Smooth Intentional Rerouting and its Applications in ATM Networks

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1 Smooth Intentional Rerouting and its Applications in ATM Networks Reuven Cohen* Dept. of Computer Science Technion, Haifa 32000, Israel abstract Traditional communacation networks reroute connections following link or node failures. This can be regarded as forced rerouting. The next generation ATM networks are supposed to be more intelligent and to oger more services than existing networks. An intelligent network may sometimes decide to reroute a connection whose virtual channel is still alive. This can be regarded as intentional rerouting. The present paper deals wath intentional rerouting of ATM connections. It shows that intentional rerouting can ensure cell FIFO and integrity. Then, several possible applications of intentional rerouting are suggested and discussed. 1 Introduction ATM is a connection-oriented technique, that uses two levels of connections: Virtual Channel (VC) connections and Virtual Path (VP) connections. Cells sent between end nodes (actually, between users connected to the end nodes) are transported over a preestablished VC connection. A VC connection is a concatenation of one or more VP connections. A VP connection is a concatenation of one or more network links. This connection hierarchy, which allows grouping of several virtual channels, is referred to as the virtual path concept. Figure 1 shows three virtual path connections: (1) VP(A+C), a unidirectional VP connection from node A to C; (2) VP(C-G), a bidirectional VP between C and G and (3) VP(G-I) a bidirectional VP between G and I. VP(A+C) and VP(C++G) are used as building blocks of a unidirectional VC connection from A to G, VC(A+G). VP(C-G) and VP(G-I) are used as building blocks of a bidirectional VC connection between C and I, VC(C-I). This work was performed in part while the author was with IBM T.J. Watson Research Center. rcohenqcs. technion.ac.il The advantages of the virtual path concept are explained in [2, 5, 6, 7, 81. One of them, as shown in [2], is that this connection hierarchy enables fast recovery from failures: if a VP fails due to a failure of an intermediate link or node, then instead of taking down all the VC connections established over the failed VP, a single simple protocol between the two end points of the failed VP can reroute them to a parallel VP. This protocol retains the FIFO order of cells transmitted over each rerouted VC connection, but it cannot avoid cell loss. The rerouting scheme in [a] can be regarded as forced rerouting, which is triggered by a failure. The present paper, however, deals with intentional rerouting of a connection. In such a case only one connection is addressed at a time, and for this connection not necessarily only one VP is replaced. Intentional rerouting is performed by the network not due to a failure, but in order to serve some management purpose. As an example, intentional rerouting may be needed when the Quality of Service (QoS) of a connection needs to be improved or when a network node should be taken down for some management purpose, like installation of new hardware or software. The paper shows that intentional rerouting can ensure not only FIFO but also integrity of cells. Thus, it can be completely transparent to the upper (above the Network) layers of the communicating stations. Figure 2 summarizes the differences between intentional and forced rerouting. Section 2 presents two options for intentional smooth rerouting of VC connections. In both cases the protocol is triggered and controlled by the Network layers at the two ends. However, in the first case Figure 1: The Virtual Path Coccept c X/94 $ IEEE

2 U Issue I] Forced Rerouting [2] 11 Intentional Rerouting (this paper) 1 [T layers involved in the rerouting 11 Network 11 Network and AAL Figure 2: A Comparison Between Intentional and Forced Rerouting it is performed by the Segmentation And Reassembly (SAR) sublayer of the ATM Adaptation Layer (AAL), whereas in the second case it is performed by the Convergence Sublayer (CS) of the AAL. These two options are then compared. An obvious use of the rerouting mechanism is retaining the Quality of Service (QoS) of connections. This issue is addressed in the full paper. However, the paper suggests and analyzes other two possible applications of the rerouting mechanism: fast connection set up (Section 3) and bandwidth management (Section 4). 2 Smooth Rerouting It will be convenient to deal throughout this section with a unidirectional VC connection. The rerouting of a bidirectional VC connection consists of two independent protocols, each of which handles one direction. Consider two ATM network stations A and B. Suppose that a unidirectional VC connection, VC1, has been set up from A to B and data cells are transmitted over this connection. Let the multiplexing label of ATM cells transmitted by A over VC1 be u1. This means that SARA(VC~) - the Segmentation And Reassembly sublayer of the ATM Adaptation Layer in A which is in charge of VC1 - attaches to every cell to be transmitted over VC1 the label a1 in the VPI and VCI fields. Similarly, let bl be the demultiplexing label of these cells in B, which means that every cell received by the ATM layer of B with VPI/VCI = bl is submitted to SARB(VC~) for reassembly. Suppose that A and B decide to reroute the connection from VC1 to another VC (VC,). The first step to this end is setting up the new VC from A to B. This is done by the Network layer at A, B and at some of the nodes along the new VC (as explained in [2], only the end nodes of the VPs over which a VC is set up cs I I SAR(VC1 and VCa) (a) SAR rerouting (b) CS rerouting Figure 3: Two options for a Smooth Rerouting should be involved in the set up protocol). Station A selects a new multiplexing label a2 # a1 for VC2, and station B selects a new demultiplexing label b2 # bl. During the set up of the new VC, A continues sending cells to B over VC1 which is still active. The rest of the mechanism can be applied in two different ways. In the first way, both A and B have a common SAR sublayer for VC1 and VC;, (Figure 3(a)). The other option is to create in A and B a new SAR sublayer for VC2, as Figure 3(b) shows. In the following, these two options are presented and compared. Rerouting in the SAR Sublayer The SAR processes in A and B which are in charge of VC2 are those which are in charge of VC1 as well. Thus, we have SARA(VC~)=SARA(VC~) and SARB(VC~)=SARB(VC~). Consequently, every cell received by B whose VPI/VCI field is either bl or bz is submitted to SARB for the reassembly. When VC2 is ready, the Network layer at R allocates special buffers to SARB, in order to enable rerouting with no loss of data. As explained later, this extra buffer space is needed for a limited time 1 1 c

3 only. After allocating the buffers, the Network layer at B sends a REROUTE(VC1,VC2) massage to the Network layer at A, indicating that it is ready to receive cells over VC2 When the Network layer at A receives the REROUTE(VC1,VC2) message from B, it tells SARA to stop sending cells over VC1 and to start using VC2. SARA closes VC1 by sending a special control cell, called lust, over it. This cell has VPI/VCI=al like a user cell. This in-channel signalling (control data sent over a user VC) is needed in order to ensure integrity of data during the rerouting. All the cells received by SARB over VC2 are buffered in the extra buffer space, and not submitted to the upper layer regardless of their contents. However, when SARB receives the lust control cell, it processes the buffered cells as if they have just been received. Therefore, the FIFO order of the cells transmitted over VC1 and VC2 is preserved. In addition, assuming that SARB has sufficient buffer space, cells are not lost during the rerouting. After SARB receives the lust cell and processes the suspended cells, it may release the extra buffer space. In addition, it has to inform its Network layer that the rerouting has been completed. The Network layer of B then communicates with the Network layer of A in order to take VC1 down. A problematic part of the scheme as described so far is the transmission of the special control cell (lust) over VC1. Two issues here should be addressed: (1) how can an SAR sublayer send a control cell over a user channel; (2) how to ensure the receipt of this important control cell by SARI?. The first issue depends on the type of the AAL. Five different AAL types have been defined so far. For AALs 1-4, there exists an SAR header in the 48-byte SAR-PDU. This header can be used - especially in AALs 3-4, for which an ST (segment type) field is defined - in order to distinguish between user cells and control cells transmitted over the user VC. AAL 5, however, contains no SAR header. Therefore, rerouting of AAL 5 VC s is possible only if the Payload Type (PT) field in the ATM header, whose exact values have not been standardized yet, will enable to distinguish between user cells containing user data and user cells containing control data. In such a case, however, the ATM layer will have to inform the SAR sublayer about the type of every received cell. This is, of course, an awkward solution. The second issue can be solved by asking SARA to send not only one but multiple lust cells. In fact, SARA can repeatedly send a lust cell with no user data over VC1 while sending user cells over VC2, until VC1 is taken down by the Network layer of A. This happens after the latter is informed by the Network layer of B that the rerouting has been completed, which means that a last cell had been received. Even under severe congestion condition along the path of VC1, SARB will finally receive a lust cell and close VC1, thus disregarding the following lust cells. Note, however, that if this approach is employed, SARB must distinguish between the first last cell, that contains user data, and the other lust cells, that contain no user data and therefore should be dropped. This problem can be avoided if the first lust cell will also be empty. Recall that in order to ensure integrity of data, SARB needs an extra buffer space. This extra space is used for storing cells received on VC2 before a lust cell is received on VC1. Hence, (TI - 72). a extra bits are needed, where TI is an upper bound on the latency of VC1 (;.e, the maximum period of time between the submission of a cell by SARA to its ATM layer for transmission over VC1 and the delivery of this cell to SARB), r~ is a lower bound on the latency of VC2, and a is the peak rate allocation for the considered connection. Note that if 71 5 r2, which means that the lust cell must be received by SARB before any cell is received from VC2, no extra buffer space is required. Rerouting in the Convergence Sublayer It is expected that in ATM the boundary between hardware and software will be the interface between the SAR (hardware) and CS (software) sublayers of the AAL [9]. This implies that the SAR algorithm should be as simple as possible. Unfortunately, the SAR rerouting presented before is not compatible with this hypothesis, as it puts most of the rerouting burden on the SAR sublayer. The SAR in the receiving side is required to distinguish between cells received on each of the two VCs, to suspend the processing of cells received on the new VC, and to recognize the lust cell. Another issue of concern is the interface between the ATM and the AAL. Though it seems possible to associate two ATM VC connections with one AAL process, it is not clear if and how can the AAL distinguish between cells belonging to each VC. The information needed for this demultiplexing lies in the VCI/VPI portion of the ATM header, which is transparent to the AAL. In the following we present another rerouting scheme, that puts most of the burden on the CS (Convergence Sublayer) of the AAL. In this scheme, each of the VCs (VC1 and VC2) has its own SAR Service Access Point (SAP) as Figure 3(b) suggests, but the two SAR processes share a common CS c.2.3

4 U Issue II SAR Rerouting CS Rerouting changes required transmission of the last notification (in-channel signaling) last loss probability the size of the extra high speed (SAR) buffer space rerouting delay in the AAL and the interface between AAL and ATM - impossible in AAL 5 - difficult in AAL 1 - possible in AAL 2-4 low (= cell loss prob.) depends on actual parameters Network layer delay + cell transmission delay in the AAL only (or a new AAL type is defined) - impossible in AAL 1 - easy in AAL 2,3, 4 and 5 high (=CS-PDU loss mob.) constant and known in advance (the maximum CS-PDU size) Network layer delay + CS-PDU transmission delav Figure 4: A Comparison Between SAR Rerouting and CS Rerouting When the Network layer at A receives the REROUTE message from its peer entity in B, it signals the CS in the AAL to reroute the connection from VCl to VC2. As in the previous scheme, a last notification should be sent from A to B, but this time in the CS level rather than in the SAR layer. Peer CS layers communicate with each other by means of CS-PDUs. As with the SAR-PDU, the exact format of a CS-PDU depends on the AAL type. However, it is easier to implement this kind of in-channel signalling in the CS level than in the SAR level because the CS-PDU can be arbitrarily long and has enough redundant bits. For example, the CS-PDU of AAL 5 [l] has an 8-byte trailer with 2 bytes (the User to User Indication field and the Common Part Indicator field) dedicated for signalling and control. There is one exception however: AAL 1 has no CS-PDU and therefore cannot support signalling in the CS sublayer. In the next time SARA submits a CS-PDU to SARA(VC~), it indicates that this is the last CS-PDU to be transmitted over VC1. All the following CS- PDUs are submitted to SARA(VC~) and transmitted over VC2. Though unlikely, it may happen that a CS-PDU sent by SARA on VC2 is received by SARB before the lust CS-PDU. Therefore, SARB must be able to distinguish between CS-PDUs received from SARB(VC~) and those received from SARB(VC~). It must store and suspend all the CS-PDUs received from SARB (VC2) before the last CS-PDUs is received from SARB(VCI). The advantages and disadvantages of each scheme are listed in Figure 4. After they are all taken into account, it seems that the CS rerouting is a better option. 3 Supporting Fast Set Up Since in ATM data can be sent over predefined connections only, it is important to develop techniques that reduce the set up time in order to support those applications that cannot tolerate a long set up delay. One of the advantages related to the ATM 2-level connection hierarchy is that it may facilitate this purpose. Consider the network in Figure 1. As shown in Figure 5(a), if there is no VP in this network then in order to set up the VC connection between A and G, a set up protocol has to be executed by the Network layer of A, B, C, D E, F and G (see [a] for more details). Next, consider the set up of the VC connection between A and G when VP(A-C) and VP(CwG) present (Figure 5(b)). As explained in [2], in such a case node A sends a SETUP message to C, node C sends such a message to G, node G sends a REPLY message to C, and node C sends a REPLY message to A The key point here is that although a SETUP and a REPLY message traverse the entire path between A and G as in Figure 5(a), they are not processed by the Network layer at B, D and E. Therefore, the time complexity of the protocol decreases from 10 to 4 time units. (Recall that in high-speed networks, where routing is performed by hardware of a lower layer and transmission speed is very fast, one time unit can be taken as the interval of time elapsed between the time the Network layer in some node sends a message and the time its peer entity completes processing this message, regardless of the hope distance and physical distance between the sender and receiver.) In many cases, before a VC connection is set up, the originating node will have to consult with a bandwidth management node in order to locate a route with available bandwidth. This is especially true for 1 1 c

5 A B C D E F A B C D E F (a) assuming no VP exists (b) assuming VP(A-C) and VP(C-F) exist Figure 5: The Set Up of a VC between A and F connections that need a lot of bandwidth. Consider, for instance, two network nodes, A and B. Suppose that node A needs a VC connection to B. The resulting sequence of events will be as follows: 1. Node A sends a message to a bandwidth manager, asking for allocation of a route with sufficient bandwidth to B. 2. The bandwidth manager responds with a description of a route N ~ N, ~.,.,, N~ from A to B, where NI z A, NL B and L Node A initiates a VC set up protocol to B through N~,...,NL-~. Assuming that every network node has a bidirectional low speed permanent VC (PVC) to the bandwidth manager and that there is no VP from any Ni, 1 5 i < L - 2, to Nj, i < j 5 N, steps 1 and 2 would take 1 time unit each, and step 3 would take additional 2. (L - 1) time units. Thus, the total time complexity would be 2L. In order to reduce this time significantly, the following hierarchical scheme is proposed. The network is divided into clusters with each node belonging to one cluster. One node in every cluster functions as a Fast Connection Set up Server (FCSS), that has a permanent VP (PVP) to every other node A in its cluster. Such a PVP has two purposes. First, it is used as a single building block of a low-speed control PVC connection for transmission of control messages between A and its FCSS. Second, it is used as one of the building blocks of every established-on-demand VC connections originating at A for which fast set up is required. The next step is setting up a PVP connection between every two FCSSs. Again, each PVP is used as a single building block of a low-speed control PVC con- Figure 6: The Worst Case Scenario of a Fast Set Up Between Two Remote Nodes nection between the FCSSs, and as one of the building blocks of established-on-demand VC connections between nodes belonging to the clusters of the two FCSSs. Consider now a node A that needs a fast set up of a VC connection to another node B. Assuming that node A has no direct link or VP to B, A sends a SETUP message to its FCSS, FCSS(A), using the PVC between them. FCSS(A) checks whether node B also belongs to its cluster. If this is the case (i.e. FCSS(A)=FCSS(B)), FCSS(A) sends a SETUP message to B over the PVC between them, B responds with a REPLY message and FCSS(A) sends such a message to A. Consequently, the VC setup is completed within 4 time units, regardless of the distances from A and B to FCSS(A). If FCSS(A)#FCSS(B), FCSS(A) should send a SETUP message to FCSS( B), and the setup is completed within 6 time units (Figure 6). This is the worst case scenario in terms of time complexity. The obvious deficiencies of the proposed scheme are that the routes over which the VC connections are set up might be inefficient, and that the VP connections to and from each FCSS might become a bottleneck. Therefore, if the connection between A and B needs c.2.5

6 a lot of bandwidth or if it is expected to last for a long time, another VC between A and B should be set up after the first one becomes active. Unlike the first VC, the new one is set up over the best available route between A and B, after consulting with the bandwidth manager. When the set up of the new VC is completed, the intentional rerouting mechanism is invoked in order to transfer the connection from the old VC to the new one. If the connection between A and B needs low bandwidth for a short duration (like a credit card transaction), it should not be rerouted. The two-level hierarchy is suitable for a huge network. For example, if the network consists of 20,000 nodes that may require this kind of service, which is more than the number of end offices in the United States, it can be divided into 10 clusters of 2000 nodes. This would result in 45 bidirectional PVC connections between the 10 FCSSs and 20,000 PVC connections between the nodes and their FCSSs. In a moderate network, it will be sufficient to establish only one FCSS for the entire network, which will function as a fast connection hub. This would reduce the upper bound on the setup time to 4 time units. (Note, however, that since the VP field in an ATM cell header contains 12 bits, an FCSS can be connected to no more than 212 stations.) In a small private network it will be possible to dispense with FCSSs, and to set up a PVP between every pair of nodes. This would decrease the set up time complexity to exactly 2 time units only. 4 Bandwidth Management Bandwidth allocation in an ATM network is an on-line problem: the network must handle a sequence of requests for bandwidth allocation without knowledge of future requests. This may sometime result in inability to satisfy a request that could have been accommodated if previous requests had been allocated alternative routes. For instance, consider Figure 7 that shows only links with available bandwidth in a network. Suppose that the available bandwidth of every shown link is 1 Mb/s and that a VC connection of 1 Mb/s from NI to N6 is needed. This VC is allocated 1 Mb/s along the route N1 -i Nz -+ N4 -+ N6. Sometime later, a 1 Mb/s VC connection is required from Nz to N6. This connection, however, cannot be admitted. Obviously, if the connection from NI to N6 had been established over the route NI -+ N3 -+ N5 +. N6, a connection from N3 to N4 could have been set up as well. The intentional rerouting mechanism enables the network to move some VC connections to alternative routes, thus vacating bandwidth for a new connection. Figure 7: Links With Available Bandwidth It can be employed especially if the bandwidth allocation is centralized. The existence of a bandwidth management node does not necessarily imply that every bandwidth allocation should go through this node. Rather, those connections that need a low-speed channel, like telephone calls, will be established without applying to the bandwidth manager, and will be blocked if there is not enough bandwidth on their intended route. Connections that need a high-speed channel, like compressed digital video, will be handled by the bandwidth manager. This approach will avoid bottleneck at the bandwidth manager, while, on the other hand, enable to make the best efforts in order to accommodate high capacity calls, from which the network revenue is high. In the following discussion we assume that every VC connection, from node A to node B say, is associated with some bandwidth requirement P[VC(A-B)]. This might be the peak rate requirement of VC(A-B), the average requirement, or any combination of them. Similarly, every network link, from node C to node D say, is assumed to have available bandwidth of p[c-d]. If p[c-+d] 2 P[VC(A-+B)], then VC(A-+B) can be established over C-D, in which case P[C-+D] decreases by P[VC(A-+B)I. Suppose that the bandwidth manager receives a request for a VC connection between nodes A and B. Therefore, it should find a route NI, Nz,..., NL, where: N1 E A, NL B, L 2 2 and for every Z, 15 i 5 L - 1, /?[Ni-+Ni+l] 2 P[VC(A-+B)] holds. This can be done by executing an algorithm for finding a route from A to B on the directed graph (V, A), where A is the set of links whose available bandwidth is 2 VC(A-+B), and Y is the set of network nodes connected to one or more links in A. For instance, the Breadth-First Search (BFS) algorithm can find the shortest route in time linear in the size of A. Suppose that the BFS fails in finding a route from A to B in the digraph (V,d). This implies that 11 c

7 VC(A+B) cannot be accommodated due to a lack of bandwidth. However, if this connection has a high priority, the bandwidth manager may consider to move some other VC connections to alternative routes using the intentional rerouting mechanism. (A cruel approach, where the bandwidth manager takes down low-priority connections in order to admit the new one is described in [3]). To this end, the bandwidth manager should address the following VCR (Virtual Channel Rerouting) problem: is it possible to reroute existing VC connections such that the new one can be admitted? if the answer is the affirmative, which of the existing VC connections should be rerouted and what should their new routes be? In the following we show that the VCR problem is NP-complete. Therefore, it is unlikely that an efficient (polynomial time) algorithm for this problem exists. Proposition 1 the VCR problem is NP-complete Pro0 f The proof is given in the full paper. It is shown that the Disjoint Connection Path for Directed Graph problem, which is known to be NP-complete (see [4], pp. 217), can be transformed in polynomial time to the VCR problem. 0 Even if the network manager is ready to reroute existing VC connections in order to admit a new one, the burden to the network must be as small as possible. Rerouting several existing VC connections in order to admit a single, high-priority. one will be impractical. This gives rise to another question, referred to as L- VCR (Limited VCR), which looks more practical: is it possible to reroute a single existing VC connection such that the new one can be admitted? As shown in the full paper, although the L-VCR is a private case of the VCR problem, it is an NPC problem as well. The conclusion is that some heuristic approaches are required in order to decide whether it is possible to set up a new VC connection that currently cannot be accommodated by rerouting one or more existing connections, and in order to determine which connection(s) should be rerouted. In the following we give a necessary but insufficient condition for the admission success of a new VC by rerouting other VCs. Let VC1,VC2,...,VCN-~ be the existing VC connections, and VCN be the new one that cannot be admitted. Let Si, Di and p[vci] be the source, destination, and required bandwidth of VC,, 1 < i < N. Let S be an imaginary super-source and D be an imaginary super-destination. Let S be connected by an imaginary directed link with capacity /?(VCi) to every Si. Similarly, let every Di be connected by an imaginary directed link whose capacity is p( VCi) to D. Let the other links have their original bandwidth (without VCI,VC~,...,VCN-1). Then, Proposition 2 if the network can accommodate VCN by reroutin existing VCs, there must exist a feasible n9 flow of P( VCi) from S to D. Pro0 f If the network can accommodate VC1,VC2;..,VCN, then there is a feasible flow of,b[vc,] from Si to Di for every 1 5 i 5 N that does not use the imaginary directed links from S and the imaginary directed links to D. Thus, there exists a feasible flow of EL1 p(vci) from S to D that uses the appended links. 0 Proposition 2 gives a necessary but insuficaent condition for the possibility of accommodating a new connection by rerouting existing ones. Thus, it can be used as a preliminary simple test before another, probably backtracking, exhausting algorithm is employed. The Edmonds-Karp algorithm for finding maximum flow from S to D runs in O(VA2) time. In the rest of this section, a heuristic algorithm that solves the rerouting problem is presented. The algorithm relies on the following two assumptions: 1. The number M of VC connections we are ready to reroute in order to accommodate a new blocked connection is bounded and small. M might depend on the priority of the blocked Connection, and on the revenue it brings. A reasonable value of M is less than The routes over which a connection between two nodes A and B can be established are pre-defined, and their total number R is bounded and small. R might depend on A and B. A reasonable value in a large network is less than 10. These assumptions can be easily justified in a real network: The profit of accommodating a blocked VC connection will not justify rerouting of many existing connections, due to the overhead of each rerouting. The route over which a connection between A and B is established will usually be the shortest, or relatively short, one. The latter is because establishing a connection over a long route would result in a loss of bandwidth and many blocked connections c.2.7

8 for i := 1 to M do repeat choose i existing VC connections, and "remove" them from the network for each pre-defined route between A and B do if the new connection can be established over this route then try to accommodate the i rerouted connections Figure 8: Heuristic algorithm for Rerouting Based on these two assumptions, the algorithm presented in Figure 8 can be executed in order to determine if a blocked VC connection can be accommodated by rerouting up to A4 existing VC connections. Let N be the number of existing VC connections. Thus, there are (? possible ways to choose i ex- isting connections which will be subject for rerouting. Following the assumption where each connection can be established over no more than R routes, there are Ri possible ways to re-establish the i removed connections in the network. Thus, the complexity of the algorithm is where P = O (d) is the time required in order to check whether a given route can accomodate a given connection (recall that A is the number of edges in the network). (\ /., ) R' 5 CE,(RN)' holds. Since both R and M are considered as relatively small constants, we get a time complexity of O(RN)M*O(d) = O (NMd) - a polynomially bounded function of d and N. 5 Conclusions The paper has addressed the issue of intentional VC connection rerouting in ATM as a network management tool. It has shown that an ATM connection using an operable (not failed) VC can be smoothly rerouted to another VC. Then, the paper has suggested some applications of the intentional rerouting mechanism. It has shown that using the two-level connection hierarchy of ATM, a VC connection can be set up very fast on some predetermined, and usually more expensive, route. After the VC is set up and the exchange of data begins, the rerouting mechanism can be invoked in order to set up the connection over a better VC. Another possible application of intentional rerouting is bandwidth management. As has been shown, deciding if a new connection can be admitted by rerouting existing connections is an NP-complete problem. Thus, a heuristic algorithm, relying on practical assumptions, has been presented. References AAL Type 5, Draft Recommendation Text for Section 6 of 1.363, January R. Cohen and A. Segall. Connection management and rerouting in ATM networks. In INFOCOM, J. Garay and I. Gopal. Call preemption in communication networks. In INFOCOM, pages , 92. M. Garey and D. Johnson. Computers and Intractability. W.H. Freeman and Company, R. Handell and M. Huber. Integrated Broadband Networks. Addison-Wesley, J. Le Boudec. The asynchronous transfer mode: A tutorial. Computer Networks and ISDN Systems, 24: , S. Ohta and K. Sato. Dynamic bandwidth control of virtual path in an asynchronous transfer mode network. IEEE Transactions on Communications, 40(7): , July K. Sato, S. Ohta, and I. Tokizawa. Broadband ATM network architecture based on virtual paths. IEEE Transactions on Communications, 38(8): , August C. Traw and J. Smith. Hardware/software organization of a high-performance ATM host interface. IEEE Journal on Selected Areas in Communications, 11(2), February c