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Stable scheduling policies for fading wireless channels
 IEEE/ACM Trans. Networking
, 2005
"... We study the problem of stable scheduling for a class of wireless networks. The goal is to stabilize the queues holding information to be transmitted over a fading channel. Few assumptions are made on the arrival process statistics other than the assumption that their mean values lie within the capa ..."
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Cited by 132 (38 self)
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We study the problem of stable scheduling for a class of wireless networks. The goal is to stabilize the queues holding information to be transmitted over a fading channel. Few assumptions are made on the arrival process statistics other than the assumption that their mean values lie within the capacity region and that they satisfy a version of the law of large numbers. We prove that, for any mean arrival rate that lies in the capacity region, the queues will be stable under our policy. Moreover, we show that it is easy to incorporate imperfect queue length information and other approximations that can simplify the implementation of our policy. 1
Local Search Scheduling Algorithms for Maximal Throughput In . . .
, 2004
"... We consider the (generalized) packet switch scheduling problem, where the switch service configuration has to be dynamically chosen based on observed queue backlogs, so as to maximize the throughput. A class of recently developed `projective' scheduling algorithms, which substantially generaliz ..."
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Cited by 21 (10 self)
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We consider the (generalized) packet switch scheduling problem, where the switch service configuration has to be dynamically chosen based on observed queue backlogs, so as to maximize the throughput. A class of recently developed `projective' scheduling algorithms, which substantially generalize the wellknown maximum weight matching (MWM) algorithms for crossbar switches, are explored from the perspective of complexity. The typically huge number of possible switch configurations that the scheduler has to consider in each timeslot has been previously observed to lead to an impractical computational requirement. We introduce
Projective Cone Schedules in Queueing Structures; Geometry of Packet Scheduling
 in Communication Network Switches. Conference Proceedings, Allerton Conference on Communication, Control and Computing
, 2002
"... We consider a processing system having several queues, where Xq is the workload in queue q. At any point in time, the system can be set to one of several service configurations, which form a set S. When the system is set to service configuration/vector S ∈ S, queue q receives service at rate Sq. It ..."
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Cited by 8 (5 self)
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We consider a processing system having several queues, where Xq is the workload in queue q. At any point in time, the system can be set to one of several service configurations, which form a set S. When the system is set to service configuration/vector S ∈ S, queue q receives service at rate Sq. It has been known [2, 3, 4] that – under very general traffic traces – the schedule, which chooses the service vector S maximizing the inner product 〈S, AX 〉 = � q SqαqXq when the workload vector is X, provides the highest possible throughput under any fixed diagonal matrix A = diag{αq} with positive entries. That is, it stabilizes the system under the maximum possible traffic load, for very general traffic traces. In this paper, the above result is substantially extended. It is shown that throughput maximization is achieved by any schedule, which chooses a service vector S ∈ S that maximizes the inner product
PROJECTIVE CONE SCHEDULING (PCS) ALGORITHMS FOR PACKET SWITCHES OF MAXIMAL THROUGHPUT
"... 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 id ..."
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Cited by 7 (6 self)
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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 throughputoptimal 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 positivedefinite, symmetric matrices with negative or zero offdiagonal elements. In contrast, positive offdiagonal 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 maximumweightmatching (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 timelag without compromising throughput. It enables asynchronous or delayed PCS implementations and various examples are discussed.
Efficient and Fair Scheduling for Wireless Networks
"... This dissertation addresses the problem of scheduling inelastic and elastic flows in multihop wireless networks. Schedulers, by setting the rules for transmission strategies, play a critical role in determining the performance of the network. Thus, a good understanding of schedulers is vital for th ..."
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Cited by 5 (4 self)
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This dissertation addresses the problem of scheduling inelastic and elastic flows in multihop wireless networks. Schedulers, by setting the rules for transmission strategies, play a critical role in determining the performance of the network. Thus, a good understanding of schedulers is vital for the design of high performance networks. Towards this goal, we start by studying the problem of stable scheduling for a class of cellular wireless networks. The goal is to stabilize the queues holding information to be transmitted over a fading channel. Few assumptions are made on the arrival process statistics other than the assumption that their mean values lie within the capacity region and that they satisfy a version of the law of large numbers. We prove that, for any mean arrival rate that lies in the capacity region, the queues are stable under the policy we propose. Moreover, we show that it is easy to incorporate imperfect queue length information and other approximations that simplify the implementation of our policy. Next, we focus on the performance of wellknown schedulers for serving delayconstrained traffic. In particular, we provide analytical as well as numerical analysis of Opportunistic and
Dynamic quality of service control in packet switch scheduling
 In Proceedings of IEEE International Conference on Communications
, 2005
"... Abstract — Recent research in packet switch scheduling algorithms has moved beyond throughput maximization to quality of service (QoS) control. Several classes of algorithms have been shown to achieve maximal throughput under certain system conditions. Between classes and within each class, QoS perf ..."
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Cited by 3 (0 self)
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Abstract — Recent research in packet switch scheduling algorithms has moved beyond throughput maximization to quality of service (QoS) control. Several classes of algorithms have been shown to achieve maximal throughput under certain system conditions. Between classes and within each class, QoS performance varies based on arrival traffic and properties of the scheduling algorithm being utilized. Here we compare two classes of throughputmaximizing algorithms and their performance with respect to buffer sizes. These classes are randomized algorithms, which can be characterized as offline algorithms, and projective cone scheduling algorithms, which are online since they respond to the current workload in the system. In each class, parameters can be finetuned to reflect the priorities of individual switch ports. We show how the online algorithms lead to significantly better quality of service performance. I.
CONE SCHEDULES FOR PROCESSING SYSTEMS IN RANDOM ENVIRONMENTS
"... We consider a generalized processing system having several queues, where Xq is the workload in queue q. The resources for serving the queues are fluctuating over time due to reliability and availability variations, and the objective is to allocate the resources (and corresponding service rates) in r ..."
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We consider a generalized processing system having several queues, where Xq is the workload in queue q. The resources for serving the queues are fluctuating over time due to reliability and availability variations, and the objective is to allocate the resources (and corresponding service rates) in response to both backlog and service capacity considerations. When the system is set to a service mode m (selected from the available ones), queue q receives service at rate Sm q. Positive values of Sm q correspond to actual service (flow out of the queue), while negative values correspond to forwarded workload (flow into the queue). It has been known [20] that in a timeslotted processing system when there is a fixed resource set and no forwarding is allowed, the schedule which chooses the service mode m maximizing the inner product 〈Sm, BX 〉 = ∑ ∑ p q Sm p BpqXq for workload vector is X, provides the highest possible throughput under any fixed matrix B = {Bpq} that is positivedefinite, has negative or zero offdiagonal elements, and is symmetric. That is, it stabilizes the system under the maximum possible traffic load, for very general traffic traces. These are called Cone Schedules and leverage the ‘geometry ’ associated with
Geometry of Packet Switching: Maximal Throughput Cone Scheduling Algorithms
"... In this chapter, we discuss the key ideas underlying some recent developments in packet switching. They concern algorithms for scheduling packets through switching fabrics, primarily to maximize throughput and support differentiated quality of service. We first develop a model capturing the packet q ..."
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In this chapter, we discuss the key ideas underlying some recent developments in packet switching. They concern algorithms for scheduling packets through switching fabrics, primarily to maximize throughput and support differentiated quality of service. We first develop a model capturing the packet queueing and scheduling dynamics of the switch in a ‘vectorized’ framework, which allows for the rich geometry of the switching problem to emerge. We then present a class of algorithms that dynamically schedule packets for transfer through the switching fabric, based on which conic space the packet backlog vector resides. Appropriate construction of the cones leads to maximum throughput. Cone algorithms subsume the well known ‘maximum weight matching’ ones for packet switching as a special case. We discuss various aspect of cone algorithms including robustness, scalability, throughput and quality of service support.