Replicated Object Management with Periodic Maintenance in Mobile Wireless System

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Replicated Object Management with Periodic
Maintenance in Mobile Wireless System

• DING-CHAU WANG, ING-RAY CHEN, CHIH-PING CHU and
  I-LING YEN
• Presented by Jeff Joyner Hui Zhang

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Agenda

• Introduction
• System Model
• Performance Model
• Analysis
• Conclusion

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Introduction

• Periodic maintenance strategies are studied for
  managing replicated objects in mobile wireless
  environment
• Data Replication is a proven technical for
  improving fault tolerance and performance of
  distributed and database system

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Data Replication

• Static scheme
• The number of replicas and their placement is
  predetermined and fixed.
• The number or placement of the replicas and dose
  not change as user patterns change
• Dynamic scheme
• the number of replicas and placement are changed
  on demands

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Basic Cost of an object

• Read Cost the saving cost due to local replicas
• CR is the cost saved due to a read if the cell
  has a replica of the object
• NR is the number of local reads
• Write Cost extra cost due to local replicas
• CW is the extra cost incurred due to a write if
  the cell has a replica of the object locally
• NW is the number of remote writes performed on a
  data object
• Periodic maintenance cost
• Objectives
• Saving cost Extra Cost
• CR NR CW NW
• Minimize the total cost
• ReadCost WriteCost MaintenanceCost

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System Model

• Three kinds of cells in a mobile wireless
  environment
• A primary cell
• A local cell
• Neighboring cells

P
N
N
L
N
N
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A primary cell

• Keeps the authoritative copy of an object
• Periodically checks the status of the network to
  determine if service could be efficiently
  provided by having replicas of the object held at
  various cells throughout the system

P
N
N
L
N
N
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The local cell

• Read
• Read an object from nearest neighboring cell if
  no one exits in local cell
• The more replicas, the lower read cost
• Write
• The changed object is recorded by the primary
  cell and propagate to others possessing the
  object
• The more replicas, the higher cost for writing

P
N
N
L
N
N
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Two basic conditions

• Condition 1 A replica is maintained or created
  in the local cell
• n2dR n1dW
• Condition 2 a local replica is eliminated from
  local cell
• n2dR lt n1dW

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The Factors influence the cost
P
N
N
L
N
N
A user in local cell MU
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Assumption

• Exponentially distributed
• ? is the rate at which a user moves from the
  network at large to the local cell.
• µ is the rate at which a user moves from the
  local cell back into the network.
• sd is the rate at which a connected user
  disconnects from the network.
• sr is the rate at which a disconnected user
  reconnects to the network.
• both the write rate and the read rate for a
  particular data object can be determined from
  historical information.
• The write rate (dW) is the average rate at which
  a user in the network will write to the data
  object.
• The read rate (dR) is the average rate at which a
  user in the network will read the data object.

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The Factors

• T The time interval over which this checking
  occurs is denoted by a fixed periodic maintenance
  interval
• to operate efficiently, the primary cell must
  periodically check the status of a remote cell to
  determine whether or not a copy is justified at
  that location. This periodic checking occurs on a
  deterministic basis.
• N the total number of users in the system
• n1 the number of outside of the local cell
• n2 the number of users at the local cell

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SPN Model

• Enter and Exit events
• States
• Local_users local cell
• global_users outside of the local cell
• Transactions
• t_enter n1?
• t_exit n2µ

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Markov Model

• The state is label by n2, the number of users in
  the local cell
• Total number of users in the system, N, is 10

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Steady State Analysis

• when the arrival rate ? is much higher than the
  departure rate µ, say ?/µ 10, there is a high
  probability (0.771) that at least 9 users are
  inside the local cell.
• if theratio is small, say, ?/µ 1, then the
  probability that at least 9 users are inside the
  cell is low (0.01)

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Periodic Maintenance Events

• Periodically checking whether or not there should
  exit a replica of an object in the local cell
• Checking interval is T, prefixed, and the rate
  for Transaction tT is 1/T
• When tT is fired, there is a token goes to
  time_event,representing the event that a
  periodic maintenance check has just started

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Periodic Maintenance Events

• Place object means there is a replica in the
  local cell
• Place no_object means there is no a replica in
  the local cell.
• One token is in either Place object or Place
  no_object.

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Periodic Maintenance Events

• Initially, the token is in Place no_object
• If token in Place no_object, and the guard is
  satisfied, the token will be moved to Place
  object by t1
• Priority(t1)gtPriority(t3) to ensure that t3 will
  vanish the token in place event only if t1 fails
  to move the token

Guard n2dR n1dW
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Periodic Maintenance Events

• If there is a token in object, and there is a
  token in time_event, t2 will fire and move the
  token out of object to no_object as long as the
  guard is satisfied
• Priority(t1)gtPriority(t3) to ensure that t3 will
  vanish the token in place event only if t1 fails
  to move the token

Guard n2dR lt n1dW
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Cost Model

• 3 cost metrics
• Cread Cost rate for missed read
• Cwrite Cost rate for write propagations
• Cperiodic Cost rate for periodic system check
• Overall Cost
• Coverall Cread Cwrite Cperiodic

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Overall Read Cost

• Average cost rate incurred because of reading the
  object when there is no replica at the local cell

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Overall Write Propagation Cost

• Cost rate incurred because of write propagations
  when a replica exists in the local cell

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Periodic System Check Cost

• Cperiodic CT/T
• T periodic maintenance interval
• CT cost of each periodic system check
• The entire system cost can be reduced by
  optimizing the periodic maintenance interval

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Connection considerations

• Original model did not consider
  disconnection/reconnection Mobile users
  disconnect and reconnect to avoid high
  communication cost and save battery life
• An extension to the model provides considerations
  for disconnection and reconnection in a wireless
  environment

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Connection extension
Original System Model with no Connection
considerations
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Connection extension
New Place for Disconnected Global Users
New Transition for Arrivals
New Transition for Departures
New Place for Disconnected Local Users
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Connection extension
New Transition for Reconnection
New Transition for Disconnection
New Transition for Reconnection
New Transition for Disconnection
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Analysis

• For all analysis results, to fairly compare all
  read-write ratios on the overall cost, the
  combined read-write rate is fixed to be a
  constant.
• dR Read rate
• dW Write rate
• Combinations 9-9, 12-6, 16-2

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Rate Effects

• Arrival-departure and read-write rate ratios can
  counterbalance each other
• An arrival-departure rate that favors arrivals
  and a read-write ratio that favors write actions
  is matched by reversing the ratios

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Rate Scenarios

• High Cost
• High arrival rate, ?, and low read rate
• Low departure rate, µ, and high write rate
• Low arrival rate, ?, and high read rate
• High departure rate, µ, and low write rate
• Low Cost
• High arrival rate, ?, and high read rate
• Low departure rate, µ, and low write rate
• Low arrival rate, ?, and low read rate
• High departure rate, µ, and high write rate

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Rate Trials

• High cost working in conflict
• Low cost working in unison

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Periodic Maintenance Interval

• There exists an optimal maintenance period T in
  every system model
• The general trend for determining the optimal
  periodic maintenance rate is that the higher the
  overall cost rate, the higher the required
  periodic maintenance rate to obtain the minimum
  cost point on the curve

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Periodic Maintenance Interval
Periodic Rate .001 essentially means no periodic
maintenance of the system is required
Optimal Periodic Maintenance Rate
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Periodic Maintenance Event Cost

• CT Average cost per periodic maintenance event
• There exists an optimal periodic maintenance
  event cost CT
• For testing purposes, values of .1, .3, and .5
  were used for CT

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Periodic Maintenance Event Cost
Optimal Maintenance Event Cost proves to be the
lowest cost value of .1 with a sufficiently high
periodic maintenance rate
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Number of Users
All other variables were held constant for this
scenario representing a high cost
case Arrival-departure 15 Read-write 162 CT
0.1
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Sensitivity of Time Distributions
TimeNet is consistently lower because of the more
uniform timer which leads to more stability, less
conflicts and a lower overall cost
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Conclusions

• The system can improve system performance by
  optimizing the periodic maintenance interval to
  reduce the overall cost
• The higher the overall cost, the higher the
  periodic maintenance rate will have to be set to
  achieve the minimal cost

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Questions?