A hierarchical multicriteria routing model with traffic splitting for MPLS networks

A hierarchical multicriteria routing model with traffic splitting for MPLS networks João Clímaco, José Craveirinha, Marta Pascoal jclimaco@inesccpt, jcrav@deecucpt, marta@matucpt University of Coimbra and INESC Coimbra PORTUGAL IIASA 2006 p1/14

Abstract Routing problems in multiservice communication networks involve the calculation of paths satisfying multiple constraints and seeking simultaneously to optimise the relevant metrics We address a novel bilevel multicriteria routing model for MPLS networks using traffic-splitting and propose a resolution approach We will begin by describing a previous bilevel multicriteria routing model for multiservice networks and its application to a video-traffic routing problem where the objective functions of the first level seek to minimise the negative impact of the use of a path in the remaining traffic flows of the network, while the second level objective functions seek to optimise transmission parameters of the flow associated with the chosen path An extension of this model, suitable for MPLS networks using a two-path routing scheme with traffic splitting will be presented IIASA 2006 p2/14

Contents 1 Introduction 2 Routing models in multiservice networks 3 A bilevel multicriteria routing model for multiservice networks (a) Mathematical formulation (b) Basis of the resolution approach (c) Application model and computational tests 4 A hierarchical routing model with traffic splitting for MPLS networks (a) Extension of the previous model (b) Mathematical formulation 5 Basis of the resolution approach 6 Conclusions IIASA 2006 p3/14

1 Introduction Routing problems in communication networks supporting multiple services, namely multimedia applications, involve the selection of paths satisfying multiple constraints of a technical nature, designated as QoS (Quality of Service) requirements and seeking simultaneously to optimise the chosen objective functions The objective functions are concerned with the necessity of minimizing the consumption of (transmission) resources along a path and to obtain a minimum negative impact in all traffic flows that may use the network The specific models of these cost functions and of the QoS constraints depend on the type of multimedia service associated with the calls which are being routed from origin to destination, as it is case in the recent MPLS (Multiprotocol Label Switching) Internet technology IIASA 2006 p4/14

2 Routing Models in Multiservice Networks Although traditional models in this area are single-objective, in many situations it is important to consider explicitly different, eventually conflicting objectives Most routing algorithms that have been traditionally employed in current networks or proposed for this type of problem, are heuristics based on Dijkstra or Bellman-Ford shortest path algorithm Therefore this is an area where there are potential advantages in introducing multicriteria routing approaches, taking into account the major network functional features and the nature of the multiple QoS (Quality of Service) metrics IIASA 2006 p5/14

3 A Bilevel Multicriteria Routing Model for Multiservice Networks We consider: 1 st level Objective functions seek to diminish the negative impact on the remaining traffic flows resulting from the utilisation of a given path by the considered nodeto-node flow and to minimise the blocking probability of the given node-to-node traffic flow: 1 cost of accepting a call in a path expressed in the available bandwidth in its arcs (or links ): the cost of an arc varies inversely with the available bandwidth, 2 number of arcs in a path (its minimisation tends to optimise the number of used resources per connection and favours path reliability) IIASA 2006 p6/14

3 A Bilevel Multicriteria Routing Model for Multiservice Networks 2 nd level Objective functions seek to optimise the path from the point of view of the transmission conditions (QoS parameters) of the considered node-to-node flow: 1 bottleneck bandwidth i e the minimal available bandwidth among the links of a path, 2 total delay experienced along a path expressed in the delays on the links Constraints on the paths: minimal bandwidth required by a connection request in the flow, maximal allowed delay, maximal allowed jitter, which may be expressed, for certain queueing disciplines in terms of a constraint on the number of links per path IIASA 2006 p6/14

31 Mathematical Formulation This multimedia traffic routing problem is formulated as a hierarchical multicriteria network problem Values associated with each arc (or link) (i, j) in (N, A): b ij IR + representing the available bandwidth on (i, j), c ij IR + representing the cost of using (i, j), c ij = 1/b ij in this model, d ij IR + representing the associated delay, R ij IR + representing the capacity of (i, j) Moreover: c(p) = (i,j) p c ij, (path cost), b(p) = min (i,j) p {b ij }, (bottleneck bandwidth), d(p) = (i,j) p d ij, (total delay), h(p) = number of arcs of path p IIASA 2006 p7/14

31 Mathematical Formulation Given jitter IN, bandwidth IR + and delay IR +, where jitter is a limit on the number of arcs related to a bound on the jitter The problem is to determine loopless paths p satisfying the constraints: b(p) bandwidth, d(p) delay, p has at most jitter arcs which are solutions of the bilevel multicriteria routing problem: 1 st level min{c(p) : p P} min{h(p) : p P} (path cost) (number of arcs of the path) 2 nd level max b(p) min d(p) (bottleneck bandwidth) (path delay) IIASA 2006 p7/14

31 Mathematical Formulation In general such a problem does not have a solution due to possible conflict between the considered functions Thus, it will be useful to consider the set of non-dominated solutions, ie paths such that there is no other feasible path which improves one objective function without worsening at least one of the other objective functions The set of non-dominated solutions concerning the 1 st level is defined as follows: Given paths p and q, p dominates q (p D q) if and only if c(p) c(q), h(p) h(q) and at least one of the inequalities is strict Path q is dominated if and only if there is another path p such that p D q P N denotes the set of non-dominated paths IIASA 2006 p7/14

32 Basis of the Resolution Approach In the 1 st level a bicriterion problem is solved by an adaptation of Clímaco & Martins algorithm, based on a loopless paths ranking method by Martins et al (MPS) Compute p the path with less arcs, ĉ = c(p) Compute q the lowest cost path, m h = h(q), M c = c(q) Rank loopless paths p k by non-decreasing order of c, until c(p k ) > ĉ Apply a dominance test to p k (compare p k with previous loopless paths): c(p k ) = M c If h(p k ) < m h, then p k dominates the stored candidates and it is candidate to be non-dominated If h(p k ) = m h, then p k is candidate to be non-dominated If h(p k ) > m h, then p k P N c(p k ) > M c If h(p k ) < m h, then the stored candidates belong to P N, p k is candidate to be non-dominated If h(p k ) m h, then p k P N IIASA 2006 p8/14

32 Basis of the Resolution Approach Note that the relaxation of the non-dominance definition can be useful in this context So, we also tested the calculation of ǫ-non-dominated solutions, where ǫ = (ǫ c, ǫ h ) and ǫ c, ǫ h are small and positive IIASA 2006 p8/14

32 Basis of the Resolution Approach Preference thresholds are defined for the solutions of level 1, enabling the definition of priority regions Required (aspiration level) and acceptable (reservation level) values of h: ( arcs > 2), where: h req = int(m p ) + 1, h acc = int(m p ) + arcs 1, int(x): the smallest integer greater than or equal to x, and m p : average value of the shortest paths length for all node pairs Required and acceptable values of c: where: c req = c min + c m 2, c acc = c max + c m 2 c min, c max : average minimal and maximal path costs for all node pairs, c m = c min + c max 2, IIASA 2006 p8/14

32 Basis of the Resolution Approach Priority regions: h acc h h req B 1 A C B 2 c req c c acc IIASA 2006 p8/14

32 Basis of the Resolution Approach Solutions from level 1 are considered in level 2, namely: 1 being filtered according to acceptable bounds defined for the functions of level 2, 2 ordering the resulting according to a specific metric The acceptable bounds, b m (lower-bound) and d M (upper-bound), are: b m = b(p ), where p = argmin q P 1 N {d(q)} d M = d(p ), where p = argmax q P 1 N {b(q)} and P 1 N is the set of non-dominated solutions of level 1 Finally, in each priority area of level 1 a ranking is made of the solutions taking into account the objective functions of level 2 In a priority area the resulting solutions are ordered according to a weighted Chebyshev distance to the ideal solution IIASA 2006 p8/14

32 Basis of the Resolution Approach Solutions of level 1 are aggregated with acceptable and preference levels defined by the Decision Maker, regarding the two criteria of level 2 Then, solutions in the same priority area are ranked according to a weighted Chebyshev distance to the ideal solution of the considered area The weights follow the proportionality of the intervals regarding both criteria in the considered area IIASA 2006 p8/14

33 Application Model and Computational Tests A video traffic routing problem in random generated networks was considered for application of this model Each node is modeled as a queueing system using Weighted Fair Queueing (WFQ) service discipline, enabling to represent the bound on jitter through a constraint on the number of arcs jitter Given a link (i, j), we considered: random b ij {052, 252,, 15052} (in Mb/s), for a total link capacity of 15552 Mb/s; c ij = 1/b ij ; ( d ij = S max r k ) + S max R ij + D ij 2c/3 (in ms), where D ij is the Euclidean distance between nodes of coordinates (x i, y i ) and (x j, y j ), c is the speed of light, R uv = 15552 10 6 bit/s is the bandwidth capacity of (u, v), r k = 15 10 6 bit/s is the token generation rate of the leaky bucket, and S max = 53 8 bit is the size of an ATM cell IIASA 2006 p9/14

33 Application Model and Computational Tests bandwidth = 15 Mb/s, jitter = ma(s, t) + arcs, with: arcs = 4, and ma(s, t) = minimal number of arcs of a feasible path from s to t Partition of {052, 252,,15052} in 5 classes with equal amplitude, with a predefined percentage of values of b ij I 0 I 1 I 2 I 3 I 4 50% 20% 15% 10% 5% IIASA 2006 p9/14

33 Application Model and Computational Tests Computational tests) Tests were performed for a set of randomly generated networks constructed on a grid with 400 240 points (mesh space unit 10 Km) and average node degree equal to 4, with: n {500, 1000, 1500, 2000, 2500, 3000}, n 2 s-t node pairs, and 25000 10 different seeds Code and computer: C language, AMD Athlon at 13 GHz, with 512 Mbytes of RAM, Linux IIASA 2006 p9/14

33 Application Model and Computational Tests Solutions for one pair of nodes (n = 1000) ǫ c = ǫ h = 0 1 st level solutions: Zone c 10 2 h b d C 4235 6 13452 437075 C 4943 5 6452 315921 h c 10 2 Req 4 40540 Acc 6 55880 Solutions filtered by the bounds of the 2 nd level (both with the same rank): c 10 2 h b d 4235 6 13452 437075 4943 5 6452 315921 d M b m Acc 437075 6452 IIASA 2006 p9/14

33 Application Model and Computational Tests Solutions for one pair of nodes (n = 1000) ǫ c = 10%, ǫ h = 1 1 st level solutions: Zone c 10 2 h b d C 4235 6 13452 437075 C 4527 6 12252 609800 C 4587 6 11852 542588 C 4676 6 10052 477221 C 4943 5 6452 315921 h c 10 2 Req 4 40540 Acc 6 55880 Solutions filtered by the bounds of the 2 nd level (both with the same rank): c 10 2 h b d 4235 6 13452 437075 4943 5 6452 315921 d M b m Acc 437075 6452 IIASA 2006 p9/14

33 Application Model and Computational Tests Solutions for one pair of nodes (n = 1000) 1 st level solutions Solutions filtered by the bounds of the 2 nd level h acc h req h c c req c acc IIASA 2006 p9/14

33 Application Model and Computational Tests Solutions for one pair of nodes (n = 2000) ǫ c = ǫ h = 0 1 st level solutions: Zone c 10 2 h b d B 1 4117 5 11052 358444 h c 10 2 Req 4 42350 Acc 6 56100 Solutions filtered by the bounds of the 2 nd level: c 10 2 h b d 4117 5 11052 358444 d M b m Acc 358444 11052 IIASA 2006 p9/14

33 Application Model and Computational Tests Solutions for one pair of nodes (n = 2000) ǫ c = 10%, ǫ h = 1 1 st level solutions: Zone c 10 2 h b d B 1 4117 5 11052 358444 C 4574 5 8052 227663 C 4578 6 12252 360932 h c 10 2 Req 4 42350 Acc 6 56100 Solutions filtered by the bounds of the 2 nd level: c 10 2 h b d 4117 5 11052 358444 4574 5 8052 227663 4578 6 12252 360932 d M b m Acc 360932 8052 IIASA 2006 p9/14

33 Application Model and Computational Tests Solutions for one pair of nodes (n = 2000) 1 st level solutions Solutions filtered by the bounds of the 2 nd level h acc h req h c c req c acc IIASA 2006 p9/14

33 Application Model and Computational Tests Solutions for one pair of nodes (n = 2000) Ideal point: (d, b ) = (227663, 12252) Chebyshev distance: C(p) = max{w b d(p) d, w d b(p) b } where w b = b M b m = 42 and w d = d M d m = 133269 Solutions selected by non-decreasing order of C: Rank C c 10 2 h b d 1 54928 4578 6 12252 360932 2 55977 4117 5 11052 358444 3 55977 4574 5 8052 227663 This process of aggregation is subjective, as all, but it has the great advantage of being defined as with basis on the intervals defined by the decisions relatively to the preferences for each criterion IIASA 2006 p9/14

33 Application Model and Computational Tests CPU times 16 16 S ec 12 S ec 12 s 8 4 s 8 4 0 0 500 1000 1500 2000 2500 3000 500 1000 1500 2000 2500 3000 n n (a) ǫ c = ǫ h = 0 (b) ǫ c = 10%, ǫ h = 1 Average Max Min IIASA 2006 p9/14

33 Application Model and Computational Tests Number of obtained solutions # n d s o ls 50 40 30 20 10 0 # n d s o ls 350 300 250 200 150 100 50 0 500 1000 1500 2000 2500 3000 500 1000 1500 2000 2500 3000 n n (a) ǫ c = ǫ h = 0 (b) ǫ c = 10%, ǫ h = 1 Average Max Min IIASA 2006 p9/14

4 A Hierarchical Multicriteria Routing Model with traffic splitting for MPLS Networks We propose an extension of the previous model, suitable for MPLS networks using a two-disjoint path routing scheme with traffic splitting such that the bandwidth required by each node-to-node traffic flow is divided by the two paths MPLS is a recent Internet technology based on the forwarding of packets using a specific label switching technique Among other advanced routing mechanisms it enables the utilisation of explicit-routes characterised by the fact the path followed by each node-to-node packet stream, of a certain type, is entirely determined by the ingress router (corresponding to the originating node) This technological platform is prepared to deal with multi-path routing, using the concept of the traffic of the splitting that consists of the division of the packet stream of each flow, along two or more disjoint paths such that the sum of the bandwidths available in those paths satisfies the bandwidth requirement of each type of flow, depending on the service class IIASA 2006 p10/14

41 Hierarchical Formulation of the Multicriteria Routing Model for MPLS Networks 1 st level objective functions: 1 a load balancing cost function that is the sum of the cost associated with the two paths, where the load balancing of an arc is a piecewise linear function of the bandwidth used in the arc, as proposed in previous MPLS routing models, eg [Erbas et al, 2003] The minimisation of this function aims at minimising the negative impact on the remaining network flows resulting from the utilisation of a given path by the considered node-to-node flow IIASA 2006 p11/14

41 Hierarchical Formulation of the Multicriteria Routing Model for MPLS Networks 1 st level objective functions: min {Φ(q) + q,q P Φ(q )}, Φ(p) = (i,j) p φ ij where φ ij is the load balancing cost associated with arc (i, j), given by φ ij = o ij, 0 o ij /R ij 05 2o ij 1 2 R ij, 05 < o ij /R ij 06 5o ij 23 10 R ij, 06 < o ij /R ij 07 15o ij 93 10 R ij, 07 < o ij /R ij 08 60o ij 453 10 R ij, 08 < o ij /R ij 09 300o ij 2613 10 R ij, 09 < o ij /R ij 1 where o ij = R ij b ij is the bandwidth occupied in arc (i, j), and b ij is the available bandwidth in arc (i, j) with capacity R ij φ ij is a convex piecewise linear function which increases monotonically with o ij IIASA 2006 p11/14

41 Hierarchical Formulation of the Multicriteria Routing Model for MPLS Networks 1 st level objective functions: 2 non-blocking probability S on both disjoint paths simultaneously, to be maximised (equivalent to minimise the blocking probability, L, of the traffic flow, using both paths simultaneously) max S(q, q,q P q ) = (1 B(q))(1 B(q )) min L(q, q,q P q ) = 1 S(q, q ), where B(p) is the blocking probability on path p Assuming statistical independence in the link occupations B(p) = 1 Π (i,j) p (1 B ij ), where B ij is the blocking probability on link (i, j) To obtain an additive metric we consider as coefficients of the objective function to be minimised c 2 ij = ln(1 B ij), leading to: min q,q P L (q, q ) = (i,j) q,q c 2 ij IIASA 2006 p11/14

41 Hierarchical Formulation of the Multicriteria Routing Model for MPLS Networks 2 st level objective functions: 1 minimal available bandwidths in the links of the paths (bottleneck bandwidths) to be maximised: max q,q P { min{b(q), b(q )} = } min (i,j) q,q {b ij}, This function aims at distributing the load of the flows through the least occupied links 2 average delay experienced along the two paths to be minimised: min max{d(q), q,q P d(q )}, where d(p) = (i,j) p d ij and d ij is the average packet delay on link (i, j) This function seeks the choice of pairs of paths with minimal average packet delay Note that the criteria formulation in the model needs experimental validation with realistic data and possible adjustments may be required IIASA 2006 p11/14

41 Hierarchical Formulation of the Multicriteria Routing Model for MPLS Networks Constraints: 1 The first constraint corresponds to a traffic-splitting requirement using two paths, ie, the sum of the bottleneck bandwidths in the two paths cannot be less than the bandwidth required by micro-flows of the considered node-to-node flow, bandwidth : For any q, q P, b(q) + b(q ) bandwidth 2 The second constraint is a jitter related constraint, which can be transformed for certain queueing disciplines, into a constraint on the maximal number of arcs per path, jitter : For any q, q P, h(q), h(q ) jitter, where h(p) denotes the number of arcs of paths p This constraint is important for certain types of QoS traffic flows (ie with guaranteed levels of Quality of Service) as in the case of video traffic and should be eliminated for Best Effort traffic IIASA 2006 p11/14

41 Hierarchical Formulation of the Multicriteria Routing Model for MPLS Networks The addressed hierarchical multicriteria routing problem consists of finding satisfactory solutions (q, q ), q, q P, where q and q are disjoint loopless paths, taking into account the optimisation hierarchy IIASA 2006 p11/14

5 Basis of the Resolution Approach Network modification Modification of the network topology: Duplicate the nodes: N = N {i : i N }, Duplicate the arcs and add a new arc linking t and the new s : A = A {(i, j ) : (i, j) A} {(t, s )}, Maintain the initial node: s, Consider a new terminal node: t New costs: c i j = c ij, if (i, j) A, and c t,s = 0 Each simple path p from s to t in (N, A ) corresponds to a pair of paths from s to t in (N, A), ie, there exist q P st and q P s t, such that p = q (t, s ) q Thus, if q q =, then q, q correspond to a pair of disjoint simple paths in (N, A) IIASA 2006 p12/14

5 Basis of the Resolution Approach Network modification s t s t s t When implementing the modified network (N, A ): A copy of any node is created There only has to be one new arc: (t, s ) Arcs starting at i are (i, j ) such that (i, j) A (There s no need to enlarge the set of arcs) IIASA 2006 p12/14

5 Basis of the Resolution Approach In the 1 st level a bicriterion problem is solved calculating the non-dominated solutions set by an adaptation of Clímaco & Martins algorithm, based on a simple path ranking method by Martins et al Ranking simple paths from s to t in (N, A ) by non-decreasing order of the number of arcs, until a feasible one (with respect to constraint (1)) is found, p = q (t, s ) q Ranking simple paths from s to t in (N, A ) by non-decreasing order of Φ, until a feasible one (with respect to constraints (1) and ( 2)) is found, p = q (t, s ) q Φ Φ(q) + Φ(q ), ˆL L (q) + L (q ) Ranking simple paths from s to t in (N, A ) by non-decreasing order of L, until a feasible one (with respect to constraints (1) and ( 2)) is found, p = q (t, s ) q M Φ ˆΦ Φ(q) + Φ(q ), m L L L (q, q ) IIASA 2006 p13/14

5 Basis of the Resolution Approach Ranking simple feasible paths (with respect to constraints (1) and ( 2)) p k = q k (t, s ) q k from s to t in (N, A ) by non-decreasing order of L, until L (q k, q k ) > ˆL Apply a dominance test to p k (compare p k with previous simple feasible paths): L (q k, q k ) = M L If Φ(q k ) + Φ(q k ) < m Φ, then p k dominates the stored candidates and it is candidate to be non-dominated If Φ(q k ) + Φ(q k ) = m Φ, then p k is candidate to be non-dominated If Φ(q k ) + Φ(q k ) > m Φ, then p k P N L (q k, q k ) > M L If Φ(q k ) + Φ(q k ) < m Φ, then the stored candidates belong to P N, p k is candidate to be non-dominated If Φ(q k ) + Φ(q k ) m Φ, then p k P N IIASA 2006 p13/14

5 Basis of the Resolution Approach Preference thresholds are defined for the solutions of level 1, enabling the definition of priority regions Required (aspiration level) and acceptable (reservation level) values of L : L req = ( L min + L m)/2, L acc = ( L max + L m)/2, where: L min, L max : average minimal and maximal path blocking probability obtained for the pairs of paths associated with all node-to-node flows, L m = (L min + L max)/2 Required and acceptable values of C: C req = ( C min + C m )/2, C acc = ( C max + C m )/2, where: C min, C max : average minimal and maximal path costs for all node pairs, C m = (C min + C max )/2 IIASA 2006 p13/14

5 Basis of the Resolution Approach Solutions from level 1 are then filtered according to acceptable bounds defined for the functions of level 2, which are applied to both paths of each candidate solution Those acceptable bounds for the subpaths q, q of the path p = q (t, s ) q, b m (lower bound) and d M (upper bound), are defined as follows: b m = min{b(q ), b(q )}, where p = argmin{max{d(q), d(q )} : p = q (t, s ) q P N}, with P N the set of non-dominated paths with respect to the objective functions of the 1 st level in network (N, A ) d M = max{d(q ), d(q )}, where p = argmax{min{b(q), b(q )} : p = q (t, s ) q P N } Finally, in each priority area of level 1 a ranking can be made of the solutions taking into account the objective function of level 2 IIASA 2006 p13/14

Conclusions A hierarchical multicriteria routing model to calculate and select a set of non-dominated paths for traffic flows associated with multimedia type services in multiservice networks was developed: 1 st level obj functions seek to diminish the negative impact on the remaining flows, resulting from the utilisation of a given path 2 nd level obj functions seek to optimise the path from the point of view of the transmission conditions of the considered node-to-node flow A variant of this model and the corresponding algorithm suitable for MPLS networks using a two-path routing scheme with traffic splitting will be presented The formulated problem involves the calculation of a pair of disjoint paths such that the sum of the minimal available bandwidth in the two paths is not less than the bandwidth required for the considered traffic flow (two-path traffic-splitting); a constraint related to the allowed jitter is also considered IIASA 2006 p14/14