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

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

Multi-cost Routing  Each link is characterized by a k-dimensional cost vector u l =(u 1l,u 2l, …, u kl )  For each path P a cost vector is produced based on its constituent links’ vectors V p =(v 1p, v 2p,…,v kp )  The way the parameters are combined depends on their type  Each cost parameter is obtained using a (different) associative operator סּ : v ip = סּ u il l on path P

Multi-cost Routing  additive:  restrictive:  maximum representative:  Boolean operators (AND, OR) (e.g., path capacity, node residual energy on the path) (e.g., delay, # of hops, dispersion, # of amplifiers, total consumed 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)

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) Non-dominated paths  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 paths P n-d for a given source - destination pair: no path in the set dominates another path.  P n-d can be found using a multi-dimensional Dijkstra-like algorithm.  Complexity can be polynomial or exponential depending on the type of the parameters

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

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, …) # of hops path delay path capacity total consumed power minimum node residual energy The parameters and the choice of function f( ) may depend on the QoS of the user, or the interests of the network

Energy-Aware Routing algorithms Wireless 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 links on the path (restrictive): R=min R i  The total consumed energy T of the transmitting nodes the links on the path (additive): T= Σ T i  The maximum consumed energy T’ on the path (maximum representative): T’= max Ti links i on path

Routing algorithms tested Wireless Ad-Hoc Networks  SUM/MIN Energy:  SUM/MIN Energy-Hop:  SUM/MIN Energy-Half-Hop: 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: =√ h T/R =T′/R =hT′/R =√ h T′/R =T/R =hT/R  Note: each optimization function corresponds to a different routing algorithm

The infinite time horizon model Wireless 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

The network evacuation model Wireless 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.

Network Evacuation model Wireless Ad-Hoc Networks The Minimum-Hop 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:

Minimum-Hop …but the Minimum-Hop algorithm also gives the worst variance of the residual energy σ 2 Ε and the worst energy-depletion times DT : Minimum-Hop: SUM/MIN Energy: SUM/MIN Energy-Hop: Network Evacuation model Wireless Ad-Hoc Networks

SUM/MIN Energy: SUM/MIN Energy-Hop: Minimum-Hop: Node energy-depletion times:

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

The average length of paths used: Minimum-Hop: SUM/MIN Energy: SUM/MIN Energy-Hop: Network Evacuation model Wireless Ad-Hoc Networks

Minimum-Hop: SUM/MIN Energy: SUM/MIN Energy-Hop: Effect of the topology Update Interval:

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

Simulation Results – infinite time horizon Multicost algorithm with

Infinite time horizon model Wireless Ad-Hoc Networks

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 is processed electronically; the burst follows after an offset time and stays in the optical domain. Tell-and-wait protocols Tell-and-go protocols

Burst Routing and Scheduling Problem  Given: Network with links of known propagation delays d l 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

Multicost Burst Routing and Scheduling  Each link l is assigned a vector V l V l =(d l, Ĉ l )=(d l, c 1,l,c 2,l,…,c d,l )  A cost vector is defined for a path p based on the cost vectors of its links  p 1 dominates p 2 (notation: p1 >p2) iff 1)Calculate the set P n-d of non-dominated paths 2)Apply an optimization function f(V(p)) to the path cost vectors to select the optimal one

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

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 set P n-ps-d P n-d of non-pseudo-dominated paths of polynomial cardinality  E.g. (Availability Weighted heuristic algorithm): p 1 pseudo-dominates p 2 (p 1 > ps p 2 ) iff

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

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

Routing algorithms tested Max–Min Fair Share Networks Multicost cost functions (h,r,d):  f(h,r) = h/r  f(d,b,r) = d + b/r  f 1 (d,b,r,h) = (d + b/r)*h  f 2 (d,b,r,h) = (d + b/r)*h n 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. b: the amount of data to be transmitted

Simulation Results Max–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.

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

Max–Min Fair Share Networks MCR ≠ 0, Mesh topology, f(d,b,r,h) = (d + b/r)*h 0.5

Simulation Results Max–Min Fair Share Networks Capacity availability definition MCR = 0, Mesh and Random topology, f(d,b,r,h) = (d + b/r)*h 0.5

Simulation Results Max–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)*h 0.5

Conclusions for 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, packets dropped, 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) =

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

Conclusions for 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)*h 0.5 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.