Kumar N. Sivarajan

Routing and wavelength assignment in all-optical networks

Considers routing connections in a reconfigurable optical network using WDM. Each connection between a pair of nodes in the network is assigned a path through the network and a wavelength on that path, such that connections whose paths share a common link in the network are assigned different wavelengths. The authors derive an upper bound on the carried traffic of connections (or equivalently, a lower bound on the blocking probability) for any routing and wavelength assignment (RWA) algorithm in such a network. The bound scales with the number of wavelengths and is achieved asymptotically (when a large number of wavelengths is available) by a fixed RWA algorithm. The bound can be used as a metric against which the performance of different RWA algorithms can be compared for networks of moderate size. The authors illustrate this by comparing the performance of a simple shortest-path RWA (SP-RWA) algorithm via simulation relative to the bound. They also derive a similar bound for optical networks using dynamic wavelength converters, which are equivalent to circuit-switched telephone networks, and compare the two cases. Finally, they quantify the amount of wavelength reuse achievable in large networks using the SP-RWA via simulation as a function of the number of wavelengths, number of edges, and number of nodes for randomly constructed networks as well as de Bruijn networks. They also quantify the difference in wavelength reuse between two different optical node architectures. >

Design of logical topologies for wavelength-routed optical networks

The problem of designing a logical topology over a wavelength-routed all-optical network (AON) physical topology is studied. The physical topology consists of the nodes and fiber links in the network. On an AON physical topology, we can set up lightpaths between pairs of nodes, where a lightpath represents a direct optical connection without any intermediate electronics. The set of lightpaths along with the nodes constitutes the logical topology. For a given network physical topology and traffic pattern, our objective is to design the logical topology and the routing algorithm so as to minimize the network congestion while constraining the average delay seen by a source-destination pair and the amount of processing required at the nodes (degree of the logical topology). Ignoring the delay constraints can result in fairly convoluted logical topologies with very long delays. On the other hand, in all our examples, imposing it results in a minimal increase in congestion. While the number of wavelengths required to imbed the resulting logical topology on the physical all optical topology is also a constraint in general, we find that in many cases of interest this number can be quite small. We formulate the combined logical topology design and routing problem described above as a mixed integer linear programming problem which we then solve for a number of cases of a six-node network. This programming problem is split into two subproblems: logical topology design, and routing. We then compare the performance of several heuristic topology design algorithms against that of randomly generated topologies, as well as lower bounds.

Efficient network QoS provisioning based on per node traffic shaping

This paper addresses the problem of providing per-connection end-to-end delay guarantees in a high-speed network. We consider a network comprised of store-and-forward packet switches, in which a packet scheduler is available at each output link. We assume that the network is connection oriented and enforces some admission control which ensures that the source traffic conforms to specified traffic characteristics. We concentrate on the class of rate-controlled service (RCS) disciplines, in which traffic from each connection is reshaped at every hop, and develop end-to-end delay bounds for the general case where different reshapers are used at each hop. In addition, we establish that these bounds can also be achieved when the shapers at each hop have the same minimal envelope. The main disadvantage of this class of service discipline is that the end-to-end delay guarantees are obtained as the sum of the worst-case delays at each node, but we show that this problem can be alleviated through proper reshaping of the traffic. We illustrate the impact of this reshaping by demonstrating its use in designing RCS disciplines that outperform service disciplines that are based on generalized processor sharing (GPS). Furthermore, we show that we can restrict the space of good shapers to a family which is characterized by only one parameter. We also describe extensions to the service discipline that make it work conserving and as a result reduce the average end-to-end delays.

Design of logical topologies: a linear formulation for wavelength-routed optical networks with no wavelength changers

We consider the problem of constructing logical topologies over a wavelength-routed optical network with no wavelength changers. We present a general linear formulation which considers routing traffic demands, and routing and assigning wavelengths to lightpaths, as a combined optimization problem. The formulation also takes into account the maximum number of hops a lightpath is permitted to take, multiple logical links in the logical topology, multiple physical links in the physical topology, and symmetry/asymmetry restrictions in designing logical topologies. The objective is to minimize congestion. We show by examples how equality and inequality logical degree constraints have a bearing on congestion. We prove that, under certain conditions, having equality degree constraints with multiple edges allowed in the design of logical topologies does not affect congestion. This helps in reducing the dimensionality of the search space and hence speeds up the search for an optimal solution of the linear formulation. We solve the linear formulation for small examples and show the tradeoff between congestion, number of wavelengths available and the maximum number of hops a lightpath is allowed to take. For large networks, we solve the linear formulation by relaxing the integer constraints. We develop topology design algorithms for large networks based on rounding the solutions obtained by solving the relaxed problem. Since the whole problem is linearizable, the solution obtained by relaxation of the integer constraints yields a lower bound on congestion. This is useful in comparing the efficiency of our heuristic algorithms. Following Bienstock and Gunluk (1995), we introduce a cutting plane which helps in obtaining better lower bounds on congestion and also enables us to reduce the previously obtained upper bounds on congestion.

Algorithms for routing and wavelength assignment based on solutions of LP-relaxations

In this letter, we consider the problem of maximizing the number of lightpaths that may be established in a wavelength routed optical network (WRON), given a connection matrix, i.e., a static set of demands, and the number of wavelengths the fiber supports. The problem of establishing all the connections of the connection matrix using the fewest number of wavelengths has been investigated in Banerjee and Mukherjee (1996) and Baroni et al. (1998). We call the former problem max-RWA (problem of maximizing the number of lightpaths) and the latter problem min-RWA (minimizing the number of wavelengths). In this letter, we only consider WRONs with no wavelength conversion capabilities. We formulate the max-RWA problem when no wavelength conversion is allowed as an integer linear programme (ILP) which may be solved to obtain an optimum solution. We hope to solve the ILP exactly for small size networks (few nodes). For moderately large networks (tens of nodes) we develop algorithms based on solutions obtained by solving the LP-relaxation of the ILP formulation. Results obtained for networks such as NSFNET and EONNET are presented.

An efficient communication protocol for high-speed packet-switched multichannel networks

A media-access protocol for high-speed packet-switched multichannel networks that are based on a broadcast topology, such as optical passive star networks using wavelength-division multiple access, is described. The protocol supports connection-oriented traffic with or without bandwidth reservation, as well as datagram traffic to integrate transport-layer functions with the media-access layer. It uses the bandwidth efficiently while keeping the processing requirements low by requiring stations to compute their transmission and reception schedules only at the start and end of each connection. Analysis results show that low blocking probabilities for connections and high network throughput can be achieved. >

Blocking in all-optical networks

We present a new analytical technique, based on the inclusion-exclusion principle from combinatorial mathematics, for the analysis of all-optical networks with no wavelength conversion and random wavelength assignment. We use this technique to propose two models of low complexity for analysing networks with arbitrary topologies and traffic patterns. The first model improves the current technique by Birman (1996) in that the complexity of calculation is independent of hop-length and scales only with the capacity of the link as against that of Birmans method which grows exponentially with hop-length. We then propose a new heuristic to account for wavelength correlation and show that the second model is accurate even for sparse networks. Our technique can also be extended to analyse fixed alternate and least loaded routing.

Performance analysis of channelized cellular systems with dynamic channel allocation

We present an analytical model to compute the blocking probability in channelized cellular systems with dynamic channel allocation. We model the channel occupancy in a cell by a two-dimensional (2D) Markov chain, which can be solved to obtain the blocking probability in each cell. We apply our analytical model to linear highway systems with and without lognormal shadowing and then extend it to 2D cellular systems with lognormal shadowing. We show that, for linear highway systems, distributed dynamic channel-allocation schemes perform similarly to the centralized dynamic channel-allocation schemes in terms of blocking probability. However, for 2D cellular systems, the improvement in the performance is significant and the reduction in the blocking probability in systems with distributed dynamic channel allocation is by almost one order of magnitude, when compared to that in systems with centralized dynamic channel allocation. In practice, our analysis of linear highway systems is applicable to Digital European Cordless Telephony (DECT) and that of 2D cellular systems is applicable to global systems for mobile communications (GSM).

A new approach to dimensioning optical networks

A network dimensioning method allocates appropriate capacities to the links based on the network topology and traffic requirements. We introduce the concept of absorption probability instead of blocking probability which is a more appropriate measure to express the grade of service of an optical network, in many cases. Absorption probability can be obtained from transient analysis of a Markov chain. Computation of exact absorption probabilities requires large computing resources and is thus feasible only for small networks. We present a method to approximate the absorption probability of a wavelength-routed network with arbitrary topology and traffic patterns assuming the nodes have full wavelength conversion capability. We show that the approximation method performs well especially in the desired range of absorption probabilities and it is computationally efficient.

Capacity evaluation for CDMA cellular systems

In this paper, we find bounds and approximations for the capacity of mobile cellular communication networks based on code division multiple access (CDMA). We develop efficient analytic techniques for capacity calculations of CDMA cellular networks. Each cell is modeled as an independent M/G//spl infin/ queue and traffic capacity assessed based on the maximum Erlang traffic that leads to acceptable link quality with high probability. Subsequently, approximations and bounds for the outage probability and hence traffic capacity are obtained using asymptotic expansions and large deviations theory. Numerical examples, considering uniform and normalized truncated Gaussian user density in the system are evaluated. The propagation model we consider takes care of distance and lognormal shadowing losses.