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.
