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47
Queueing and scheduling in random environments
 Adv. Appl. Prob
, 2004
"... We consider a processing system comprised of several parallel queues and a processor, which operates in a timevarying environment that fluctuates between various states or modes. The service rate at each queue depends on the processor bandwidth allocated to it, as well as the environment mode. Each ..."
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Cited by 19 (3 self)
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We consider a processing system comprised of several parallel queues and a processor, which operates in a timevarying environment that fluctuates between various states or modes. The service rate at each queue depends on the processor bandwidth allocated to it, as well as the environment mode. Each queue is driven by a job traffic flow, which may also depend on the environment mode. Dynamic processor scheduling policies are investigated for maximizing the system throughput, by adapting to queue backlogs and the environment mode. We show that allocating the processor bandwidth to the queues, so as to maximize the projection of the service rate vector to a linear function of the workload vector, can keep the system stable under the maximum possible traffic load. The analysis of the system dynamics is first done under very general assumptions, addressing rate stability and flow conservation on individual traffic and environment evolution traces. The connection to stochastic stability is later discussed for stationary and ergodic traffic and environment processes. Various extensions to feedforward networks of such nodes, the multiprocessor case, etc. are also discussed. The approach advances the methodology of tracebased modelling of queueing structures. Applications of the model include bandwidth allocation in wireless channels with fluctuating interference, allocation of switching bandwidth to traffic flows in communication networks with fluctuating congestion levels and various others.
Scheduling bursts in timedomain wavelength interleaved networks
 IEEE J. Select. Areas Commun
, 2003
"... Abstract—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 pr ..."
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Cited by 17 (5 self)
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Abstract—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 sourcedestination 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 wellknown 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 factortwo 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 U% of optimum) delay/throughput performance in realistic network examples. Index Terms—Birkhoffvon Neumann theorem, burst scheduling, constrained queueing systems, dynamic throughput
Flowlevel Stability of UtilityBased Allocations for NonConvex Rate Regions
, 2006
"... We investigate the stability of utilitymaximizing allocations in networks with arbitrary rate regions. We consider a dynamic setting where users randomly generate data flows according to some exogenous traffic processes. Network stability is then defined as the ergodicity of the process describing ..."
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Cited by 17 (1 self)
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We investigate the stability of utilitymaximizing allocations in networks with arbitrary rate regions. We consider a dynamic setting where users randomly generate data flows according to some exogenous traffic processes. Network stability is then defined as the ergodicity of the process describing the number of active flows. When the rate region is convex, the stability region is known to coincide with the rate region, independently of the considered utility function. We show that for nonconvex rate regions, the choice of the utility function is crucial to ensure maximum stability. The results are illustrated on the simple case of a wireless network consisting of two interacting base stations.
Distributed fair resource allocation in cellular networks in the presence of heterogeneous delays
 In Proceedings of International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOPT
, 2005
"... We consider the problem of allocating resources at a base station to many competing flows, where each flow is intended for a different receiver. The channel conditions may be timevarying and different for different receivers. It has been shown in [6] that in a delayfree network, a combination of q ..."
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Cited by 14 (8 self)
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We consider the problem of allocating resources at a base station to many competing flows, where each flow is intended for a different receiver. The channel conditions may be timevarying and different for different receivers. It has been shown in [6] that in a delayfree network, a combination of queuelengthbased scheduling at the base station and congestion control at the end users can guarantee queuelength stability and fair resource allocation. In this paper, we extend this result to wireless networks where the congestion information from the base station is received with a feedback delay at the transmitters. The delays can be heterogenous (i.e., different users may have different roundtrip delays) and timevarying, but are assumed to be upperbounded, with possibly very large upper bounds. We will show that the joint congestion controlscheduling algorithm continues to be stable and continues to provide a fair allocation of the network resources. 1
Stochastic Network Utility Maximization A tribute to Kelly’s paper published in this journal a decade ago
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Network Coding in a Multicast Switch
 in Proceedings of IEEE Infocom, 2007
"... Abstract—We consider the problem of serving multicast flows in a crossbar switch. We show that linear network coding across packets of a flow can sustain traffic patterns that cannot be served if network coding were not allowed. Thus, network coding leads to a larger rate region in a multicast cross ..."
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Cited by 11 (6 self)
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Abstract—We consider the problem of serving multicast flows in a crossbar switch. We show that linear network coding across packets of a flow can sustain traffic patterns that cannot be served if network coding were not allowed. Thus, network coding leads to a larger rate region in a multicast crossbar switch. We demonstrate a traffic pattern which requires a switch speedup if coding is not allowed, whereas, with coding the speedup requirement is eliminated completely. In addition to throughput benefits, coding simplifies the characterization of the rate region. We give a graphtheoretic characterization of the rate region with fanout splitting and intraflow coding, in terms of the stable set polytope of the “enhanced conflict graph ” of the traffic pattern. Such a formulation is not known in the case of fanout splitting without coding. We show that computing the offline schedule (i.e. using prior knowledge of the flow arrival rates) can be reduced to certain graph coloring problems. Finally, we propose online algorithms (i.e. using only the current queue occupancy information) for multicast scheduling based on our graphtheoretic formulation. In particular, we show that a maximum weighted stable set algorithm stabilizes the queues for all rates within the rate region. I.
Projective Processing Schedules in Queueing Structures; Applications to Packet Scheduling in Communication Network Switches
 ENGINEERING LIBRARY, STANFORD UNIVERSITY
, 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. I ..."
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Cited by 9 (6 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 [1, 2, 3] 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 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.
Dynamic Scheduling of Optical Data Bursts in TimeDomain Wavelength Interleaved Networks
"... 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. In [10] we considered the static scheduling problem of meeting demand in the minimal time. Here we substantially extend these results to the case of online, ..."
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Cited by 6 (2 self)
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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. In [10] we considered the static scheduling problem of meeting demand in the minimal time. Here we substantially extend these results to the case of online, dynamic scheduling. Due to the high data rates employed on the optical links, the burst transmissions typically last for very short times compared to the round trip propagation times between sourcedestination pairs. A good schedule ensures that (i) there are no transmit/receive conflicts, (ii) throughput is maximized, and (iii) propagation delays are observed. We formulate the scheduling problem as a generalization of the wellknown crossbar switch scheduling problem. We show that the algorithms presented in [10] can be implemented in dynamic form to give 100% throughput. Further, we show that one of the more intuitive solutions does not lead to maximal throughput. In particular, we show advantages of adaptive batch sizes rather than fixed batch sizes for both throughput and performance. 1