Multi-cost Routing and its use in Wireless Ad-Hoc Optical Burst Switched Max-Min Fair Share

1. Multi-cost Routing and its use in Wireless Ad-Hoc Optical Burst Switched Max-Min Fair Share Networks Manos Varvarigos University of Patras, Greece

2. Multi-cost Routing • Traditional algorithms use single-cost routing • Limited types of cost criteria • Inability to incorporate QoS • Single path computed for each source-destination • The multi-cost routing approach: • Link costs are vectors • Path costs are also vectors For each source-destination pair, a set of candidate paths is maintained • For each packet (or session) a different cost function may be optimized • The set of cost functions that can be used is substantially enlarged

3. l on path P Multi-cost Routing • Each link is characterizedby a k-dimensional cost vector ul=(u1l,u2l, …, ukl) • For each path P a cost vector is produced based on its constituent links’ vectors Vp=(v1p, v2p,…,vkp) • The way the parameters are combined depends on their type • Each cost parameter is obtained using a (different) associative operator סּ: vip = סּuil

4. Multi-cost Routing • additive: • restrictive: • maximum representative: • Boolean operators (AND, OR) (e.g., delay, # of hops, dispersion, # of amplifiers, total consumed energy on the path) (e.g., path capacity, node residual energy on the path) (e.g., node transmission power, BER, interference on the path) (e.g.,all links, or at least one link on the path must have a certain property)

5. Non-dominated paths d here is any additive cost parameter (e.g. delay, hops, energy consumed) c here is any restrictive parameter (e.g., capacity, residual node energy) • A path is said to dominate another path when all its cost components are superior to those of the other path • Set of non-dominated pathsPn-d for a given source - destination pair: no path in the set dominates another path. • Pn-d can be found using a multi-dimensional Dijkstra-like algorithm. • Complexity can be polynomial or exponential depending on the type of the parameters

6. Multi-cost Routing Calculation of non-dominated paths example (cont):

7. minimum node residual energy total consumed power path capacity # of hops path delay The parameters and the choice of function f( ) may depend on the QoS of the user, or the interests of the network Multi-cost Routing A multi-cost algorithm consists of two phases: • Enumeration of a set of non-dominated paths for a given source-destination pair • The optimum path from this set is chosen according to some optimization function f (h, d, c, T, R, BER, …)

8. Energy-Aware Routing algorithmsWireless Ad-Hoc Networks • We propose multi-cost energy-aware routing algorithms that use the following parameters: • The number of hops h(additive) • The residual energy R at the transmitting nodes of the linkson the path(restrictive): R=min Ri • The total consumed energy T of the transmitting nodes the linkson the path(additive): T= Σ Ti • The maximum consumed energy T’ on the path(maximum representative): T’=max Ti links i on path links i on path links i on path

9. Routing algorithms tested Wireless Ad-Hoc Networks Various optimization functions f (h, R, T, T′) were tested and compared: • Minimum-Hop: • MAX/MIN Energy: • MAX/MIN Energy-Hop: • MAX/MIN Energy-Half-Hop: • SUM/MIN Energy: • SUM/MIN Energy-Hop: • SUM/MIN Energy-Half-Hop: =T′/R =hT′/R =√ h T′/R =T/R =hT/R =√ h T/R • Note: each optimization function corresponds to a different routing algorithm

10. The infinite time horizon modelWireless Ad-Hoc Networks • Packets and energy are generated at each node continuously, over an infinite time horizon. • The objective is: • to achieve the maximum throughput, • small average packet delay for a given throughput

11. The network evacuation modelWireless Ad-Hoc Networks • The network starts with a certain number of packets to be transmitted to their destination. • Each node has a certain amount of energy. • The objective is: • to serve the packets in the smallest number of steps • or serve as many packets as possible before the energy at the nodes is depleted.

12. Network Evacuation modelWireless Ad-Hoc Networks The Minimum-Hop algorithm gives the best average node residual energy at the end of the evacuation problem, but… Minimum-Hop: MAX/MIN Energy: MAX/MIN Energy-Hop:

13. Network Evacuation modelWireless Ad-Hoc Networks …but the Minimum-Hop algorithm also gives the worst variance of theresidual energyσ2Εand the worst energy-depletion times DT : Minimum-Hop: SUM/MIN Energy: SUM/MIN Energy-Hop:

14. Network Evacuation modelWireless Ad-Hoc Networks Node energy-depletion times: Minimum-Hop: SUM/MIN Energy: SUM/MIN Energy-Hop:

15. Evacuation problem RS : Received/Sent ratio SUM/MIN Energy: - SUM/MIN Energy-Hop: Minimum-Hop: -

16. Network Evacuation modelWireless Ad-Hoc Networks The average length of paths used: Minimum-Hop: SUM/MIN Energy: SUM/MIN Energy-Hop:

17. Network Evacuation modelWireless Ad-Hoc Networks Effect of thetopology Update Interval: Minimum-Hop: SUM/MIN Energy: SUM/MIN Energy-Hop:

18. Capacity constraint Limitations on an ad-hoc networkunder the infinite time horizon modelWireless Ad-Hoc Networks Upper bound on p • Energy constraint X • R is the transmission range • L is the average physical source-destination distance • ρis the energy network density • X is the recharging rate • K, K’ are constants, 2≤α≤4 • p = Bernoulli packet generation probability per node

19. Simulation Results – infinite time horizon Multicost algorithm with

20. Infinite time horizon modelWireless Ad-Hoc Networks

21. Optical Burst Switched Networks Packets destined to the same egress node and with similar QoS requirements are aggregated into bursts. A control packet is sent to reserve resources and isprocessed electronically; the burst follows after an offset time and stays in the optical domain. Tell-and-go protocols Tell-and-wait protocols

22. Burst Routing and Scheduling Problem • Given: Network with linksof known propagation delays dl and link utilization profiles.Source A wants to send a burst of size I bits and duration B=I/C to some destination G • We want to find a feasible path and the time at which the burst should start transmission, so as to optimize the burst reception time at its destination (or hop count, or…) • A tell-and-go or a tell-and-wait reservation scheme is used to send the burst

23. Multicost Burst Routing and Scheduling • Each link l is assigned a vector VlVl=(dl, Ĉl)=(dl, c1,l,c2,l,…,cd,l) • A cost vector is defined for a path p based on the cost vectors of its links • p1 dominates p2 (notation: p1 >p2) iff • Calculate the set Pn-dof non-dominated paths • Apply an optimization function f(V(p)) to the path cost vectors to select the optimal one

24. Path Binary Capacity Availability Vector • Transmission of the CAV from node A to a source node C requires time equal to the propagation delay dA,C • Assuming that the propagation delays are the same in both directions any data sent from A will incur to reach C:dA,C • Source A shifts the received CAV by 2·dA,C • The Capacity Availability Vector of a path is computed:

25. Polynomial Time Heuristic Algorithm • The number of non-dominated paths may be exponential • Heuristic variations of the multicost algorithm  define a pseudo-domination relation >ps • The pseudo-domination relation can be used to prune paths, yielding a setPn-ps-d Pn-dof non-pseudo-dominated paths of polynomial cardinality • E.g. (Availability Weighted heuristic algorithm): p1 pseudo-dominates p2 (p1 >psp2) iff

26. Delay vs traffic load ( =300kB) • The optimal multicost algorithm outperforms the Dijkstra and the Dijkstra/CA algorithms • Marginal difference between the optimal algo and the AW and CSA heuristic algorithms • The propagation delays in the network play a significant role on the link state information exchange mechanism

27. Max–Min Fair Share Networks • In a max­min fair share network, the connections using a particular link get a “fair share” of the link bandwidth. • Cost Parameters • h: number of links • r: available capacity. Usually, the capacity of a link is taken to be the residual link bandwidth. In the max­min fair share networks, however, r is an estimate of the max­min fair rate that would be obtained by the new connection if admitted. • d: path propagation delay

28. Routing algorithms tested Max–Min Fair Share Networks Widest-shortest path:min(h) In case of a tie, the one with maximum capacity is selected. Shortest-widest path:max(r) In case of a tie, the one with the minimum # of hops is selected. Multicost cost functions (h,r,d): • f(h,r) = h/r • f(d,b,r) = d + b/r • f1(d,b,r,h) = (d + b/r)*h • f2(d,b,r,h) = (d + b/r)*hn • b: the amount of data to be transmitted

29. Simulation ResultsMax–Min Fair Share Networks • Metrics: • Average delay (when MCR = 0 ) • Probability of success for a new connection (when MCR ≠ 0) Topologies considered: a random network and a 4x4 mesh network, with varying capacities.

30. Max–Min Fair Share Networks MCR = 0, Random topology, f(d,b,r,h) = (d + b/r)*h

31. Max–Min Fair Share Networks MCR ≠ 0, Mesh topology, f(d,b,r,h) = (d + b/r)*h0.5

32. Simulation ResultsMax–Min Fair Share Networks Capacity availability definition MCR = 0, Mesh and Random topology, f(d,b,r,h) = (d + b/r)*h0.5

33. Simulation ResultsMax–Min Fair Share Networks Link utilization information updates (P = 10, 50, 100) MCR = 0, transmission time >> propagation time, Mesh topology, f(d,b,r,h) = (d + b/r)*h0.5

34. Conclusionsfor Wireless Ad-Hoc Networks Multi-cost algorithms that take energy into account result in: • Increased network lifetime • More evenly spread energy consumption • Higher throughput The SUM/MIN energy-hop algorithm where the cost function is: gives the most balanced results (in terms of node residual energy, energy variance, packetsdropped, depletion times, number of hops on paths taken). The performance benefits diminish when the limitation posed by the network capacity is approached f (h, T, R) =

35. Conclusions for OBS networks • The proposed multicost burst routing and scheduling algorithm and its heuristic variations significantly outperform other simulated algorithms • The optimal multicost algorithm is not polynomial, but the proposed AW multicost heuristic algorithm has polynomial complexity, and performance that is very close to that of the optimal algorithm • The improvements obtained are more significant for small propagation delays

36. Conclusionsfor max-min fare share networks Multi-cost algorithms can result in: • Lower blocking probability • Lower average delay The algorithm that uses the cost function: f(d,b,r,h) = (d + b/r)*h0.5 gives the best results. The term r is an estimate of the max­min fair rate that would be obtained by the new connection if admitted.