We consider scheduling strategies for multiantenna and multibeam cellular wireless systems for high-speed packet data services on the downlink. We establish a fundamental connection between the stability region of the queuing system and the set of feasible transmission rates, which provides the basis for the scheduling algorithm proposed in this paper. Transmission using adaptive steerable beams and fixed sector beams are considered and average delay versus throughput results are obtained through simulations for the proposed scheduling scheme in each case. While in single antenna systems multiuser diversity gains are achieved by the scheduling algorithms that transmit to a single user in each scheduling interval, our results show that with multiple antennas, transmitting to a carefully chosen subset of users has superior performance. The multiantenna scheduling problem is closely related to the problem of coordinated scheduling for transmission through multiple base stations, where a user can receive signals from several base stations simultaneously. We consider the special case when three single-antenna base stations are allowed to cooperate and transmit to the users in the triangular region between the base stations and propose scheduling strategies that demonstrate significant gains.

We formulate and analyze the problem of optimal downlink scheduling with instantaneous channel and queue size information when both power and bandwidth may be adaptively split among multiple users. We derive optimal solutions of low computational complexity, as well as faster and simpler approximations, to various versions of this problem when the power, rate, and bandwidth allocations to the users can all take continuous values. For this case, we show that the optimal scheme requires transmission to no more than two users during each time slot when users can receive at arbitrary rates, even when the user rate per unit of bandwidth is upper bounded by the best available modulation scheme. Our methods also extend easily to incorporate other intuitive constraints such as upper limits on user rates to improve frame fill efficiency. Simulation results suggest that the simple approximations work nearly as well as the throughput optimal schemes when continuous bandwidth and power partitions are allowed. In practice, the rate and bandwidth assignments to users take discrete values, and we present heuristic methods motivated by the continuous optimum to this discrete case.

We present the optimal solution to the problem of allocating bandwidth and power across users for downlink transmission in wireless systems when multiple users can be scheduled for transmission simultaneously. We include maximum and minimum rate per user constraints and a maximum rate per unit bandwidth constraint in the formulation. When only the constraint of a maximum rate per unit bandwidth is imposed we show that scheduling at most two users simultaneously is sufficient for optimality.

Uplink scheduling in wireless systems is gaining importance due to arising uplink intensive data services (ftp, image uploads etc.), which could be hampered by the currently in-built asymmetry in favor of the downlink. In this work, we propose and study algorithms for efficient uplink packet-data scheduling in a CDMA cell. The algorithms attempt to maximize system throughput under transmit power limitations on the mobiles assuming instantaneous knowledge of user queues and channels. However no channel statistics or traffic characterization is necessary. Apart from increasing throughput, the algorithms also improve fairness of service among users, hence reducing chances of buffer overflows for poorly located users. The major observation arising from our analysis is that it is advantageous on the uplink to schedule "strong" users one-at-a-time, and "weak" users in larger groups. This contrasts with the downlink where one-at-a-time transmission for all users has shown to be the preferred mode in much previous work. Based on the optimal schedules, we propose less complex and more practical approximate methods, both of which offer significant performance improvement compared to one-at-a-time transmission, and the widely acclaimed Proportional Fair (PF) algorithm, in simulations. When queue content cannot be fed back, we propose a simple modification of PF, Uplink PF (UPF), that offers similar improvement.

Uplink scheduling in wireless systems is gaining importance due to arising uplink intensive data services, which could be hampered by the currently in-built asymmetry in favor of the downlink. In prior work, (K. Kumaran and L. Qian, 2002, Apr. 2003), we proposed optimal algorithms for uplink scheduling in a CDMA cell that does not employ any form of interference cancellation. In this work, we modify the approach to incorporate successive interference cancellation (SIC), which has been shown to be optimal in an information theoretic sense (G. Caire and S. Shamai, 2000). As in K. Kumaran and L. Qian ( 2002, Apr. 2003), no statistical assumptions are made about channel or traffic behavior, but feedback to communicate current channel state and queue state is assumed. Our results demonstrate that the throughput optimal scheduling strategy takes a particularly simple form with SIC as compared to without, (K. Kumaran and L. Qian, 2002, Apr. 2003), apart from providing some level of performance improvement. A reasonable alternative algorithm based purely on received power can be constructed based on early work on SIC (P. Patel and J. Holtzman, June 1994). Considering decoding errors, only strongly received users can benefit from SIC. Our simulation experiments suggest that our throughput optimal scheduling improves performance over the alternative when users have similar received power. Combining the above observation, we also propose a hybrid scheduling algorithm that performs SIC for strong users and simultaneous transmission for weak users.

A time-domain wavelength interleaved network (TWIN) (Widjaja, I. et al., IEEE Commun. Mag., vol.41, 2003) is an optical network with an ultrafast tunable laser and a fixed receiver at each node. We consider the problem of scheduling bursts of data in a TWIN. Due to the high data rates employed on the optical links, the burst transmissions typically last for very short times compared with the round trip propagation times between source-destination pairs. A good schedule should ensure that: 1) there are no transmit/receive conflicts; 2) propagation delays are observed; 3) throughput is maximized (schedule length is minimized). We formulate the scheduling problem with periodic demand as a generalization of the well-known crossbar switch scheduling. We prove that even in the presence of propagation delays, there exist a class of computationally viable scheduling algorithms which asymptotically achieve the maximum throughput obtainable without propagation delays. We also show that any schedule can be rearranged to achieve a factor-two approximation of the maximum throughput even without asymptotic limits. However, the delay/throughput performance of these schedules is limited in practice. We consequently propose a scheduling algorithm that exhibits near optimal (on average within ∼7% of optimum) delay/throughput performance in realistic network examples.

Large-scale location, sizing and homing problems of distributed network elements, have received much attention recently due to the massive deployment of broadband communication networks for services like Internet telephony and Web caching. Key considerations in designing these networks include modularity of capacity, economies of scale in cost, and reliability. We formulate a general class of such network design problems as Mixed-Integer Programs. These problems are computationally intractable in general; under various asymptotic conditions, we show how to compute near-optimal solutions. To deal with arbitrary instances, we develop new algorithms based on linear programming, as well as greedy randomized adaptive search. These algorithms achieved near-optimal solutions with reasonable computation time for our experiments.

The main network solutions for supporting QoS rely on traffic policing (conditioning, shaping). In particular, for IP networks the IETF has developed Intserv (individual flows regulated) and Diffserv (only aggregates regulated). The regulator proposed could be based on the (dual) leaky-bucket mechanism. This explains the interest in network element performance (loss, delay) for leaky-bucket regulated traffic. This paper describes a novel approach to the above problem. Explicitly using the correlation structure of the sources' traffic, we derive approximations for both small and large buffers. Importantly, for small (large) buffers the short-term (long-term) correlations are dominant. The large buffer result decomposes the traffic stream in a stream of constant rate and a periodic impulse stream, allowing direct application of the Brownian bridge approximation. Combining the small and large buffer results by a concave majorization, we propose a simple, fast and accurate technique to statistically multiplex homogeneous regulated sources. To address heterogeneous inputs, we present similarly efficient techniques to evaluate the performance of multiple classes of traffic, each with distinct characteristics and QoS requirements. These techniques, applicable under more general conditions, are based on optimal resource (bandwidth and buffer) partitioning. They can also be directly applied to set GPS (generalized processor sharing) weights and buffer thresholds in a shared resource system.

Generalized processor sharing (GPS) is a scheduling discipline which provides minimum service guarantees as well as fair resource sharing. The performance of GPS is governed by the scheduling weights associated with individual connections. We address the design of the GPS weights, along with the related connection admission control (CAC). Our main goal is to achieve statistical multiplexing gains in the presence of multiple traffic and quality-of-service (QoS) classes of connections that share a common trunk. We present novel techniques to compute and adapt the weights. We also characterize the capacity region of the system, and propose a natural CAC procedure. Numerical results on 2-class and 3-class examples demonstrate the effectiveness of our methods.

We present an approach for efficient design of a signaling network for a network of software switches supporting Internet telephony. While one may take an integer programming approach to solve this problem, it quickly becomes intractable even for modest-sized networks. Instead, our topology design uses random graphs that we show to be nearly optimal in cost, highly connected, and computationally efficient even for large networks. We then formulate a quadratic assignment problem (QAP) to map the abstract topology into the physical network to achieve optimal load balancing for given demand forecasts, which we solve using randomized heuristics. Numerical results on several example networks illustrate the performance and computational efficiency of our method. A graphical design tool has been developed based on our algorithms.

We have been developing a stochastic model for figure-ground separation. The model selects/constructs the foreground with preference for figures with “more convex” shapes. When these models are applied to illusory figures they yield perceptually accurate selection of figure and background. The approach is based on an “entropy” measure of a region diffusion Markov model from a set of local figure/ground hypothesis. The contour boundaries are implicitly represented, via the thresholding of the diffusion result. What optimal properties do the illusory contours satisfies? We show that the entropy criteria selects contours such as to minimize a Taylor series of the even derivatives with respect to the length of the contour. The coefficients are positive and they get exponentially smaller as the derivatives increase. The zeroth order term suggest that small length contours are preferred, the second order terms suggests that curvature-like term is minimized (with less strength compared to the zero order one), and higher order derivatives give additional contour smoothness constraints.

We consider the problem of scheduling packets in an input-queued switch when both unicast and multicast traffic is present. In contrast to current approaches which mostly isolate unicast from multicast, we propose an integrated scheduling procedure that packs unicast cells into idle slots left by the multicast schedule. While the optimal integrated schedule can be shown to be NP-hard to obtain, we propose both off-line and on-line algorithms with strong theoretical guarantees to perform integration efficiently, Simulations suggest significant improvement in switch throughput using the integrated schedule. To further reinforce the importance of performing integration, we study the multicast scheduling problem with and without fanout splitting. Again, we prove hardness of the problem and several of its variants, and propose competitive algorithms. The hardness of multicast scheduling hence emphasizes the importance of integrated scheduling for switch performance.

We study the design and performance of underlay-overlay (U-O) wireless networks, which promise capacity gains over conventional fixed-reuse cellular networks. To address the two principal problems in U-O networks, namely, (a). Where are the underlay boundaries to be placed? (b). How are the channels to be allocated? we propose an optimization procedure and a traffic model respectively. Our objective is to match spectrum allocated to the underlay to absorption (proportion of underlay traffic), subject to statistical interference constraints. Numerical results demonstrate the effectiveness of our design procedure and suggest substantial capacity gains from U-O networks.

We address the problem of estimating the spectrum required in a wireless network for a given demand and interference pattern. This problem can be abstracted as a generalization of the graph coloring problem, which typically presents additional degree of hardness compared to the standard coloring problem. It is worthwhile to note that the question of estimating the spectrum requirement differs markedly from that of allocating channels. The main focus of this work is to obtain strong upper and lower bounds on the spectrum requirement, as opposed to the study of spectrum allocation/management. While the relation to graph coloring establishes the intractability of the spectrum estimation problem for arbitrary network topologies, useful bounds and algorithms are obtainable for specific topologies. We establish some new results regarding generalized coloring, which we use to derive tight bounds for specific families of graphs. We also examine the hexagonal grid topology, a commonly used topology for wireless networks. We design efficient algorithms that exploit the geometric structure of the hexagonal grid topology to determine upper bounds on the spectrum requirement for arbitrary demand patterns. The slack in our upper bounds is estimated by analyzing subgraphs with specific properties. While we consider the worst-case demand patterns to evaluate the performance of our algorithms, we expect them to perform much better in practice.

We consider a switching system which has multiple ports that share a common buffer, in which there is a FIFO logical queue for each port. Each port may support a large number of flows or connections, which are approximately homogeneous in their statistical characteristics, with common QoS requirements in cell loss and maximum delay. Heterogeneity may exist across ports. Our first contribution is a buffer management scheme based on buffer admission control, which is integrated with connection admission control at the switch, and is at the same time fair, efficient and robust in sharing the buffer resources across ports. Our scheme is based on the resource-sharing technique of virtual partitioning. Our second major contribution is to advance the practice of discrete-event fluid simulations. Such simulations are approximations to cell-level simulations and offer orders of magnitude speed-up. A third contribution of the paper is the formulation and solution of a problem of optimal allocation of bandwidth and buffers to each port having specific delay bounds, in a lossless multiplexing framework. Finally, we report on extensive simulation results. The scheme is found to be effective, efficient and robust.

We describe the simulation of a new dynamic channel assignment algorithm in FDMA/TDMA wireless networks. The algorithm relies on periodic interference measurements by each of the base stations on the inactive frequencies, so as to identify appropriate candidate channels. The adaptive nature provides automatic configuration at the time of system initialization and adaptation to system expansion and traffic patterns with spatial or temporal variations. By eliminating the manual frequency planning process inherent to today's fixed channel assignment procedures, the self-organizing capability guarantees ease of operation for service providers, while increasing both capacity and voice quality. Our simulation experiments demonstrate stability of the algorithm and confirm its self-organizing capability. They also indicate a significant decrease of call blocking and dropping and other quality-of-service improvements.

A common factor in all illusory contour figures is the perception of a surface occluding part of a background. In our previous work, we have shown we could diffuse a proper set of junction hypothesis (what is salient or background) to obtain a surface where their boundaries represented illusory contours. Amodal completions emerge at the overlapping surfaces. We address the problem of selecting the best image organization (set of hypothesis). We propose an optimization criteria based on a coherence measure between pairs of junctions (correlation between the diffusion of each pair). A statistical physics approach to select the best organization is applied. The experiments suggest that despite the large number of possible organizations our approach may take only a few steps (in organization space) to select the best one.