1. 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

2. 2 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.

3. 3 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.

4. 4 Factors for replica management λ: arrival rate to a local cell µ : user departure rate out of a local cell δ R : read rate to read data item in a local cell δ W : write rate to update existing data item σ r : reconnection rate of a disconnected user σ d : disconnection rate of a connected user T: time interval for primary cell to determine if a local cell need to contain a replica C T : cost incurred to perform a periodic check N: number of users in the system

5. 5 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.

6. 6 Replica allocation/deallocation conditions n 1 : number of users outside the local cell n 2 : number of users at the local cell A replica is created/maintained in the local cell if n 2 *δ R ≥ n 1 *δ W A local replica is eliminated from the local cell if n 2 *δ R < n 1 *δ W

7. 7 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: n 1 *λ t-exit transition rate: n 2 * µ

8. 8 Markov Model for “enter and exit events” Model the user arrival/departure behavior System user N=10

9. 9 Periodic maintenance events

10. 10 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

11. 11 Periodic maintenance events (cont.) Transition t1: –No replica at a local cell –guard(t1): n 2 *δ R ≥ n 1 *δ W 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): n 2 *δ R < n 1 *δ W True: deallocate replica from local cell False: t3 fires, periodic maintenance doesn’t alter the state of cell.

12. 12 Cost model C read : average cost rate incurred because of missing reads –C read =∑P i *C read,i –C read,i =n 2 δ R if no replica at the local cell –C read,i =0 otherwise C write : average cost rate incurred because of write propagations –C write =∑P i *C write,i –C write,i =n 1 δ W if there is replica at the local cell –C write,i =0 otherwise

13. 13 Cost model (cont.) C periodic : cost rate to perform the periodic system check –C T : average overhead cost –Check rate: 1/T –C periodic =C T /T Overall system cost rate –C overall =C read +C write +C periodic

14. 14 Extension to Petri-net model Consider the user disconnection and connection behaviors

15. 15 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

16. 16 Effects of the Arrival-Departure Rate and Read-Write Rate N = 10 and C T = 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, C write ￪ 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, C read ￪

17. 17 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, C read ￬ 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, C write ￬

18. 18 Optimal Periodic Maintenance Interval

19. 19 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 & C T = 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

20. 20 Effects of Changing the Periodic Maintenance Event Cost

21. 21 Effects of Changing the Periodic Maintenance Event Cost (cont.) Figure 6: Impact of different C T (0.1, 0.3, 0.5) on C overall Scenario: 1:5 arrival-departure rate / 16:2 read-write rate / N = 10 At low rate of checking: same C overall for all three C T At the increasing rate of checking: C T ￪  C overall ￪  Because a high cost associated with periodic checking increases C periodic (=C T /T) in C overall (= C read + C write + C periodic ) Observe an optimal periodic maintenance rate at each curve in Figure 6 Result: As C T increases, the optimal periodic maintenance rate (1/T) has a smaller value in order to reduce the overhead associated with C periodic.

22. 22 Effects of Changing the Number of Users

23. 23 Effects of Changing the Number of Users (cont.) Figure 7: Impact of increasing the number of users on C overall Scenario: 1:5 arrival-departure rate / 16:2 read-write rate / C T = 0.1 Number of users in the system ￪  C overall ￪ 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 ￪  C write ￪ 2. When the local cell does not contain a replica: N ￪  relatively users in the local cell needs to read ￪  C read ￪ Result: As more users are in the system, the optimal periodic maintenance interval (1/T) increases in order to reduce C read and C write so as to minimize C overall at the expense of increasing C periodic (=C T /T)

24. 24 Sensitivity of Time Distribution

25. 25 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 / C T = 0.1 Scenario 2: 1:20 arrival-departure rate / 16:2 read-write rate / C T = 0.1 The reason to choose TimeNET over SPNP: TimeNET provides deterministic transitions. Result: TimeNET graph lines are slightly lower in C overall 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

26. 26 Conclusions Working in conflict (high arrival and high write & low departure and low read ratios or vice versa)  high C overall Working in harmony (high arrival and high read & low departure and low write or vice versa)  low C overall Always an optimal periodic maintenance interval exists that minimizes C overall. Higher C overall  Higher the periodic maintenance rate (1/T) to to achieve the minimal cost.