Bülent Yener

A study of upper and lower bounds for minimum congestion routing in lightwave networks

This paper considers the combined problem of finding allocation of wavelengths to the stations (configuration) and finding the associated routing of the traffic to minimize congestion (the amount of maximum flow on any link). This work presents efficient algorithms for computing both upper and lower bounds on the congestion. The upper bounds-to obtain approximate solutions of this problem-are based modification of two heuristics (i) variable depth local search, and (ii) simulated annealing. A more significant contribution is a lower bound computation based on building flow trees to find a lower bound on the total flow, and then distributing the total flow over the links provide a lower bound on the congestion. This technique yields a tool which can be used in evaluating the quality of heuristic algorithms, and determining a termination criteria during minimization. This technique can be applied to other problems with flow-based objectives. Performance of the heuristics is analysed, and compared via simulation studies. It is shown that the heuristics perform on the average, within 20% of the computed lower bound, and 15% better than the previous methods to solve this problem.<<ETX>>

Combinatorial design of congestion-free networks

This paper presents a new design methodology and tools to construct a packet switched network with bursty data sources. This network design combines two important properties for arbitrary traffic pattern: (1) the aggregate throughput is scalable and (2) there is no packet loss within the subnet. More specifically, given a bounded number of ports in every switching node, the design is based on the construction of multiple virtual rings under the following constraints: (1) the virtual rings are pairwise edge-disjoint and (2) there is at least one virtual ring between any pair of nodes. The target topology is obtained from the edge union of the multiple virtual rings. The two constraints ensure no loss due to congestion inside a network with arbitrary traffic pattern and that packets will reach (or converge) their destinations. The virtual rings are constructed by using combinatorial block designs together with an algorithm for realizing any size networks. It is shown that the bound on the maximum route length, under the two constraints, is O(/spl radic/N) for an N-node network, This sublinear bound facilitates the throughput scalability property.

Design and performance of convergence routing on multiple spanning trees

This paper presents a new design, and a performance study for convergence routing in a general network with multiple spanning trees suggested as a switch-based LAN. In particular, a new algorithm for constructing two edge-disjoint spanning trees of a given network is presented, and the resulting trees are used for convergence routing (a variant of deflection routing with destination convergence guaranteed). It is shown empirically that convergence routing on two edge-disjoint spanning trees yields a better bound than a single spanning tree, on the maximum route length. The construction of the two edge-disjoint spanning trees is done with specific strategies for achieving certain tree properties that improve the systems performance.

Topological design of loss-free switch-based LANs

The paper presents a new design methodology and tools to construct a switch-based LAN with (i) scalable throughput, (ii) no loss due to congestion, and (iii) two routing modes: FIFO or non-FIFO. More specifically, given a bounded degree (number of switch ports) at each node, the design is based on the construction of multiple virtual rings under the following constraints: (i) the virtual rings are pairwise edge-disjoint, and (ii) there is at least one virtual ring between any pair of nodes. The target topology is obtained from the edge union of the multiple virtual rings. The objectives of the above two constraints are (i) to ensure no loss due to congestion inside the network of bursty traffic sources, and (ii) to ensure convergence of packets/cells to their destinations. The virtual rings are constructed by a new methodology that employs combinatorial block designs together with a new algorithm for realizing any size networks. It is shown that the bound on the maximum route length, under the two constraints, is O(/spl radic/N) for an N-node network.

Iterative approach to optimizing convergence routing priorities

This paper shows how to optimize the routing decisions in a nondeterministic routing algorithm called convergence routing in which routes may change depending on the traffic conditions. The routing algorithm guarantees a loss-free delivery of data packets from bursty sources, and a deterministic bound on the route length in arbitrary topology networks. The routing decisions are based on assigning routing priorities to the links such that a packet is forwarded to the highest priority link which is not blocked. Routing priorities are assigned using a local-greedy metric which minimizes the distance (number of hops) to the destination. This work shows that routing decisions using a local-greedy metric are not optimal, and the performance of the algorithm can be improved substantially by using new measures. Thus, various look-ahead metrics which take into account the potential gain on the other switching nodes toward the destination of a packet are suggested. The contributions of this work are: (1) a new analytical model to capture the behavior of a switching node; (2) an iterative optimization technique to set routing priorities according to various look-ahead measures; and (3) heuristics to ensure the stability of the routing priorities. The optimization objective is to maximize the throughput by minimizing the maximum total flow carried on a link in the network under static traffic model. The performance is studied computationally on various networks and traffic matrices. It is shown that up to a 50% performance increase can be obtained by optimizing the routing priorities.

Concurrent asynchronous broadcast on the MetaNet

The problem solved in this work is how multiple nodes in a network with an arbitrary topology can broadcast concurrently, in an asynchronous manner, to all other nodes. Asynchronous means that the nodes do not coordinate their broadcast, and, therefore, it is possible that all nodes will start to broadcast at the same time. Simultaneous broadcast by many nodes can cause traffic congestion, which can result in a traffic loss. The main property of the broadcast algorithms presented in this work is that under any arbitrary broadcast pattern there will be no packet or cell loss due to internal traffic congestion. The routing mechanism used by the broadcast algorithm can be viewed as a variant of deflection routing, which means that a node makes on-line routing decisions based on the local flow of traffic (i.e., internal load conditions). Unlike other deflection techniques, the MetaNet routing is along a global sense of direction, which guarantees that packets will reach their destinations. Thus, we call this method convergence routing (previous deflection algorithms did not guarantee deterministic routing convergence, i.e., a cell/packet can be deflected indefinitely inside the network). As a result of the convergence property, the deflection routing used in this work is the only one with broadcast capability.

Reliable concurrent multicast from bursty sources

This paper presents a protocol and design for concurrent and reliable group multicast (many-to-many) from bursty data sources in general networks. In a group multicast, any node can be a multicast source and multiple nodes may start to multicast simultaneously, i.e., an asynchronous access to the network. The reliable multicast protocol presented in this work is window based with a combined sender and receiver initiation of the recovery protocol. In reliable multicasting the necessary requirement is to ensure that data is received correctly by all the active members of the multicast group. The approach taken in this work is to combine the multicast operation with the internal flow control, as a result, it is possible to provide: (1) loss-free multicast routing with a single and immediate acknowledgement message to the sender. Furthermore, in every multicast, (2) a node can access all the capacity allocated to its group with no delay, however, if several nodes are active in the same group then the capacity will be shared fairly. In addition, (3) each sender in the multicast group uses a single timer, and (4) a node can join and leave a multicast group in a transparent fashion, i.e., there is no need to explicitly notify the members of the group. A multiple criteria optimization study of the bandwidth allocation to each multicast group is presented. The optimization problem has two min-max objective functions: (1) for delay, which caused by the number of links needed to connect the group, and (2) for congestion, which is caused by sharing a link among multiple multicast groups. The bandwidth allocation among multicast group sharing the same link are further optimized using the max-min fairness criterion.

Convergence routing on disjoint spanning trees

This paper presents a new design and a performance study for convergence routing in a general network with multiple spanning trees. Such an arbitrary topology network is used in the design of a switch-based LAN/MAN architecture. Convergence routing can be viewed as a variant of deflection routing which combines, in a dynamic fashion, the on-line routing decision with the traffic load inside network. However, unlike other deflection techniques, convergence routing guarantees that packets will reach (or converge) to their destinations. In particular, a new algorithm for constructing two edge-disjoint spanning trees of a given network is presented, and the resulting trees are used for convergence routing. It is shown empirically that convergence routing on two edge-disjoint spanning trees yields a better bound than a single spanning tree, on the maximum route length. The construction of the two edge-disjoint spanning trees is done with specific strategies for improving the fault-tolerance and performance of the system.

Simultaneous strong separations of probabilistic and unambiguous complexity classes

We study the relationship between probabilistic and unambiguous computation, and provide strong relativized evidence that they are incomparable. In particular, we display a relativized world in which the complexity classes embodying these paradigms of computation are mutually immune. We answer questions formulated in—and extend the line of research opened by—Geske and Grollmann [15] and Balcázar and Russo [3].

Fault-tolerant convergence routing

This paper presents fault-tolerant protocols for fast packet switch networks with convergence routing. The objective is to provide, after a link or a node (switch) failure, fast reconfiguration and continuous host-to-host communication. Convergence routing is a variant of deflection routing, which combines in a dynamic fashion, the on-line routing decision with the traffic load inside the network. Unlike other deflection techniques, convergence routing guarantees that packets will reach or converge to their destinations. This fault-tolerant solution is designed for a switch-based (i.e., arbitrary topology) LAN architecture called MetaNet. The original MetaNets convergence routing scheme has been modified in order to facilitate the property that the packet header need not be recomputed after a failure and/or a reconfiguration. This is achieved by having, at the network interface, a translator that maps the unique destination address to a virtual address. The virtual addresses are stored at the packet header, and used for convergence routing, with a global sense of direction over (i) a single spanning tree, and (ii) over two edge-disjoint spanning trees, for redundancy (fault tolerance) and greater efficiency.<<ETX>>