Replicated Object Management with Periodic Maintenance in Mobile Wireless Systems

By Ding-Chau Wang, In-Ray Chen, Chin-Ping Chu, and I-ling Yen

CS5214 Jin-Hee Cho & Yongjie Fan

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Data Replication

• Data replication can improve system fault tolerance, performance, and efficiency.

• In mobile wireless network, cost will change dynamically depended on the number and placement of data replicas.

• To optimize the cost of replicated data management, periodic maintenance scheme is used.

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System Model

• Wireless environment: primary cell, neighboring cells, a local cell

• Primary Cell: periodically check network status to determine allocate/deallocate a replica

• User in local cell has to read from neighboring cells if local cell has no local copy.

• Replica in local cell can lower the cost for user reading, but it increases the cost incurred by writing for update.

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Factors for replica management • λ: arrival rate to a local cell • µ: user departure rate out of a local cell• δR: read rate to read data item in a local cell• δW: write rate to update existing data item• σr: reconnection rate of a disconnected user• σd: disconnection rate of a connected user• T: time interval for primary cell to determine if a local cell

need to contain a replica• CT: cost incurred to perform a periodic check• N: number of users in the system

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Cost analysis

• Local miss reading cost normalized to 1– No replica at local node: obtain a copy from a

neighboring cell with replica copy• Remote write cost normalized to 1

– Write operation occurs by propagation from primary node to neighboring node with replica, then to the local cell

• Cost analysis is based on a normalized cost of 1 for each missing reading read or remote write operation.

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Replica allocation/deallocation conditions

• n1: number of users outside the local cell

• n2: number of users at the local cell

• A replica is created/maintained in the local cell if n2*δR ≥ n1*δW

• A local replica is eliminated from the local cell if n2*δR < n1*δW

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Petri-Net Model for “enter and exit events”

• Model the movement of users between network (global_users) and the local cell (local_users)

• t-enter transition rate: n1*λ

• t-exit transition rate: n2*µ

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Markov Model for “enter and exit events”

• Model the user arrival/departure behavior• System user N=10

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Periodic maintenance events

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Periodic maintenance events (cont.)

• Initially, no replica in the local cell (no_object state)

• Periodic checking – determine if allocate/deallocate a local replica

at a local cell– Transition tT: interval T

• Time_event– start a periodic maintenance check once tT fires

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Periodic maintenance events (cont.)

• Transition t1:– No replica at a local cell– guard(t1): n2*δR ≥ n1*δW

• True :allocate replica at local cell• False: t3 fires, periodic maintenance doesn’t alter the state of cell.

• Transition t2:– Replica at a local cell– guard(t2): n2*δR < n1*δW

• True: deallocate replica from local cell• False: t3 fires, periodic maintenance doesn’t alter the state of cell.

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Cost model

• Cread: average cost rate incurred because of missing reads– Cread=∑Pi*Cread,i

– Cread,i=n2δR if no replica at the local cell– Cread,i=0 otherwise

• Cwrite: average cost rate incurred because of write propagations– Cwrite=∑Pi*Cwrite,i

– Cwrite,i=n1δW if there is replica at the local cell– Cwrite,i=0 otherwise

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Cost model (cont.)

• Cperiodic : cost rate to perform the periodic system check– CT: average overhead cost – Check rate: 1/T– Cperiodic=CT/T

• Overall system cost rate– Coverall=Cread+Cwrite+Cperiodic

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Extension to Petri-net model

• Consider the user disconnection and connection behaviors

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Analysis

• Effects of the Arrival-Departure Rate and Read-Write Rate

• Optimal Periodic Maintenance Interval• Effects of Changing the Periodic

Maintenance Event Cost• Effects of Changing the Number of Users• Sensitivity of Time Distributions

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Effects of the Arrival-Departure Rate and Read-Write Rate

• N = 10 and CT = 0.1• The arrival-departure & read-write ratios can counterbalance each other.• The arrival-departure & read-write ratios work in conflict.• Trial #1: High arrival rate and high write rate. Users in the local cell ￪ Needs to place a replica at the local cell ￪ however, high write rate given Therefore, Cwrite ￪• Trial #2: High departure rate and high read rate. Users in the local cell ￬ Needs to place a replica at the local cell ￬ however, high read rate given Therefore, Cread ￪

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Effects of the Arrival-Departure Rate and Read-Write Rate (cont.)

• Difference from Table 3: The arrival-departure & read-write ratios work in harmony.

• Trial #3: High arrival rate and high read rate. Users in the local cell ￪ Needs to place a replica at the local cell ￪

further, high read rate given Therefore, Cread ￬• Trial #4: High departure rate and high write rate. Users in the local cell ￬ Needs to place a replica at the local cell ￬

further, high write rate given Therefore, Cwrite ￬

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Optimal Periodic Maintenance Interval

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Optimal Periodic Maintenance Interval :Figure 5 (cont.)

• The system performs a check in every fixed T period to determine if a replica should be allocated or deallocated in the local cell.

• Number of users accessing to the replicated object = 10 & CT = 0.1• The highest cost : 1:5 arrival-departure rate / 16:2 read-write rate -- Conflict in two sets of parameters high overall cost scenario -- The lowest periodic maintenance rate at 1/T = 12• The lowest cost : 7: 1 arrival-departure rate / 16:2 read-write rate -- Harmony in two sets of parameters low overall cost scenario -- The lowest periodic maintenance rate at 1/T = 0.001 -- In practice, no need for periodic maintenance of the system allocate a

replica in the local cell virtually all the time.• Result: higher overall cost rate higher periodic maintenance rate

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Effects of Changing the Periodic Maintenance Event Cost

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Effects of Changing the Periodic Maintenance Event Cost (cont.)

• Figure 6: Impact of different CT (0.1, 0.3, 0.5) on Coverall • Scenario: 1:5 arrival-departure rate / 16:2 read-write rate / N = 10• At low rate of checking: same Coverall for all three CT

• At the increasing rate of checking: CT ￪ Coverall ￪ Because a high cost associated with periodic checking increases

Cperiodic (=CT/T) in Coverall (= Cread + Cwrite + Cperiodic)• Observe an optimal periodic maintenance rate at each curve in Figure

6• Result: As CT increases, the optimal periodic maintenance rate (1/T)

has a smaller value in order to reduce the overhead associated with Cperiodic.

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Effects of Changing the Number of Users

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Effects of Changing the Number of Users(cont.)

• Figure 7: Impact of increasing the number of users on Coverall

• Scenario: 1:5 arrival-departure rate / 16:2 read-write rate / CT = 0.1• Number of users in the system ￪ Coverall ￪• Interpretation in two cases:1. When the local cell contains a replica: N ￪ users outside the local

cell ￪ relative needs to write to the replica in the local cell ￪ Cwrite ￪

2. When the local cell does not contain a replica: N ￪ relatively users in the local cell needs to read ￪ Cread ￪

• Result: As more users are in the system, the optimal periodic maintenance interval (1/T) increases in order to reduce Cread and Cwrite so as to minimize Coverall at the expense of increasing Cperiodic (=CT/T)

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Sensitivity of Time Distribution

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Sensitivity of Time Distribution (cont.)• The difference between SPNP and TimeNET: the periodic maintenance

time in the SPNP model is exponentially distributed with the average time of T.

• Figure 8: Data obtained from the SPNP model and the TimeNET model.

• Scenario 1: 1:5 arrival-departure rate / 16:2 read-write rate / CT = 0.1• Scenario 2: 1:20 arrival-departure rate / 16:2 read-write rate / CT = 0.1• The reason to choose TimeNET over SPNP: TimeNET provides

deterministic transitions.• Result: TimeNET graph lines are slightly lower in Coverall because the

deterministic characteristics of the timer are more uniform than the exponential characteristics of the SPNP.

• A large deviation in 1:20 arrival-departure curve: the variance in T in two different models.

• SPNP: an exponentially distributed random variable with the average time T

• TimeNET: a fixed constant T

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Conclusions• Working in conflict (high arrival and high write & low

departure and low read ratios or vice versa) high Coverall • Working in harmony (high arrival and high read & low

departure and low write or vice versa) low Coverall • Always an optimal periodic maintenance interval exists

that minimizes Coverall.

• Higher Coverall Higher the periodic maintenance rate (1/T) to to achieve the minimal cost.