We consider the problem of scheduling bursts of data in an optical network with an ultrafast tunable laser and a fixed receiver at each node. 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; and 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.

Abstract-We study the (generalized) packet switch scheduling problem, where service configurations are dynamically chosen in response to queue backlogs, so as to maximize the throughput without any knowledge of the long term traffic load. Service configurations and traffic traces are arbitrary.First, we identify a rich class of throughput-optimal linear controls, which choose the service configuration S maximizing the projection S, BX when the backlog is X. The matrix B is arbitrarily fixed in the class of positive-definite, symmetric matrices with negative or zero off-diagonal elements. In contrast, positive off-diagonal elements may drive the system unstable, even for subcritical loads. The associated rich Euclidian geometry of projective cones is explored (hence the name projective cone scheduling PCS). The maximum-weight-matching (MWM) rule is seen to be a special case, where B is the identity matrix.Second, we extend the class of throughput maximizing controls by identifying a tracking condition which allows applying PCS with any bounded time-lag without compromising throughput. It enables asynchronous or delayed PCS implementations and various examples are discussed.

I n many call centers, agents are trained to handle all arriving calls but exhibit very different performance for the same call type, where we define performance by both the average call handling time and the call resolution probability. In this paper, we explore strategies for determining which calls should be handled by which agents, where these assignments are dynamically determined based on the specific attributes of the agents and/or the current state of the system. We test several routing strategies using data obtained from a medium-sized financial service firm's customer service call centers and present empirical performance results. These results allow us to characterize overall performance in terms of customer waiting time and overall resolution rate, identifying an efficient frontier of routing rules for this contact center.

Optimal scheduling of air traffic over the entire National Airspace System is a computationally difficult task. In this paper, Dantzig-Wolfe decomposition is applied to a linear integer programming approach for assigning delays to flights. The optimization model is proven to have the block-angular structure necessary for Dantzig-Wolfe decomposition. The subproblems for this decomposition are solved in parallel via independent computation threads. Experimental evidence presented here suggests that as the number of subproblems/threads increases (and their respective sizes decrease), the solution quality, convergence, and runtime improve. A demonstration of this is provided by using one flight per subproblem, which is the finest possible decomposition. This results in thousands of subproblems and associated computation threads. This massively parallel approach is compared to one with few threads and to standard (non-decomposed) approaches in terms of solution quality and runtime. Since this method generally provides a non-integral (relaxed) solution to the original optimization problem, two heuristics are developed to generate an integral solution. Dantzig-Wolfe followed by these heuristics can provide a near-optimal (sometimes optimal) solution to the original problem hundreds of times faster than standard (non-decomposed) approaches. In addition, when massive decomposition is employed, the solution is shown to be more likely integral, which obviates the need for an integerization step. These results indicate that nationwide, real-time, high fidelity, optimal traffic flow scheduling is achievable for (at least) 3 hour planning horizons.

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