Dynamic Server Allocation over Time Varying Channels with Switchover Delay

We consider a dynamic server allocation problem over parallel queues with randomly varying connectivity and server switchover delay between the queues. At each time slot the server decides either to stay with the current queue or switch to another queue based on the current connectivity and the queue length information. Switchover delay occurs in many telecommunications applications and is a new modeling component of this problem that has not been previously addressed. We show that the simultaneous presence of randomly varying connectivity and switchover delay changes the system stability region and the structure of optimal policies. In the first part of the paper, we consider a system of two parallel queues, and develop a novel approach to explicitly characterize the stability region of the system using state-action frequencies which are stationary solutions to a Markov Decision Process (MDP) formulation. We then develop a frame-based dynamic control (FBDC) policy, based on the state-action frequencies, and show that it is throughput-optimal asymptotically in the frame length. The FBDC policy is applicable to a broad class of network control systems and provides a new framework for developing throughput-optimal network control policies using state-action frequencies. Furthermore, we develop simple Myopic policies that provably achieve more than 90% of the stability region. In the second part of the paper, we extend our results to systems with an arbitrary but finite number of queues.Comment: 38 Pages, 18 figures. arXiv admin note: substantial text overlap with arXiv:1008.234

Stability and Capacity Regions or Discrete Time Queueing Networks

We consider stability and network capacity in discrete time queueing systems. Relationships between four common notions of stability are described. Specifically, we consider rate stability, mean rate stability, steady state stability, and strong stability. We then consider networks of queues with random events and control actions that can be implemented over time to affect arrivals and service at the queues. The control actions also generate a vector of additional network attributes. We characterize the network capacity region, being the closure of the set of all rate vectors that can be supported subject to network stability and to additional time average attribute constraints. We show that (under mild technical assumptions) the capacity region is the same under all four stability definitions. Our capacity achievability proof uses the drift-plus-penalty method of Lyapunov optimization, and provides full details for the case when network states obey a decaying memory property, which holds for finite state ergodic systems and more general systems.Comment: 19 page

Structure-Aware Stochastic Control for Transmission Scheduling

In this paper, we consider the problem of real-time transmission scheduling over time-varying channels. We first formulate the transmission scheduling problem as a Markov decision process (MDP) and systematically unravel the structural properties (e.g. concavity in the state-value function and monotonicity in the optimal scheduling policy) exhibited by the optimal solutions. We then propose an online learning algorithm which preserves these structural properties and achieves -optimal solutions for an arbitrarily small . The advantages of the proposed online method are that: (i) it does not require a priori knowledge of the traffic arrival and channel statistics and (ii) it adaptively approximates the state-value functions using piece-wise linear functions and has low storage and computation complexity. We also extend the proposed low-complexity online learning solution to the prioritized data transmission. The simulation results demonstrate that the proposed method achieves significantly better utility (or delay)-energy trade-offs when comparing to existing state-of-art online optimization methods.Comment: 41page

Scheduling with Rate Adaptation under Incomplete Knowledge of Channel/Estimator Statistics

In time-varying wireless networks, the states of the communication channels are subject to random variations, and hence need to be estimated for efficient rate adaptation and scheduling. The estimation mechanism possesses inaccuracies that need to be tackled in a probabilistic framework. In this work, we study scheduling with rate adaptation in single-hop queueing networks under two levels of channel uncertainty: when the channel estimates are inaccurate but complete knowledge of the channel/estimator joint statistics is available at the scheduler; and when the knowledge of the joint statistics is incomplete. In the former case, we characterize the network stability region and show that a maximum-weight type scheduling policy is throughput-optimal. In the latter case, we propose a joint channel statistics learning - scheduling policy. With an associated trade-off in average packet delay and convergence time, the proposed policy has a stability region arbitrarily close to the stability region of the network under full knowledge of channel/estimator joint statistics.Comment: 48th Allerton Conference on Communication, Control, and Computing, Monticello, IL, Sept. 201

QPS-r: A Cost-Effective Crossbar Scheduling Algorithm and Its Stability and Delay Analysis

In an input-queued switch, a crossbar schedule, or a matching between the input ports and the output ports needs to be computed in each switching cycle, or time slot. Designing switching algorithms with very low computational complexity, that lead to high throughput and small delay is a challenging problem. There appears to be a fundamental tradeoff between the computational complexity of the switching algorithm and the resultants throughput and delay. Parallel maximal matching algorithms (adapted for switching) appear to have stricken a sweet spot in this tradeoff, and prior work has shown the following performance guarantees. Using maximal matchings in every time slot results in at least 50% switch throughput and order-optimal (i.e., independent of the switch size N) average delay bounds for various traffic arrival processes. On the other hand, their computational complexity can be as low as $O(log^2N)$ per port/processor, which is much lower than those of the algorithms such as maximum weighted matching which ensures better throughput performance. In this work, we propose QPS-r, a parallel iterative switching algorithm that has the lowest possible computational complexity: O(1) per port. Using Lyapunov stability analysis, we show that the throughput and delay performance is identical to that of maximal matching algorithm. Although QPS-r builds upon an existing technique called Queue-Proportional Sampling (QPS), in this paper, we provide analytical guarantees on its throughput and delay under i.i.d. traffic as well as a Markovian traffic model which can model many realistic traffic patterns. We also demonstrate that QPS-3 (running 3 iterations) has comparable empirical throughput and delay performances as iSLIP (running $log_2 N$ iterations), a refined and optimized representative maximal matching algorithm adapted for switching.Comment: 10 page

To Motivate Social Grouping in Wireless Networks

We consider a group of neighboring smartphone users who are roughly at the same time interested in the same network content, called common interests. However, ever-increasing data traffic challenges the limited capacity of base-stations (BSs) in wireless networks. To better utilize the limited BSs' resources under unreliable wireless networks, we propose local common-interests sharing (enabled by D2D communications) by motivating the physically neighboring users to form a social group. As users are selfish in practice, an incentive mechanism is needed to motivate social grouping. We propose a novel concept of equal-reciprocal incentive over broadcast communications, which fairly ensures that each pair of the users in the social group share the same amount of content with each other. As the equal-reciprocal incentive may restrict the amount of content shared among the users, we analyze the optimal equal-reciprocal scheme that maximizes local sharing content. While ensuring fairness among users, we show that this optimized scheme also maximizes each user's utility in the social group. Finally, we look at dynamic content arrivals and extend our scheme successfully by proposing novel on-line scheduling algorithms.Comment: 32 pages (single column), submitted for possible journal publicatio

Adaptive Policies for Scheduling with Reconfiguration Delay: An End-to-End Solution for All-Optical Data Centers

All-optical switching networks have been considered a promising candidate for the next generation data center networks thanks to its scalability in data bandwidth and power efficiency. However, the bufferless nature and the nonzero recon- figuration delay of optical switches remain great challenges in deploying all-optical networks. This paper considers the end-to- end scheduling for all-optical data center networks with no in- network buffer and nonzero reconfiguration delay. A framework is proposed to deal with the nonzero reconfiguration delay. The proposed approach constructs an adaptive variant of any given scheduling policy. It is shown that if a scheduling policy guarantees its schedules to have schedule weights close to the MaxWeight schedule (and thus is throughput optimal in the zero reconfiguration regime), then the throughput optimality is inherited by its adaptive variant (in any nonzero reconfiguration delay regime). As a corollary, a class of adaptive variants of the well known MaxWeight policy is shown to achieve throughput optimality without prior knowledge of the traffic load. Further- more, through numerical simulations, the simplest such policy, namely the Adaptive MaxWeight (AMW), is shown to exhibit better delay performance than all prior work

Characterization of the Burst Stabilization Protocol for the RR/RR CICQ Switch

Input buffered switches with Virtual Output Queueing (VOQ) can be unstable when presented with unbalanced loads. Existing scheduling algorithms, including iSLIP for Input Queued (IQ) switches and Round Robin (RR) for Combined Input and Crossbar Queued (CICQ) switches, exhibit instability for some schedulable loads. We investigate the use of a queue length threshold and bursting mechanism to achieve stability without requiring internal speed-up. An analytical model is developed to prove that the burst stabilization protocol achieves stability and to predict the minimum burst value needed as a function of offered load. The analytical model is shown to have very good agreement with simulation results. These results show the advantage of the RR/RR CICQ switch as a contender for the next generation of high-speed switches.Comment: Presented at the 28th Annual IEEE Conference on Local Computer Networks (LCN), Bonn/Konigswinter, Germany, Oct 20-24, 200

EUROPEAN CONFERENCE ON QUEUEING THEORY 2016

International audienceThis booklet contains the proceedings of the second European Conference in Queueing Theory (ECQT) that was held from the 18th to the 20th of July 2016 at the engineering school ENSEEIHT, Toulouse, France. ECQT is a biannual event where scientists and technicians in queueing theory and related areas get together to promote research, encourage interaction and exchange ideas. The spirit of the conference is to be a queueing event organized from within Europe, but open to participants from all over the world. The technical program of the 2016 edition consisted of 112 presentations organized in 29 sessions covering all trends in queueing theory, including the development of the theory, methodology advances, computational aspects and applications. Another exciting feature of ECQT2016 was the institution of the Takács Award for outstanding PhD thesis on "Queueing Theory and its Applications"