Integer Programming for Media Streams Planning Problem

Transcription

1 Integer Programming for Media Streams Planning Problem Pavel Troubil Hana Rudová MEMICS 2010, October 24, 2010

2 Motivation Advanced collaborative environments Setup communication similarly as a phone call Setup many components End applications, data distribution paths, network links,...

3 Why Special Data-distribution Approaches? 1:n transmissions Multicast not continously deployed High bandwidth Best effort hop-by-hop routing not suitable

4 Problem Network topology Set of data producers Sets of data consumers Distribution tree for each producer All transmissions concurrent

5 User s view of a network User does not know a physical topology Dynamic changes, security When should we consider two nodes as "connected"? Defined full-mesh subnets

6 Nodes, applications Nodes End-nodes, servers v V Applications Producers Distributors Consumers p P d D c C Applications are limited on a single node

7 Links Links Data transmission between nodes l L Parameters Capacity Latency cap(l) latency(l)

8 Interfaces Network interfaces Several on a node Defined capacity i I capi (i) i 1 i 5 i 3 i 4 i 2 i 6

9 Streams Stream Transmission demand Producer Consumer/s s S producer(s) consumers(s) Parameter Bandwidth cap(l)

10 Data distribution Make multiple copies of the data

11 Data distribution Make multiple copies of the data All packets to a single consumer through the same path 1/2 1/2

12 Linear programming Linear objective function c 1 x 1 + c 2 x c n x n Linear constraints a 1,1 x 1 + a 1,2 x a 1,n x n b 1. a m,1 x 1 + a m,2 x a m,n x n b m Significantly harder for integer variables Solvers commercial as well as open-source

13 IP model Binary decision variable x s,l = { 1 if s is transmitted over l, 0 otherwise. 0 1

14 Objective function Minimize overall latency min s S x s,l latency(l) l L

15 Constraint groups 1. Capacity constraints 2. Sending / receiving 3. Tree distribution 4. Cycle elimination

16 IP constraints Link capacity bw(s) x s,l cap(l) Streams transmitted over a link must fit in s S

17 IP constraints Interface capacity Streams transmitted over an interface must fit in s S l links(i) bw(s) x s,l capi (i)

18 IP constraints Who is allowed to send data? There is not producer(s) neither any distributor on a starting node of l x s,l = 0

19 IP constraints Who is allowed to receive? There is not any distributor neither stream consumer on an ending node of l x s,l = 0

20 IP constraints Producer transmits single copy of the data x s,l = 1 l outlinks(producer(s)) P

21 IP constraints Consumer receives single copy of the data x s,l = 1 l inlinks(c) C

22 IP constraints Distributor receives data at most once x s,l 1 s S l inlinks(d)? D

23 IP constraints Distributor forwards the incoming stream l inlinks(d) x s,l l outlinks(d) x s,l D

24 IP constraints Distributor forwards the incoming stream l inlinks(d) x s,l l outlinks(d) x s,l D

25 IP constraints No data "emerges" at a distributor outlinks(d) x s,l l inlinks(d) l outlinks(d) x s,l D

26 IP constraints No data "emerges" at a distributor outlinks(d) x s,l l inlinks(d) l outlinks(d) x s,l D

27 Cycle elimination C D C P D D C D D At most k 1 active links among each k-tuple of nodes per stream

28 Cycle elimination C D C P D D C D D At most k 1 active links among each k-tuple of nodes per stream

29 Testing topologies Measuring time needed to find an optimal solution Comparison to previous constraint programming (CP) based solver

30 1:n-s topology measurement Run time [ms] Links IP CP Links Sites 0

31 1:n-r topology measurement Run time [ms] Links IP CP Links Sites 0

32 m:n topology measurement Run time [ms] Links IP CP Links Sites 0

33 Conclusion and Future work Conclusions New integer programming model for the media streams planning problem Performance improvement compared to previous solver Future work Cycle elimination methods Different models Heuristics Extensions of the problem