solutions have to collect the load information and adjust the load through transferring data or virtual servers, which results in increasing load information collection overhead and load migration overhead a lot. Consequently, we will evaluate load collection overhead and load migration overhead. Here, load collection overhead is evaluated with the DHT routing hops for load collection per heavy-node which could also represent the convergence rate of the system; load migration overhead is evaluated with bandwidth consumption for transfer load, transfer load times delay. As shown in Fig. 2, experimental results as follows:

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0 20 40 60 80 100 120 140 threshold(e) DHT ro u ti n g h o p s fo r lo ad co ll ecti o n p er h eavy n o d e

load collection overhead

0.1 0.15 0.2 0.25 0.3 0.35 0.4 1 2 3 4 5 6x 10 9 threshold(e) tran sfer lo ad * d el ay

Load migration overhead ANT-algorithm O2O-algorithm M2M-algorithm ANT-algorithm O2O-algorithm M2M-algorithm

Figure 2. The load balancing Overhead

(1) The mean of the DHT routing hops load collection per heavy nodes for ANT-algorithm, O2O

and M2M algorithms are distributed in [15,20], [25,45], [110,140] range respectively, indicating that

ANT-algorithm can reduce the load collection overhead. Because it is a non-direct collaboration way, blind search services can be avoided. So, it can improve the convergence rate of the system.

(2) The data migration overhead of our ANT-algorithm is lower than the other two algorithms obviously. It is because that candidate nodes discovery mechanism introduces physical distance, and target node selection mechanism makes a compromise between load balancing effect and overhead.

4.2. The Effect of System and algorithm parameters on algorithm performance

This section analysis how system and algorithm parameters affect the performance of proposed algorithm in depth. It is evaluated with following considerations:

(1) This simulation analysis how the system size and load balancing requirements affect the

performance of ANT-algorithm. Here, load balancing requirement is expressed by threshold(e),

range [0.1, 0.4], the interval value is 0.05; system size N is in the range of [21, 216].

(2) Mechanism based on Ant Colony contains some adjustable parameters. However, the values

of these parameters are not strictly theoretical guidance. So, it needs to determine the

optimal parameter through several experiments. In formula (5), [α, β] is important to ANT-algorithm, so, in simulation, the value of [α, β] is [0.4, 0.6], [0.5, 0.5], [0.6, 0.4], [0.8, 0.2] respectively.

(3) Different algorithm parameters [α, β], with the change of threshold(e) or N, this paper analysis

the load balancing effect and overhead.

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.05 0.1 0.15 0.2 0.25 threshold(e) L o ad d evi ati o n rate (stan d ard d evi ati o n )

Load balancing effect

0.1 0.15 0.2 0.25 0.3 0.35 0.4 18.8 19 19.2 19.4 19.6 threshold(e) DHT ro u ti n g h o p s fo r lo ad co ll ecti o n p er h eavy n o d e

Load collection overhead

0.1 0.15 0.2 0.25 0.3 0.35 0.4 1 2 3 4 5x 10 10 threshold(e) T ran sfer lo ad * d el ay

Load migration overhead

a=0.4;b=0.6 a=0.5;b=0.5 a=0.6;b=0.4 a=0.8;b=0.2 a=0.4;b=0.6 a=0.5;b=0.5 a=0.6;b=0.4 a=0.8;b=0.2 a=0.4;b=0.6 a=0.5;b=0.5 a=0.6;b=0.4 a=0.8;b=0.2

100 500 900 1300 1700 0.148 0.15 0.152 0.154 0.156 0.158 0.16 N L o ad d evi ati o n rate (stan d ard d evi ati o n )

Load balancing effect

100 500 900 1300 1700 12 14 16 18 20 22 N DHT ro u ti n g h o p s fo r lo ad co ll ecti o n p er h eavy n o d es

Load collection overhead

100 500 900 1300 1700 2.6 2.8 3 3.2 3.4 3.6 3.8x 10 10 N T ran sfer lo ad * d el ay

Load migration overhead

a=0.4;b=0.6 a=0.5;b=0.5 a=0.6;b=0.4 a=0.8;b=0.2 a=0.4;b=0.6 a=0.5;b=0.5 a=0.6;b=0.4 a=0.8;b=0.2 a=0.4;b=0.6 a=0.5;b=0.5 a=0.6;b=0.4 a=0.8;b=0.2

Figure 4. Simulation results under different N and algorithm parameter [α, β] As shown in Fig. 3 and Fig. 4, experimental results are as follows:

(1) threshold(e) represents the load balancing requirements, so, threshold(e) becomes greater, the load balancing effect becomes worse and the load balancing overhead decreases.

(2) With changing of the system size N, load balancing effect and overhead appear to be leveling off.

While the fluctuation of load collection overhead is relatively large, because as N increases,

the ant's TTL is is logarithmic growth. So ANT-algorithm has a good scalability.

(3) In the candidate node discovery mechanism, α, β represent the relative importance of available

capacity and delay respectively. With the increase of α (decrease of β), load balancing effect appears a

good trend, the convergence rate becomes faster, and load balancing overhead is increased.

5. Conclusions

This paper has presented an Ant-based load balancing in structured P2P network called ANT-algorithm. Considering load balancing effect and overhead, it designs a candidate nodes discovery mechanism and a target nodes selection mechanism. Two types of agents are cooperating to realize these mechanisms: Search ant and Guide ant. Performance evaluation shows that, compared to the classical algorithms, the convergence rate and load balancing overhead are significantly raised. In the future, based on the collected load information, we still need to develop systemic analysis for the specific load adjustment schemes.

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