Stability and asymptotic optimality of generalized maxweight policies

Abstract It is shown that stability of the celebrated MaxWeight or back pressure policies is a consequence of the following interpretation: either policy is myopic with respect to a surrogate value function of a very special form, in which the "marginal disutility" at a buffer vanishes for vanishingly small buffer population. This observation motivates the h-MaxWeight policy, defined for a wide class of functions h. These policies share many of the attractive properties of the MaxWeight policy: (i) Arrival rate data is not required in the policy. (ii) Under a variety of general conditions, the policy is stabilizing when h is a perturbation of a monotone linear function, a monotone quadratic, or a monotone Lyapunov function for the fluid model. (iii) A perturbation of the relative value function for a workload relaxation gives rise to a myopic policy that is approximately average-cost optimal in heavy traffic, with logarithmic regret. The first results are obtained for a general Markovian network model. Asymptotic optimality is established for a general Markovian scheduling model with a single bottleneck, and homogeneous servers

Fairness in overloaded parallel queues

Maximizing throughput for heterogeneous parallel server queues has received quite a bit of attention from the research community and the stability region for such systems is well understood. However, many real-world systems have periods where they are temporarily overloaded. Under such scenarios, the unstable queues often starve limited resources. This work examines what happens during periods of temporary overload. Specifically, we look at how to fairly distribute stress. We explore the dynamics of the queue workloads under the MaxWeight scheduling policy during long periods of stress and discuss how to tune this policy in order to achieve a target fairness ratio across these workloads

Large deviations sum-queue optimality of a radial sum-rate monotone opportunistic scheduler

A centralized wireless system is considered that is serving a fixed set of users with time varying channel capacities. An opportunistic scheduling rule in this context selects a user (or users) to serve based on the current channel state and user queues. Unless the user traffic is symmetric and/or the underlying capacity region a polymatroid, little is known concerning how performance optimal schedulers should tradeoff "maximizing current service rate" (being opportunistic) versus "balancing unequal queues" (enhancing user-diversity to enable future high service rate opportunities). By contrast with currently proposed opportunistic schedulers, e.g., MaxWeight and Exp Rule, a radial sum-rate monotone (RSM) scheduler de-emphasizes queue-balancing in favor of greedily maximizing the system service rate as the queue-lengths are scaled up linearly. In this paper it is shown that an RSM opportunistic scheduler, p-Log Rule, is not only throughput-optimal, but also maximizes the asymptotic exponential decay rate of the sum-queue distribution for a two-queue system. The result complements existing optimality results for opportunistic scheduling and point to RSM schedulers as a good design choice given the need for robustness in wireless systems with both heterogeneity and high degree of uncertainty.Comment: Revised version. Major changes include addition of details/intermediate steps in various proofs, a summary of technical steps in Table 1, and correction of typos

Stable Wireless Network Control Under Service Constraints

We consider the design of wireless queueing network control policies with particular focus on combining stability with additional application-dependent requirements. Thereby, we consequently pursue a cost function based approach that provides the flexibility to incorporate constraints and requirements of particular services or applications. As typical examples of such requirements, we consider the reduction of buffer underflows in case of streaming traffic, and energy efficiency in networks of battery powered nodes. Compared to the classical throughput optimal control problem, such requirements significantly complicate the control problem. We provide easily verifyable theoretical conditions for stability, and, additionally, compare various candidate cost functions applied to wireless networks with streaming media traffic. Moreover, we demonstrate how the framework can be applied to the problem of energy efficient routing, and we demonstrate the aplication of our framework in cross-layer control problems for wireless multihop networks, using an advanced power control scheme for interference mitigation, based on successive convex approximation. In all scenarios, the performance of our control framework is evaluated using extensive numerical simulations.Comment: Accepted for publication in IEEE Transactions on Control of Network Systems. arXiv admin note: text overlap with arXiv:1208.297

On Asymptotic Optimality of Dual Scheduling Algorithm In A Generalized Switch

Generalized switch is a model of a queueing system where parallel servers are interdependent and have time-varying service capabilities. This paper considers the dual scheduling algorithm that uses rate control and queue-length based scheduling to allocate resources for a generalized switch. We consider a saturated system in which each user has infinite amount of data to be served. We prove the asymptotic optimality of the dual scheduling algorithm for such a system, which says that the vector of average service rates of the scheduling algorithm maximizes some aggregate concave utility functions. As the fairness objectives can be achieved by appropriately choosing utility functions, the asymptotic optimality establishes the fairness properties of the dual scheduling algorithm. The dual scheduling algorithm motivates a new architecture for scheduling, in which an additional queue is introduced to interface the user data queue and the time-varying server and to modulate the scheduling process, so as to achieve different performance objectives. Further research would include scheduling with Quality of Service guarantees with the dual scheduler, and its application and implementation in various versions of the generalized switch model