Introduction Queueing Theory Analysis: Analytic Results Consistency Summary Scalability Analysis of the Hierarchical Architecture for Distributed Virtual Environments Michael Kwok Johnny W. Wong Presentation by Alexander Pokluda Cheriton School of Computer Science, University of Waterloo, Canada IEEE Transactions on Parallel and Distributed Systems 2008
Introduction Queueing Theory Analysis: Analytic Results Consistency Summary Outline Introduction 1 Hierarchical Architecture Model of a Distributed Virtual Environment Queueing Theory Analysis: Analytic Results 2 Analysis of Arrival Rates Results and Discussion 3 Consistency Consistent and Inconsistent States Virtual Vision Domain Performance Evaluation
Introduction Queueing Theory Analysis: Analytic Results Consistency Summary What is a Distributed Virtual Environment? Definition A Distributed Virtual Environment is a shared virtual environment where users at their workstations interact with each other over a network
Introduction Queueing Theory Analysis: Analytic Results Consistency Summary Design and Performance of a Virtual Environment Infrastructure In terms of scalability, a promising system architecture is a two-level hierarchical architecture Although the two-level hierarchical architecture is believed to have good properties with respect to scalability, not much is known about its performance characteristics Contributions Queueing theory is used to develop a performance model for the two-level architecture and obtain analytic results on the workload experienced by each server The authors also investigate the issue of consistency and develop a novel technique to achieve weak consistency among the copies of the virtual environments at the various servers
Introduction Queueing Theory Analysis: Analytic Results Consistency Summary Hierarchical Architecture Two-Level Hierarchical Architecture At the lower level users assigned to c 6 c 5 servers based on c 7 c 4 load-balancing S 3 S 2 consideration At the higher level c 3 servers communicate S 4 S 1 c 2 among themselves c 1 to ensure that updates are sent to S 5 S 6 affected users and that their VEs are as c 8 c 10 consistent as c 9 possible
Introduction Queueing Theory Analysis: Analytic Results Consistency Summary Hierarchical Architecture Update Message Flow c 6 c 5 c 7 c 4 Suppose user c 4 is S 3 S 2 assigned to server S 2 and moves his/her avatar c 3 to user to a new location S 4 S 1 c 2 c 1 S 5 S 6 c 8 c 10 c 9
Introduction Queueing Theory Analysis: Analytic Results Consistency Summary Hierarchical Architecture Update Message Flow c 6 c 5 c 7 c 4 c 4 Suppose user c 4 is S 3 S 2 S 2 assigned to server S 2 and moves his/her avatar c 3 to user to a new location update packet is 1 S 4 S 1 c 2 sent to local server c 1 S 5 S 6 c 8 c 10 c 9
Introduction Queueing Theory Analysis: Analytic Results Consistency Summary Hierarchical Architecture Update Message Flow c 6 c 5 c 7 c 4 c 4 Suppose user c 4 is S 3 S 3 S 2 S 2 assigned to server S 2 and moves his/her avatar c 3 to user to a new location update packet is 1 S 4 S 1 c 2 sent to local server syn packet is sent to 2 c 1 remote servers S 5 S 5 S 6 c 8 c 10 c 9
Introduction Queueing Theory Analysis: Analytic Results Consistency Summary Hierarchical Architecture Update Message Flow c 6 c 6 c 5 c 7 c 4 c 4 Suppose user c 4 is S 3 S 3 S 2 S 2 assigned to server S 2 and moves his/her avatar c 3 to user to a new location update packet is 1 S 4 S 1 c 2 sent to local server syn packet is sent to 2 c 1 remote servers S 5 S 5 S 6 update packet is 3 sent to remote users c 8 c 8 c 10 c 9 c 9
Introduction Queueing Theory Analysis: Analytic Results Consistency Summary Model of a Distributed Virtual Environment Avatars and Vision Domains Our VE is modelled as a 2D unit square grid Avatars can only be located at a grid intersection ( x , y ) Each avatar is at the centre of its vision domain B vision domain avatar V . . . U 1 0 . . . 0 1 A
Introduction Queueing Theory Analysis: Analytic Results Consistency Summary Model of a Distributed Virtual Environment User Movement When the user makes a move, she can move up, down left or right according to a probability distribution Assumptions Movement of each user is modelled by a Markovian chain Probability distribution is the same for all users Time until a user makes their next move is exponentially distributed and user moves are mutually independent Let q a , b ; c , d be the probability that a user moves from ( a , b ) to ( c , d ) in one step. It follows from the above assumptions that P a , b = � A � B d = 0 p c , d q c , d ; a , b for a = 0 , 1 , ..., A ; b = 0 , 1 , ..., B c = 0 where � A � B b = 0 p a , b = 1 a = 0
Introduction Queueing Theory Analysis: Analytic Results Consistency Summary Analysis of Arrival Rates Total Arrival Rate of Update and Syn Packets to a Server Let N i be the number of logged on users at S i , i = 1 , 2 , ..., K Let γ i be the arrival rate of update packets to S i Let η k , i be the arrival rate of syn packets from S k to S i , k � = i Arrival Rate of Update Packets Let φ be the rate at which a user makes a move. The combined arrival rate of update packets to S i is given by γ i = N i φ.
Introduction Queueing Theory Analysis: Analytic Results Consistency Summary Analysis of Arrival Rates Arrival Rate of Syn Packets Consider a tagged user at S k 1 Let the probability that after the tagged user has made a 2 move there are one or more users logged on to S i who are within the tagged user’s vision domain be g k , i Let ξ k , i ( n ) be the probability that exactly n users at S i are 3 within the tagged user’s vision domain �� N i ( h ( a , b )) n ( 1 − h ( a , b )) N i − n � ξ k , i ( n ) = � A � B � p a , b a = 0 b = 0 n where h ( a , b ) = � x ∗ � y ∗ y = y ′ p x , y x = x ′ Then g k , i = 1 − ξ k , i ( 0 ) and η k , i = g k , i N k φ for N k users at S k 4 Summing over all other servers, η i = � K k = 1 , k � = i η k , i 5 The total arrival rate to S i is the sum of γ i and η i , λ i = γ i + η i .
Introduction Queueing Theory Analysis: Analytic Results Consistency Summary Results and Discussion Total Arrival Rate Results λ i , total arrival rate at S i , for a VE with size 100 × 100 and 150 × 150 and various D , where D is the width and height of the vision domain
Introduction Queueing Theory Analysis: Analytic Results Consistency Summary Results and Discussion Total Arrival Rate Discussion In all cases, we observe a reduction in the total arrival rate λ i when more servers are used A larger vision domain leads to a higher total arrival rate The fact that λ i is a decreasing function of K indicates that the two-level architecture has good properties with respect to scalability
Introduction Queueing Theory Analysis: Analytic Results Consistency Summary Results and Discussion Scalability K min , minimum number of servers required to support N users while λ i /µ i ≤ y for VE with size 100 × 100 and 150 × 150
Introduction Queueing Theory Analysis: Analytic Results Consistency Summary Results and Discussion Scalability Discussion K min increases almost linearly with N This is a good property with respect to scalability Rate of increase of K min is affective by the size of the vision domain D A large D has a negative impact on scalability A larger VE means a lower density of avatars and smaller rate of syn packets generated
Introduction Queueing Theory Analysis: Analytic Results Consistency Summary Consistent and Inconsistent States Inconsistency Scenario 1 Scenario 1: User u ’s vision domain contains users who should not be there Example At t 0 , users u and v are in each other’s vision domain VE j VE i Global View of the VE t 0 v v v u u u
Introduction Queueing Theory Analysis: Analytic Results Consistency Summary Consistent and Inconsistent States Inconsistency Scenario 1 Scenario 1: User u ’s vision domain contains users who should not be there Example At t 0 , users u and v are in each other’s vision domain At t 1 , user v at S j moves left by one step (no syn sent) VE j VE i Global View of the VE t 1 v v v u u u
Introduction Queueing Theory Analysis: Analytic Results Consistency Summary Consistent and Inconsistent States Inconsistency Scenario 1 Scenario 1: User u ’s vision domain contains users who should not be there Example At t 0 , users u and v are in each other’s vision domain At t 1 , user v at S j moves left by one step (no syn sent) At t 2 , user u at S i moves left by one step (syn packet sent) VE j VE i Global View of the VE t 2 v v v u u u
Introduction Queueing Theory Analysis: Analytic Results Consistency Summary Consistent and Inconsistent States Inconsistency Scenario 1 Scenario 1: User u ’s vision domain contains users who should not be there Example At t 0 , users u and v are in each other’s vision domain At t 1 , user v at S j moves left by one step (no syn sent) At t 2 , user u at S i moves left by one step (syn packet sent) At t 3 , v moves down by one step (consistency restored) VE j VE i Global View of the VE t 3 v u v u v u
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