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A closed asynchronous dynamic model of cellular learning automata and its application to peer-to-peer networks

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Abstract

Cellular Learning Automata (CLAs) are hybrid models obtained from combination of Cellular Automata (CAs) and Learning Automata (LAs). These models can be either open or closed. In closed CLAs, the states of neighboring cells of each cell called local environment affect on the action selection process of the LA of that cell whereas in open CLAs, each cell, in addition to its local environment has an exclusive environment which is observed by the cell only and the global environment which can be observed by all the cells in CLA. In dynamic models of CLAs, one of their aspects such as structure, local rule or neighborhood radius may change during the evolution of the CLA. CLAs can also be classified as synchronous CLAs or asynchronous CLAs. In a synchronous CLA, all LAs in different cells are activated synchronously whereas in an asynchronous CLA, the LAs in different cells are activated asynchronously. In this paper, a new closed asynchronous dynamic model of CLA whose structure and the number of LAs in each cell may vary with time has been introduced. To show the potential of the proposed model, a landmark clustering algorithm for solving topology mismatch problem in unstructured peer-to-peer networks has been proposed. To evaluate the proposed algorithm, computer simulations have been conducted and then the results are compared with the results obtained for two existing algorithms for solving topology mismatch problem. It has been shown that the proposed algorithm is superior to the existing algorithms with respect to communication delay and average round-trip time between peers within clusters.

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Authors and Affiliations

  1. Soft Computing Laboratory, Computer Engineering and Information Technology Department, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Ave., Tehran, Iran

    Ali Mohammad Saghiri & Mohammad Reza Meybodi

Authors
  1. Ali Mohammad Saghiri
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  2. Mohammad Reza Meybodi
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Correspondence to Mohammad Reza Meybodi.

Appendices

Appendix 1

The detailed descriptions of the phases of the proposed algorithm are given in this section. Before we present the proposed algorithm in more details, we need to define the followings.

  1. 1.

    Eleven types of messages (Hello, Alive, ClusteringRequest, ClusteringReply, SetRole, WarmUpCell, ReadyCell, AutomatonActivatonRequest, AutomatonActivatonReply, ReinforcementSignal, and NewConfig) are used in the proposed algorithm.

  2. 2.

    Meeting point (MP) is a global cache in the network which provides an entry point to the overlay for the new peers.

  3. 3.

    Each peer uses function M-Activate that is shown in Fig. 25 to activate the cell of its corresponding cluster. Since in the proposed algorithm, the learning automata of the cells are distributed among peers of the network, and the design of function Activate of CADCLA-VL that is shown in Fig. 3 is not appropriate for peer-to-peer networks, we designated the function M-Activate that is a customized version of function Activate. The descriptions of the function M-Activate are given in the next paragraph.

    Fig. 25
    figure 25

    Pseudo code of the procedure which a peer executes for using the cell of its corresponding cluster

    Full size image

In this function, peer i sends a WarmUpCell messages to the landmark peers of the neighboring clusters of its corresponding cluster. This message activates the cells of the neighboring clusters to compute their restructuring signals. After sending the WarmUpCell messages, peer i waits for gathering ReadyCell messages. Peer i saves the information of ReadyCell messages and calls automata trigger function to find the value of automata trigger signal. If the value of automata trigger signal is true, peer i activates its learning automaton to select an action and sends AutomatonActivationRequest messages to other peers of its corresponding cluster to activate all learning automata of its corresponding cluster to collectively select their actions. After sending AutomatonActivationRequest messages, peer i waits to gather AutomatonActivationReply messages. These messages provide required information for executing the local rule. Peer i uses gathered information and executes the local rule for finding the reinforcement signal of learning automata. The reinforcement signal is used to collectively update all learning automata of the peers of the cluster of peer i . Finally, peer i find the configuration of peers of its cluster using the structure updating rule and send NewConfig messages to all peers of its corresponding cluster to activate them to change their connections according to the result of structure updating rule. Figure 25 shows the pseudo code of the M-Activate function.

Now we describe the algorithm that a peer i executes. The pseudo code of this algorithm is given in Fig. 26. This algorithm has three phases which are described in the rest of this section.

Fig. 26
figure 26figure 26

Pseudo code of the proposed algorithm

Full size image

Construction phase: During the Construction phase performed by peer i , the peer tries to find an appropriate cluster. In the Construction phase, peer i uses the Meeting point to find clusters of the network. Peer i randomly selects one of the clusters of the network, sends Hello message to the landmark peer of the selected cluster and the landmark peers of clusters adjacent to the selected clusters. Finally, peer i connects to the landmark peer of the selected cluster, sets its role to Ordinary, and goes to the Organization phase. If peer i is unable to find any cluster, it sets its role to Landmark, registers its identifier into the Meeting point as new landmark peer, and goes to Maintenance phase.

Organization phase: During the Organization phase performed by peer i , peer i and the peers that they have the same cluster as the cluster of peer i try to find an appropriate landmark peer for their cluster using the CADCLA-VL. In the Organization phase, peer i activates the cell of its corresponding cluster by executing function M-Activate(). Then peer i sends ClusteringRequest messages to all peers of its corresponding cluster to inform them that their landmark peer is not valid. After sending the ClusteringRequest message, peer i waits for a certain threshold THRESHOLD and gathers ClusteringReply messages which consist of information about learning automata of other peers of the cluster. peer i selects one of peers (including peer i ) which the probability of selection of change the role to landmark peer action of its learning automaton is maximum. Finally, peer i sets its role and sends SetRole messages containing the selected landmark peer to the peers of its corresponding cluster. Note that, if the selected landmark peer is peer i , peer i sets its role to Landmark and sets its role to Ordinary, otherwise. At the end of Organization phase, peer i goes to the Maintenance phase.

Maintenance phase: In this phase, if the role of peer i is Landmark, peer i sends Alive messages to all the peers of its corresponding cluster. Alive message contains information about new peers of the cluster of peer i . Peer i waits for a certain duration THRESHOLD to receive one of the ClusteringRequest, Hello, Alive, SetRole, WarmUpCell, AutomatonActivationRequest, and NewConfig messages.

Peer i , upon receiving a ClusteringRequest message from a peer j , saves the information of ClusteringRequest message. Then, peer i produces a ClusteringReply message containing the action probability of selecting the “change the role to landmark peer” action of its learning automaton. After sending the ClusteringReply message to peer j , peer i restarts the Maintenance phase.

Peer i , upon receiving a Hello message or an Alive message from a peer j , saves information of peer j , connects to peer j , and restarts the Maintenance phase.

Peer i , upon receiving a SetRole message from a peer j resided in its corresponding cluster, sets the identifier of its cluster to the identifier of the new landmark peer reported by the SetRole message. If peer i has been selected as a new landmark peer, then peer i sets its role to Landmark, otherwise peer i sets its role to Ordinary and sends a Hello message to the new landmark peer. Finally, peer i restarts the Maintenance phase.

Peer i , upon receiving a WarmUpCell message from a peer j which peer j belongs to neighboring clusters of the cluster of peer i , computes the restructuring signal using the restructuring function and sends a ReadyCell message to the peer j . The ReadyCell message contains the computed restructuring signal. Finally, peer i restarts the Maintenance phase.

Peer i , upon receiving an AutomatonActivatonRequest message from a peer j , activates its learning automaton and sends AutomatonActivatonReply message to peer j . This message contains the action selected by the learning automaton of peer i , information about delays between peer i and other peers of the cluster of peer i , and information about delays between peer i and the landmark peers of the clusters adjacent to cluster of peer i . Then, peer i waits until receives a ReinforcementSignal message from peer j . After receiving the ReinforcementSignal message, peer i updates its learning automaton using reinforcement signal reported by the ReinforcementSignal message and restarts the Maintenance phase.

Peer i , upon receiving a NewConfig message from a peer j , changes its connections to its neighbors using information reported by the NewConfig message. Then, peer i restarts the Maintenance phase.

If peer i does not receive any message during the specified period of THRESHOLD or the connections of the peer i are changed, peer i checks its role. If the role of peer i is Ordinary, peer i goes to the organization phase, and restarts the Maintenance phase otherwise.

Appendix 2

Acronyms

Definition

CA

Cellular Automaton

CMO

Control Message Overhead

CLA

Cellular Learning Automaton

CADCLA

Closed Asynchronous Dynamic Cellular Learning Automaton

CADCLA-VL

A Closed Asynchronous Dynamic Cellular Learning Automaton with multiple learning automata in each cell

DCLA

Dynamic Cellular Learning Automaton

DICLA

Dynamic Irregular Cellular Learning Automaton

HDICLA

Heterogeneous Dynamic Irregular Cellular Learning Automaton

hOverlay

A version of the proposed algorithm in which the learning automata of CADCLA-VL are deactivated

kOverlay(p)

A version of the proposed algorithm which its CADCLA-VL is tuned with an algorithm described as follows. Upon activating a cell of CADCLA-VL the information about each peer of its corresponding cluster will be used with probability p

LA

Learning Automata

lOverlay

An extension of the mOverlay algorithm

MRT

Mean Round-trip Time

M-Activate

A function that executes the cell activation process of the CLA in distributed manner

MP

MP is a global cache in the network which provides an entry point to the overlay for the new peers

mOverlay

A well-known landmark clustering algorithm

nOverlay

A version of the proposed algorithm in which CADCLA-VL is replaced with a pure-chance CADCLA-VL

OADCLA

Open Asynchronous Dynamic Cellular Learning Automaton

PE

Potential Energy

SCLA

Static Cellular Learning Automaton

TCD

Total Communication Delay

xOverlay

The proposed CLA based algorithm

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Saghiri, A.M., Meybodi, M.R. A closed asynchronous dynamic model of cellular learning automata and its application to peer-to-peer networks. Genet Program Evolvable Mach 18, 313–349 (2017). https://doi.org/10.1007/s10710-017-9299-7

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