Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
Queueing Dynamics and Maximal Throughput Scheduling in Switched Processing Systems
Queueing Systems: Theory and Applications
Maximum Pressure Policies in Stochastic Processing Networks
Operations Research
On the stability of isolated and interconnected input-queueing switches under multiclass traffic
IEEE Transactions on Information Theory
Randomized scheduling algorithms for high-aggregate bandwidth switches
IEEE Journal on Selected Areas in Communications
On the stability of local scheduling policies in networks of packet switches with input queues
IEEE Journal on Selected Areas in Communications
Dynamic power allocation and routing for time-varying wireless networks
IEEE Journal on Selected Areas in Communications
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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.