The US equity exchange market is organized as a National Market System, enforcing price priority across exchanges, but otherwise allowing competition for order flow among exchanges. This flexibility has naturally evolved to a market where exchanges have varying quality and cost of execution. To meet the obligation for best execution, a broker must employ a strategy for selecting the exchange to which limit orders are placed. We consider a market consisting of exchanges with different pricing and priority schemes, and derive a theoretical model to estimate the delay until execution of limit orders. We estimate model parameters from quote and trade data of stocks in the Russell 1000 index, and use them to evaluate expected delay per exchange. We show that inverted cost exchanges and price-size priority exchanges offer improved performance over short time intervals, while traditional and price-time priority exchanges offer improved performance over longer time intervals. We observe that while exchanges with large market share may have high market order liquidity, they may in fact have low limit order liquidity. Low limit order liquidity in turn leads to low execution quality of algorithmic orders. For time-sensitive algorithmic orders, we show a trade-off between execution quality and cost, and show exchanges on an efficient frontier for each stock that achieves good trade-off performance given current exchange pricing.

Efficient operation of wireless networks requires distributed routing and scheduling algorithms that take into account interference constraints. Recently, a few algorithms for networks with primary- or secondary-interference constraints have been developed. Due to their distributed operation, these algorithms can achieve only a guaranteed fraction of the maximum possible throughput. It was also recently shown that if a set of conditions (known as Local Pooling) is satisfied, simple distributed scheduling algorithms achieve 100% throughput. However, previous work regarding Local Pooling focused mostly on obtaining abstract conditions and on networks with single-hop interference or single-hop traffic. In this paper, we identify several graph classes that satisfy the Local Pooling conditions, thereby enabling the use of such graphs in network design algorithms. Then, we study the multihop implications of Local Pooling. We show that in many cases, as the interference degree increases, the Local Pooling conditions are more likely to hold. Consequently, although increased interference reduces the maximum achievable throughput of the network, it tends to enable distributed algorithms to achieve 100% of this throughput. Regarding multihop traffic, we show that if the network satisfies only the single-hop Local Pooling conditions, distributed joint routing and scheduling algorithms are not guaranteed to achieve maximum throughput. Therefore, we present new conditions for Multihop Local Pooling, under which distributed algorithms achieve 100% throughout. Finally, we identify network topologies in which the conditions hold and discuss the algorithmic implications of the results.

We study the maximum throughput properties of dynamically reconfigurable optical networks having wavelength and port constraints. Using stability as the throughput performance metric, we outline the single-hop and multi-hop stability regions of the network. We describe throughput-optimal dynamic algorithms employing joint WDM reconfiguration and electronic layer routing decisions. Our approach is a generalization of the BvN decomposition technique that has been so effective at expressing any stabilizable rate matrix for input-queued switches as a convex combination of service configurations. We consider generalized decompositions for physical topologies with wavelength and port constraints. For the case of a single wavelength per optical fiber, we link the decomposition problem to a corresponding Routing and Wavelength Assignment (RWA) problem. We characterize the stability region of the reconfigurable network, employing both single-hop and multi- hop routing, in terms of the RWA problem applied to the same physical topology. We derive expressions for two geometric properties of the stability region: maximum stabilizable uniform arrival rate, and maximum scaled doubly substochastic region. These geometric properties provide a measure of the performance gap between a network having a single wavelength per optical fiber and its wavelength-unconstrained version. They also provide a measure of the performance gap between algorithms employing single-hop versus multi-hop electronic routing.

This paper considers the interaction between channel assignment and distributed scheduling in multi-channel multiradio Wireless Mesh Networks (WMNs). Recently, a number of distributed scheduling algorithms for wireless networks have emerged. Due to their distributed operation, these algorithms can achieve only a fraction of the maximum possible throughput. As an alternative to increasing the throughput fraction by designing new algorithms, in this paper we present a novel approach that takes advantage of the inherent multi-radio capability of WMNs. We show that this capability can enable partitioning of the network into subnetworks in which simple distributed scheduling algorithms can achieve 100% throughput. The partitioning is based on the recently introduced notion of Local Pooling. Using this notion, we characterize topologies in which 100% throughput can be achieved distributedly. These topologies are used in order to develop a number of channel assignment algorithms that are based on a matroid intersection algorithm. These algorithms partition a network in a manner that not only expands the capacity regions of the subnetworks but also allows distributed algorithms to achieve these capacity regions. Finally, we evaluate the performance of the algorithms via simulation and show that they significantly increase the distributedly achievable capacity region.

We develop algorithms for joint IP layer routing and WDM logical topology reconfiguration in IP-over-WDM networks experiencing stochastic traffic. At the WDM layer, we associate a non-negligible tuning latency with WDM reconfiguration, during which time tuned transceivers cannot service backlogged data. The IP layer is modeled as a queueing system. We demonstrate that our algorithms achieve asymptotic throughput optimality by using frame-based maximum weight scheduling decisions. We study both deterministic and random frame durations. In addition to dynamically triggering WDM reconfiguration, our algorithms specify precisely how to route packets over the IP layer during the phases in which the WDM layer remains fixed. Our algorithms remain valid under a variety of optical layer constraints. We provide an analysis of the specific case of WDM networks with multiple ports per node. In order to gauge the delay properties of our algorithms, we conduct a simulation study and demonstrate an important tradeoff between WDM reconfiguration and IP layer routing. We find that multi-hop routing is extremely beneficial at low throughput levels, while single-hop routing achieves improved delay at high throughput levels. For a simple access network, we demonstrate through simulation the benefit of employing multi-hop IP layer routes.

In a wavelength-division multiplexed (WDM)-based network, a single physical link failure may correspond to multiple logical link failures. As a result, two-connected logical topologies, such as rings routed on a WDM physical topology, may become disconnected after a single physical link failure. We consider the design of physical topologies that ensure logical rings can be embedded in a survivable manner. This is of particular interest in metropolitan area networks, where logical rings are in practice almost exclusively employed for providing protection against link failures. First, we develop necessary conditions for the physical topology to be able to embed all logical rings in a survivable manner. We then use these conditions to provide tight bounds on the number of physical links that an N-node physical topology must have in order to support all logical rings for different sizes K. We show that when K/spl ges/4 the physical topology must have at least 4N/3 links, and that when K/spl ges/6 the physical topology must have at least 3N/2 links. Subsequently, we generalize this bound for all K/spl ges/4. When K/spl ges/N-2, we show that the physical topology must have at least 2N-4 links. Finally, we design physical topologies that meet the above bounds for both K=4 and K=N-2. Specifically, our physical topology for embedding (N-2)-node rings has a dual hub structure and is able to embed all rings of size less than N-1 in a survivable manner. We also provide a simple extension to this topology that addresses rings of size K=N-1 and rings of size K=N for N odd. We observe that designing the physical topology for supporting all logical rings in a survivable manner does not use significantly more physical links than a design that only supports a small number of logical rings. Hence, our approach of designing physical topologies that can be used to embed all possible ring logical topologies does not lead to a significant overdesign of the physical topology.

In a WDM-based network, a single physical link failure may correspond to multiple logical link failures. As a result, 2-connected logical topologies, such as rings routed on a WDM physical topology, may become disconnected after a single physical link failure. We consider the design of physical topologies that ensure logical rings can be embedded in a survivable manner. First, we develop necessary conditions on the physical topology to be able to embed all logical rings in a survivable manner. We then use these conditions to provide lower bounds on the number of physical links that an TV-node physical topology must have in order to support all logical rings for even sizes K. For example, we show that when K /spl ges/ 4 the physical topology must have at least 4N/3 links, and that when K /spl ges/ 6 the physical topology must have at least 3N/2 links, and when K /spl ges/ 8 the physical topology must have at least 1.6N links. Furthermore, we show that for K /spl ges/ N - 2 the physical topology must have at least 2N - 4 links. Finally, we design a physical topology that meets the above bound for K = N - 2. We then modify this physical topology to embed rings of size K = N - 1 and K = N.