Eytan Modiano

Capacity and delay tradeoffs for ad hoc mobile networks

We consider the throughput/delay tradeoffs for scheduling data transmissions in a mobile ad hoc network. To reduce delays in the network, each user sends redundant packets along multiple paths to the destination. Assuming the network has a cell partitioned structure and users move according to a simplified independent and identically distributed (i.i.d.) mobility model, we compute the exact network capacity and the exact end-to-end queueing delay when no redundancy is used. The capacity-achieving algorithm is a modified version of the Grossglauser-Tse two-hop relay algorithm and provides O(N) delay (where N is the number of users). We then show that redundancy cannot increase capacity, but can significantly improve delay. The following necessary tradeoff is established: delay/rate/spl ges/O(N). Two protocols that use redundancy and operate near the boundary of this curve are developed, with delays of O(/spl radic/N) and O(log(N)), respectively. Networks with non-i.i.d. mobility are also considered and shown through simulation to closely match the performance of i.i.d. systems in the O(/spl radic/N) delay regime.

Dynamic power allocation and routing for time varying wireless networks

We consider dynamic routing and power allocation for a wireless network with time varying channels. The network consists of power constrained nodes which transmit over wireless links with adaptive transmission rates. Packets randomly enter the system at each node and wait in output queues to be transmitted through the network to their destinations. We establish the capacity region of all rate matrices (/spl lambda//sub ij/) that the system can stably support - where (/spl lambda//sub ij/) represents the rate of traffic originating at node i and destined for node j. A joint routing and power allocation policy is developed which stabilizes the system and provides bounded average delay guarantees whenever the input rates are within this capacity region. Such performance holds for general arrival and channel state processes, even if these processes are unknown to the network controller. We then apply this control algorithm to an ad-hoc wireless network where channel variations are due to user mobility, and compare its performance with the Grossglauser-Tse (2001) relay model.

Traffic grooming in WDM networks

The emergence of wavelength-division multiplexing technology has led to a tremendous increase In the available transmission capacity in wide area networks. Consequently, these networks may no longer be limited by the transmission bandwidth, but rather by the processing capability of electronic switches, routers, and multiplexers in the network. This realization has led to a new wave of research aimed at overcoming the electronic bottleneck by providing optical bypass at the WDM layer. Traffic grooming can be used as a bypass mechanism by which low-rate circuits are assigned to wavelengths in order to minimize the amount of electronic multiplexing equipment. This topic has received a significant amount of attention in both the research and commercial arenas. We give an overview of the traffic grooming problem and survey some representative work in this area. While most work has focused on grooming in SONET rings, grooming traffic in general mesh networks is an important emerging problem.

Traffic grooming algorithms for reducing electronic multiplexing costs in WDM ring networks

We develop traffic grooming algorithms for unidirectional SONET/WDM ring networks. The objective is to assign calls to wavelengths in a way that minimizes the total cost of electronic equipment [e.g., the number of SONET add/drop multiplexers (ADMs)]. We show that the general traffic grooming problem is NP-complete. However, for some special cases we obtain algorithms that result in a significant reduction in the number of ADMs. When the traffic from all nodes is destined to a single node, and all traffic rates are the same, we obtain a solution that minimizes the number of ADMs. In the more general case of all-to-all uniform frame we obtain a lower bound on the number of ADMs required, and provide a heuristic algorithm that performs closely to that bound. To account for more realistic traffic scenarios, we also consider distance dependent traffic, where the traffic load between two nodes is inversely proportional to the distance between them, and again provide a nearly optimal heuristic algorithm that results in substantial ADM savings. Finally, we consider the use of a hub node, where traffic can be switched between different wavelength, and obtain an optimal algorithm which minimizes the number of ADMs by efficiently multiplexing and switching the traffic at the hub. Moreover, we show that any solution not using a hub can be transformed into a solution with a hub using fewer or the same number of ADMs.

Fairness and optimal stochastic control for heterogeneous networks

We consider optimal control for general networks with both wireless and wireline components and time varying channels. A dynamic strategy is developed to support all traffic whenever possible, and to make optimally fair decisions about which data to serve when inputs exceed network capacity. The strategy is decoupled into separate algorithms for flow control, routing, and resource allocation, and allows each user to make decisions independent of the actions of others. The combined strategy is shown to yield data rates that are arbitrarily close to the optimal operating point achieved when all network controllers are coordinated and have perfect knowledge of future events. The cost of approaching this fair operating point is an end-to-end delay increase for data that is served by the network. Analysis is performed at the packet level and considers the full effects of queueing.

Maximizing throughput in wireless networks via gossiping

A major challenge in the design of wireless networks is the need for distributed scheduling algorithms that will efficiently share the common spectrum. Recently, a few distributed algorithms for networks in which a node can converse with at most a single neighbor at a time have been presented. These algorithms guarantee 50% of the maximum possible throughput. We present the first distributed scheduling framework that guarantees maximum throughput. It is based on a combination of a distributed matching algorithm and an algorithm that compares and merges successive matching solutions. The comparison can be done by a deterministic algorithm or by randomized gossip algorithms. In the latter case, the comparison may be inaccurate. Yet, we show that if the matching and gossip algorithms satisfy simple conditions related to their performance and to the inaccuracy of the comparison (respectively), the framework attains the desired throughput.It is shown that the complexities of our algorithms, that achieve nearly 100% throughput, are comparable to those of the algorithms that achieve 50% throughput. Finally, we discuss extensions to general interference models. Even for such models, the framework provides a simple distributed throughput optimal algorithm.

Power allocation and routing in multibeam satellites with time-varying channels

We consider power and server allocation in a multibeam satellite downlink which transmits data to <i>N</i> different ground locations over <i>N</i> time-varying channels. Packets destined for each ground location are stored in separate queues and the server rate for each queue <i>i</i> depends on the power <i>p_i</i> (<i>t</i>) allocated to that server and the channel state <i>c_i</i> (<i>t</i>) according to a concave rate-power curve μ_<i>i</i>(<i>p_i, c_i</i>). We establish the capacity region of all arrival rate vectors (λ₁,...,λ_<i>N</i>) which admit a stabilizable system. We then develop a power-allocation policy which stabilizes the system whenever the rate vector lies within the capacity region. Such stability is guaranteed even if the channel model and the specific arrival rates are unknown. Furthermore, the algorithm is shown to be robust to arbitrary variations in the input rates and a bound on average delay is established. As a special case, this analysis verifies stability and provides a performance bound for the <i>Choose-the-K-Largest-Connected-Queues</i> policy when channels can be in one of two states (ON or OFF) and <i>K</i> servers are allocated at every timestep (<i>K</i> < <i>N</i>). These results are extended to treat a joint problem of routing and power allocation in a system with multiple users and satellites and a throughput maximizing algorithm for this joint problem is constructed. Finally, we address the issue of interchannel interference and develop a modified policy when power vectors are constrained to feasible activation sets. Our analysis and problem formulation is also applicable to power control for wireless systems.

Minimum energy disjoint path routing in wireless ad-hoc networks

We develop algorithms for finding minimum energy disjoint paths in an all-wireless network, for both the node and link-disjoint cases. Our major results include a novel polynomial time algorithm that optimally solves the minimum energy 2 link-disjoint paths problem, as well as a polynomial time algorithm for the minimum energy k node-disjoint paths problem. In addition, we present efficient heuristic algorithms for both problems. Our results show that link-disjoint paths consume substantially less energy than node-disjoint paths. We also found that the incremental energy of additional link-disjoint paths is decreasing. This finding is somewhat surprising due to the fact that in general networks additional paths are typically longer than the shortest path. However, in a wireless network, additional paths can be obtained at lower energy due to the broadcast nature of the wireless medium. Finally, we discuss issues regarding distributed implementation and present distributed versions of the optimal centralized algorithms presented in the paper.

Cooperative Routing in Static Wireless Networks

We study the problem of transmission-side diversity and routing in a static wireless network. It is assumed that each node in the network is equipped with a single omnidirectional antenna and that multiple nodes are allowed to coordinate their transmissions in order to obtain energy savings. We derive analytical results for achievable energy savings for both line and grid network topologies. It is shown that the energy savings of and are achievable in line and grid networks with a large number of nodes, respectively. We then develop a dynamic-programming-based algorithm for finding the optimal route in an arbitrary network, as well as suboptimal algorithms with polynomial complexity. We show through simulations that these algorithms can achieve average energy savings of about in random networks, as compared to the noncooperative schemes.

Survivable lightpath routing: a new approach to the design of WDM-based networks

Network restoration is often done at the electronic layer by rerouting traffic along a redundant path. With wavelength-division multiplexing (WDM) as the underlying physical layer, it is possible that both the primary and backup paths traverse the same physical links and would fail simultaneously in the event of a link failure. It is, therefore, critical that lightpaths are routed in such a way that a single link failure would not disconnect the network. We call such a routing survivable and develop algorithms for survivable routing of a logical topology. First, we show that the survivable routing problem is NP-complete. We then prove necessary and sufficient conditions for a routing to be survivable and use these conditions to formulate the problem as an integer linear program (ILP). Due to the excessive run-times of the ILP, we develop simple and effective relaxations for the ILP that significantly reduces the time required for finding survivable routings. We use our new formulation to route various logical topologies over a number of different physical topologies and show that this new approach offers a much greater degree of protection than alternative routing schemes such as shortest path routing and a greedy routing algorithm. Finally, we consider the special case of ring logical topologies for which we are able to find a significantly simplified formulation. We establish conditions on the physical topology for routing logical rings in a survivable manner.