Murat Azizoglu

Adaptive wavelength routing in all-optical networks

We consider routing and wavelength assignment in wavelength-routed all-optical networks (WAN) with circuit switching. The conventional approaches to address this issue consider the two aspects of the problem disjointly by first finding a route from a predetermined set of candidate paths and then searching for an appropriate wavelength assignment. We adopt a more general approach in which we consider all paths between a source-destination (s-d) pair and incorporate network state information into the routing decision. This approach performs routing and wavelength assignment jointly and adaptively, and outperforms fixed routing techniques. We present adaptive routing and wavelength assignment algorithms and evaluate their blocking performance. We obtain an analytical technique to compute approximate blocking probabilities for networks employing fixed and alternate routing. The analysis can also accommodate networks with multiple fibers per link. The blocking performance of the proposed adaptive routing algorithms are compared along with their computational complexity.

On optimal converter placement in wavelength-routed networks

Wavelength converters increase the traffic-carrying capacity of circuit-switched optical networks by relaxing the wavelength continuity constraints. We consider the problem of optimally placing a given number of wavelength converters on a path to minimize the call-blocking probability. Using a simple performance model, we first prove that uniform spacing of converters is optimal for the end-to-end performance when link loads are uniform and independent. We then show that significant gains are achievable with optimal placement compared to random placement. For nonuniform link loads, we provide a dynamic programming algorithm for the optimal placement and compare the performance with random and uniform placement. Optimal solutions for bus and ring topologies are also presented. Finally, we discuss the effect of the traffic model on the placement decision.

Stochastic modeling of TCP over lossy links

An analytical framework for modeling the performance of a single TCP session in the presence of random packet loss is presented. A Markovian approach is developed that allows us to study both memoryless channels (IID packet loss) and channels with memory (correlated packet loss) modeled by a two-state continuous-time Gilbert model. The analytical results are validated against results using the ns simulator. It is shown that the model predicts throughput for LAN/WAN (low and high bandwidth-delay products) with good accuracy. Further, throughput for the IID loss model is found to be relatively insensitive to the probability density function (PDF) of the loss inter-arrival process. For channels with memory, we present an empirically validated rule of thumb to categorize the channel transition frequency.

Connectivity and sparse wavelength conversion in wavelength-routing networks

Wavelength-routing networks offer the advantages of wavelength re-use and scalability over broadcast-and-select networks and are therefore suitable for wide area networks (WANs). We study the effects of topological connectivity and wavelength conversion in circuit-switched all-optical wavelength-routing networks. An approximate blocking analysis of such network is performed. We first propose an improved framework for the analysis of networks with arbitrary topology. We introduce a simple model for networks with a variable number of converters and analyze the effect of wavelength converter density on blocking probability. We then apply this framework to two sparse network topologies, the ring and the mesh-torus, and obtain the blocking performance. The results show that, in most cases, only a fraction of the network nodes need to be equipped with wavelength conversion capability for good performance. Finally, the tradeoff between physical connectivity, wavelength conversion, and the number of available wavelengths is studied through networks with random topologies.

On the information-theoretic capacity of discrete-time queues

The information-theoretic capacity of continuous-time queues was analyzed recently by Anantharam and Verdu (see ibid. vol.42, p.4-18, 1996). Along similar lines, we analyze the information-theoretic capacity of two models of discrete-time queues. The first model has single packet arrivals and departures in a time slot and independent packet service times, and is the discrete-time analog of the continuous-time model analyzed by Anantharam and Verdu. We show that in this model, the geometric service time distribution plays a role analogous to that of the exponential distribution in continuous-time queues, in that, among all queues in this model with a given mean service time, the queue with geometric service time distribution has the least capacity. The second model allows multiple arrivals in each slot, and the queue is modeled as serving an independent random number of packets in each slot. We obtain upper and lower bounds on the capacity of queues with an arbitrary service distribution within this model, and show that the bounds coincide in the case of the queue that serves a geometrically distributed number of packets in each slot. We also discuss the extremal nature of the geometric service distribution within this model.

Impact of tuning delay on the performance of bandwidth-limited optical broadcast networks with uniform traffic

This paper studies the effects of tuning delay of transmitters in packet-based optical broadcast networks. We consider scheduling of random traffic with tunable transmitters and fixed-tuned receivers and obtain the degradation imposed by tuning delay using several performance criteria, such as schedule completion time, average packet delay, and session blocking rates. We show that for off-line scheduling the effects of tuning delay are small even if the tuning time is as large as the packet duration. We provide a lower bound to the expected completion time of any off-line schedule with an arbitrary number of wavelengths. We then describe a near-optimal schedule which is based on the principle of having idle transmitters tune to wavelengths just-in-time to start their transmissions. Stability and capacity issues in the transmission of real-time traffic are considered and a queueing-theoretic analysis of average packet delay is given. The packet delay is found to be insensitive to tuning delay under near-optimal transmission scheduling. Finally we extend the model to connection-oriented networks and evaluate the session blocking performance for scheduled circuit connections.

On the optimal placement of wavelength converters in wavelength-routed networks

We consider the problem of optimally placing a given number of wavelength converters on a path to minimize the call blocking probability. Using a simple performance model, we first prove that uniform spacing of converters is optimal for the end-to-end performance when the link loads are uniform and statistically independent. We then show that significant gains are achievable with optimal placement compared to random placement. For non-uniform link loads, we provide a dynamic programming algorithm for the optimal placement and compare the performance with random and uniform placement. Optimal solutions for bus and ring topologies are also presented.

Convexity properties in binary detection problems

The author investigates the convexity properties of error probability in the detection of binary-valued scalar signals corrupted by additive noise. It is shown that the error probability of the maximum-likelihood receiver is a convex function of the signal power when the noise has a unimodal distribution. Based on this property, the results of the optimal time-sharing strategies of transmitters and jammers, and of the optimal use of multiple channels are obtained.

Efficient scheduling of transmissions in optical broadcast networks

All-optical networks (AONs) with a broadcast-star based physical topology offer the possibility of transmission scheduling to resolve channel and receiver conflicts. This paper considers the problem of scheduling packet transmissions in a wavelength-division multiplexed (WDM) optical network with tunable transmitters and fixed-tuned receivers. The scheduling problem is complicated by tuning latency, a limited number of channels, and arbitrary traffic demands. We first analyze scheduling all-to-all packet transmissions and obtain a new lower bound for the schedule length. The lower bound is achieved by an algorithm proposed by Pieris and Sasaki (1994). We then extend the analysis to the case of arbitrary traffic demands and obtain lower bounds for the schedule length. Two constructions for scheduling algorithms are provided through list scheduling and multigraphs. The upper bounds so obtained not only provide performance guarantees with arbitrary demands, but also nearly meet the lower bound in simulations.

A performance model for wavelength conversion with non-Poisson traffic

This paper makes the first known attempt to study wavelength-routing networks and the effects of wavelength conversion under dynamic non-Poisson traffic. An approximation that characterizes any non-Poisson traffic by its first two moments is utilized. The arrival occupancy distribution of busy wavelengths for this approximate process is derived and is used to analyze the effects of wavelength conversion. The model predicts that traffic peakedness plays an important role in determining the blocking performance, and also that wavelength conversion gain is insensitive to traffic peakedness over a large range.