Distributed constrained agents for allocating service demands in multi-provider networks Monique Calisti DEIS Unversita degli Studi di Bologna Vle Risorgimento 2, 40136 Bologna Italy Voice: +39 51 6443058 Fax:+ 39 51 6443053 E-mail:
[email protected] Abstract
The aim of this work is to de ne a paradigm which supports the routing of service demands across distinct network domains. The distributed nature of this problem (i.e., network resources are spatially distributed, and distinct domains can contain heterogeneous components), and the constraints imposed by the environment suggest the use of distributed problem solving techniques and multi-agent technology. Intelligent agents enable a exible multi-domain routing since they allow routing algorithms and network management functions to be dynamically loaded in the infrastructure. Nevertheless, agent technology by itself does not improve the way di erent networks interact, unless a good strategy is de ned to allow them to coordinate their actions and solve possible con icts. This paper describes how techniques developed in the Distributed Constraints Satisfaction Problem eld supply a compact way to formalise the Quality of Service -based multi-domain routing process, and how this formalism enables a multi-agent system to dynamically route demands across several domains. Keywords: QoS-based inter-domain routing, constraint satisfaction problems, arc consistency, agent technology.
1 Introduction Today's networks are controlled at various organisational and functional layers by human managers. Many aspects of the interworking are statically xed by contracts (number and available capacity of links connecting one network domain to another, prices etc.) and many steps of the interaction are regulated by human operators via fax, e-mail, etc. What seems more suitable for the future scenarios is a management solution based on static and/or mobile software entities, collecting network state information and having the ability to directly invoke e ective changes to switch controllers, without the interaction of a human operator. The current ineciency is mainly due to the diculty for human operators to consider all various aspects which complicate the interworking process. The deregulation of the Telecommunication market implies an increasing number of actors. The co-existence of the Internet and the more traditional Telecom world is still not clear. The growth of QoS requirements for the introduction of new multimedia services. The technological heterogeneity of network components. Among all various interworking aspects, the end-to-end routing for networks which support QoS guarantees is a very complex problem [1]. The complexity increases whenever the end-points of a service demand belong to networks under the control of di erent authorities, i.e., multi-domain scenario. In this case, the routing task is made very dicult by the fact that individual network operators do not reveal detailed information about their internal network for both security and scalability reasons. This paper focuses on the QoS-based multi-domain routing process and introduces a distributed paradigm that enables routing decisions making use of restricted information. In particular, it is described how constraint-based techniques for distributed problem solving supply a compact way to formalise the inter-domain routing process, i.e., routing between provider domains, and how this formalism
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enables an agent middleware to actively route demands. Although, the intra-domain process, i.e., the routing within a single network domain, is not considered in this paper, the technique we propose shows how the intra-domain process can be made consistent with the inter-domain routing.
2 Background Although multi-domain QoS routing has been tackled from many directions(ATM and SDH network [8], [7], multi-domain management in MISA 1 and P408 2 projects, and agent interactions for routing multimedia trac over distributed networks, such as in FIPA 97 Part 7 [2] and in FACTS 3 ), no previous work has addressed the possibility of automating the provider-to-provider interaction and dynamically negotiating more than one path at a time. In our framework a multi-agent system combines the use of Distributed Constraint Satisfaction Problems (DCSP) techniques with autonomous agents. DCSP techniques are used to formalise the QoS-based multi-domain problem and deploy powerful mechanisms such as consistency and searching techniques, that ensure to nd a solution satisfying the QoS requirements. Autonomous and communicating agents allows the automation of many interworking steps currently done by humans. The use of intelligent, pro-active and reactive software entities allows in fact the dynamic negotiation of demand allocations without having to pre-select a unique path.
3 Global Framework
Network resources A provider's network, or network, is modelled as a graph, as depicted in Figure 1
case (a). A node corresponds to a network node (such as a switch or a router) or a sub-network. The set of links interconnecting the nodes are intra-domain links, and represent the communication channels existing inside a network. Communication between the networks of the providers takes place over interdomain links . Every link li (intra- or inter-domain) is characterised by a vector qosli expressing the QoS properties of the link, such as available bandwidth, bwli , and the end-to-end delay, delli . The cost costli of the link li , is assumed to be xed (and known by a network provider) for the overall duration of the inter-domain routing process. The interconnection of the di erent providers' networks can be summarised in an abstract simple graph, called the providers' graph (Figure 1 case (b)). The providers' graph consists of abstract nodes and abstract links. An abstract node represents a network provider domain, and is characterised by a node traversal delay and a node traversal cost. An abstract link between two abstract nodes clusters all inter-domain links interconnecting the two corresponding network provider domains. 1 2 3
On-line information about MISA are available at: http://www.misa.ch Eurescom project P408: http://www.eurescom.de/Public/Projects/P800-series/P804/p804.htm More details about FACTS can be found at: http://www.labs.bt.com/profsoc/facts
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Service Demands In this framework, a service demand dk is speci ed as:
dk ::= (xk ; yk ; qosreq;k ; tempreq;k ) where xk is the source node, yk the destination node, and qosreq;k the required QoS. tempreq;k is a
vector including start time and end time for the requested service. A demand may be anything from a video-conference to a virtual link in a Virtual Private Network. In this framework the QoS requirements correspond to the bandwidth and the end-to-end delay.
3.1 Problem de nition
The service demand allocation process is a very complex task for a network provider for several reasons: (1) there are distinct entities involved ( nal customers, service providers, etc.), (2) the routing must take into account Quality of Service, QoS, requirements, (3) network resources and information are distributed, (4) a trade-o between the pro t optimisation and the end-user satisfaction is required. Every network provider (i.e., the owner of the network resources) is represented by a Network Provider Agent, NPA. Whenever the service demand spans several network domains, several NPAs must interact. Every network is modelled as a set of nodes and links (Figure 2). Two main sub-problems need to be addressed: (1) Finding out the routes which satisfy QoS and connectivity constraints. (2) Selecting a speci c route by negotiating with the other providers. This paper focuses on the rst sub-task, that is reformulated in the following. When a NPA receives a demand, it has: To detect the source and the destination network domains. If the source and the destination domain are distinct the inter-domain routing process must be started. To compute an abstract path P . An abstract path is an ordered list of distinct network provider domains between the source and the destination network provider domains. To contact all the NPAs along P . To nd out the intra-domain routes, local routes. To make the set of local routes consistent with inter-domain constraints. All local routes which violate such constraints are discarded. To negotiate with other providers along P in order to allocate a global route. A global route is the end-to-end connection consisting of local routes and inter-domain links interconnecting them. If an agreement is found the network resources are reserved, otherwise the service demand is rejected.
4 Formalising the multi-domain service demand allocation Constraint satisfaction is a powerful and extensively used Arti cial Intelligence paradigm [10]. Constraint satisfaction problems (CSP) involve nding values for problem variables subject to restrictions (constraints) on which combinations of values are acceptable. CSP are solved using search (e.g., backtrack) and inference (e.g., arc consistency) methods.
Finding a route for allocating service demands that cross distinct networks, can be considered as a Distributed Constraint Satisfaction Problem [11], DCSP, since the variables are distributed among agents and since constraints exist among them. We assume that: (1) every agent has exactly one variable, (2) all inter-domain constraints are binary (i.e., they involve two variables), (3) there is at least an agent for every domain, (4) all the agents in the scenario know each other, (5) agents communicate using messages. The DCSP can be represented as a graph, the constraint graph, where variables are vertices and constraints are edges between vertices. Since each agent owns exactly one variable, a node also represents an agent. The variable every agent handles is a \local path" (actually it is not a path since it expresses just the two end points of the local path) speci ed as a couple: p ::= (inputpoint; outputpoint) The values for each `local path' are all the possible combinations of boundary points4 , i.e., input-output points, which represent the possible local routes to route the demand. Note that only simple paths, i.e., loop-free, are considered. The set of all the possible input-output points combinations is the domain for each variable. Consider the example depicted in Figure 2. Agent receives a demand dk = (a1 ; b6 ; qosreq ), and, for instance, it selects the abstract path A - B. Next, agent determines: I ;k ::= f Set of possible input points g O ;k ::= f Set of possible output points g In this example I ;k = fa1g and O ;k = fa3 ; a4 ; a7 g, since the only output points directly connected to B are a3 , a4 and a7 . The variable for agent is the couple p = (i; o), i 2 I ;k and o 2 O ;k . The domain for p is given by the set of all the possible routes connecting i to o: D ;k = f(a1 ; a3 ), (a1 ; a4 ), (a1 ; a7 )g. Agent owns the variable p = (i; o), with i 2 I ;k = fb1; b2 ; b3 g and o 2 O ;k = fb6g. Considering only the points, which are directly connected with the predecessor or with the successor along the path, allows to reduce the complexity of the solving algorithm. The fewer points there are in I ;k and O ;k , the fewer possible combinations there are for allocating a demand (search space reduction). The domain for agent is: D ;k = f(b1 ; b6 ); (b2 ; b6 ); (b3 ; b6 )g. The domains of the variables are dynamically calculated for every speci c demand. The dynamic `on-demand' computation allows: (1) to update the variable domains according to the network state, (2) to reduce the search space.
4.1 The constraints
Connectivity and QoS constraints are locally translated in constraints between the boundary points that two neighbour network domains use for the inter-domain routing. First of all, it is necessary to check which are the possible combinations of input/output points from/to each neighbour network. The set S is de ned:
S ( ; ) ::= f(o ; i ) j o 2 O ;k ; i 2 I ;k ; o ? > i g o ? > i means that o is directly connected to i . For N nodes in the network A and N in the domain B there are at most N N possible inter-domain connections, i.e., number of elements in S. Considering Figure 2, the set S of possible combinations of output points of network A and the input points of network B is: S ( ; ) = f(a3 ; b1 ); (a3 ; b2 ); (a4 ; b3); (a4 ; b2 ); (a7 ; b2 )g. We can formalise and express all the possible constraints between two agents and as follows: C ( ; ) ::= f ((i ; o ), (i ; o )) j (o ; i ) 2 S ( ; ), (i ; o ) 2 D , (i ; o ) 2 D g Note that both S ( ; ) and C ( ; ) are dynamically calculated for every speci c demand. 4
The boundary points are the network nodes, which connect every network domain to external networks.
5 The main solving paradigm The Distributed Arc Consistency (DAC) algorithm is based on the use of the arc consistency technique [4] applied to a very simple case of constraint graph. In our framework, once an abstract path P has been selected, the constraint graph is a simple chain. Arc consistency is a technique used to narrow the space of possible choices before actually performing the search: every link i ? j of the constraint network is made arc consistent by eliminating all values of the variables i and j which are not consistent with the given constraint. Every NPA along P tries to de ne the feasible set , i.e., the set of possible local paths satisfying the QoS requirements of the demand to be allocated. The arc consistency propagation works as a ltering function by eliminating inconsistent values from the feasible set. The feasible set nally contains only the consistent values for the agent's variable. In this case the arc consistency is obtained through a distributed exchange of messages between neighbouring agents. More in detail the overall multi-provider demand allocation process is solved by using the following algorithm: 1. An agent receives a service demand d. 2. Agent detects the destination and the source network domains. 3. Based on the providers' graph, which is dynamically updated by the agents, an abstract path P for d is computed. None, one or several paths may exist. If no paths exist, the demand is rejected. If more than one path exists, the shortest one which satis es QoS constraints is selected. 4. For the selected path, agent contacts every agent along P . From now on, several agents run similar routines in parallel. 5. Each agent de nes the variable domain D and the set of constraints C . C is determined considering the available QoS on the links li which interconnect every provider network with its neighbours. 6. Based on qosreq every agent reduces its variable domain D by performing node consistency: every local path (i ; o ) that cannot support the required QoS is eliminated from the domain D. If an agent has an empty variable domain D a failure message is sent to all agents along P . A new abstract path must be investigated and the algorithm backtracks to step 3. 7. Establishing arc consistency: every agent determines all the values of its domain which are compatible with the values contained in the domains of the neighbours. If an agent obtains an empty variable domain D a failure message is sent to all agents along P : d cannot be allocated along P and the algorithm backtracks to step 3. 8. If the arc consistency is successfully, at least one solution, i.e., one route along P , exists. In order to be sure that a solution will still exist after the negotiation, we assume that there exists a prereservation mechanism of the negotiated resources required by the demand. If network failures or physical changes occur the guarantee of having a solution is not valid any more. In this case every agent is noti ed by the Network Management System and the algorithm backtracks to step 3. 9. If the negotiation is successful the resources needed are reserved 5 and the service demand can be allocated, otherwise a failure message is sent to all the agents involved along P and the algorithm goes back to step 3. The node consistency process (step 6) can be supported by the Blocking Island paradigm [3]. A blocking island (BI) is a resource abstraction technique that allows to quickly assess the existence of routes between end-points with a given amount of available bandwidth, without having to explicitly search for such a route. More precisely, if the input point i and the end point o belong to the same BI at the required QoS level, then (i ; o ) 2 D, i.e., there is a local route which guarantees the qosreq . The following examples graphically show the main steps of the DAC algorithm. Consider that NPA A receives the demand d=(a1, b6, qosreq ). Figure 3 case (A) shows the situation before any computation. The routes inside every domain are speci ed as couples of end-points, e.g., (a1,a3) inside the network domain A. 5 Note that you pass from a pre-reservation, step 8, which is temporary and for all the potential resources involved, to an e ective reservation of just those resources that are e ectively required for the speci c demand.
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Figure 3: Visualising the main DAC's steps. Figure 3 case (B) indicates all the links, intra and inter domain, that satisfy the qos requirements. This is the con guration after every agent has performed steps 5 and 6 of the DAC algorithm. At step 5 the links l2 and l3 are pruned out since they cannot guarantee the qos required. At step 6 every agent check the node consistency: the local path (a1,a7) is pruned out from the variable domain D and the local paths (b2,b6) and (b3,b6) are pruned out from the variable domain D . Finally, (B) shows D =f(a1,a3),(a1,a4)g and D =f(b1,b6)g. Case (C) depicts the situation after the arc consistency propagation (step 7 of the DAC algorithm). The variable domains are : D =f(a1,a3)g and D =f(b1,b6)g. The value (a1,a4) is pruned out from D since (a1,a4) is not consistent to any value in D . There is in the end one solution given by: (a1,a3), l1, (b1,b6). The agents can still negotiate about prices. Di erent internal routes can have in fact di erent costs. Case (D) shows one speci c route.
5.1 Eciency of the Arc Consistency approach
The arc consistency approach is particularly suitable rst because it guarantees the completeness of our algorithm, and second because of the simple constraint graph (once an abstract path is selected the constraint graph becomes a simple chain). Performing arc consistency for a binary CSP is bound by O(ed3 ) [9], where e is the number of constraints, and d the upper bound on the number of values in the domain of a variable. Let P be the abstract path chosen for the current demand. In our problem, the number of binary constraints is j P j ?1, which is the number of variables (or involved domains/agents) minus 1. In order to compute the domain size j DA j of a variable A, we must consider all border nodes of a provider's network. Let nA be that number. There are two exclusive cases (remember that we suppose that source and destination end-points are not in the same domain { otherwise no inter-domain routing is required): 1. The network domain contains the source node or the destination node, but not both: j DA j nA . 2. The network domain is a transit domain, i.e., it does not contain either the source or the destination node, but is part of the abstract path P : j DA j nA (n2A ?1) . Let N be the maximal amount of boundary nodes in the network of a provider, i.e., N = maxdomains A nA . Therefore, the complexity of the arc consistency process is bound by O(j P j N 6 ). In order to prove that the DAC algorithm does not require any search some preliminary de nitions are needed. De nition 1 A constraint graph is K-consistent if the following is true: Choose values of any K ? 1 variables that satisfy all the constraints among these variables. Then choose any Kth variable. There exists a value for this variable that satis es all the constraints among these K variables.
De nition 2 A constraint graph is strongly K-consistent if it is J-consistent for all J K .
De nition 3 The width at a vertex in an ordered constraint graph is the number of constraint arcs that lead from the vertex to the previous vertex. De nition 4 The width of an ordered constraint graph is the maximum of the width of any of its
vertices.
De nition 5 The width of a constraint graph is the minimum width of all the orderings of that graph. In our case, the constraint graph has a width ! = 1, since once an abstract path has been selected, the constraint graph is a simple chain. This holds because of the following theorem [5, 6]: Theorem 1 (Freuder)At least one of the orderings of a tree-structured constraint graph has a width equal to 1. The DAC algorithm uses node consistency and arc consistency to make the graph strongly 2consistent. Therefore, the following theorem proves that the DAC algorithm does not require any search [5, 6]: Theorem 2 (Freuder) If a constraint graph is strongly k-consistent, and k > !, where ! is the width of the constraint graph, then there exists a search order that is backtrack free.
6 Conclusions This paper has described a multi-agent paradigm to support the QoS-based inter-domain routing problem in a exible and dynamic way without the need of human intervention. In particular, the paper shows how the DCSP formalism provides a powerful and intuitive way of expressing the QoS-based inter-domain routing problem and a way of solving the problem which have been so expressed. In our view, the increased exibility of our approach provides for new opportunities in the area of network inter-operability. We have built prototypes to test many of the concepts outlined in this paper. In order to validate this paradigm we are continuing to test it by constructing more realistic scenarios and designing negotiation protocols around them, a problem that is complicated by the fact that the interworking process is itself in ux and no stable data is available.
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