718 research outputs found
Stable Scheduling Policies for Maximizing Throughput in Generalized Constrained Queueing Systems
We consider a class of queueing networks referred to as generalized constrained queueing networks which form the basis of several different communication networks and information systems. These networks consist of a collection of queues such that only certain sets of queues can be concurrently served. Whenever a queue is served, the system receives a certain reward. Different rewards are obtained for serving different queues, and furthermore, the reward obtained for serving a queue depends on the set of concurrently served queues. We demonstrate that the dependence of the rewards on the schedules alter fundamental relations between performance metrics like throughput and stability. Specifically, maximizing the throughput is no longer equivalent to maximizing the stability region; we therefore need to maximize one subject to certain constraints on the other. Since stability is critical for bounding packet delays and buffer overflow, we focus on maximizing the throughput subject to stabilizing the system. We design provably optimal scheduling strategies that attain this goal by scheduling the queues for service based on the queue lengths and the rewards provided by different selections. The proposed scheduling strategies are however computationally complex. We subsequently develop techniques to reduce the complexity and yet attain the same throughput and stability region. We demonstrate that our framework is general enough to accommodate random rewards and random scheduling constraints
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
Concave Switching in Single and Multihop Networks
Switched queueing networks model wireless networks, input queued switches and
numerous other networked communications systems. For single-hop networks, we
consider a {()-switch policy} which combines the MaxWeight policies
with bandwidth sharing networks -- a further well studied model of Internet
congestion. We prove the maximum stability property for this class of
randomized policies. Thus these policies have the same first order behavior as
the MaxWeight policies. However, for multihop networks some of these
generalized polices address a number of critical weakness of the
MaxWeight/BackPressure policies.
For multihop networks with fixed routing, we consider the Proportional
Scheduler (or (1,log)-policy). In this setting, the BackPressure policy is
maximum stable, but must maintain a queue for every route-destination, which
typically grows rapidly with a network's size. However, this proportionally
fair policy only needs to maintain a queue for each outgoing link, which is
typically bounded in number. As is common with Internet routing, by maintaining
per-link queueing each node only needs to know the next hop for each packet and
not its entire route. Further, in contrast to BackPressure, the Proportional
Scheduler does not compare downstream queue lengths to determine weights, only
local link information is required. This leads to greater potential for
decomposed implementations of the policy. Through a reduction argument and an
entropy argument, we demonstrate that, whilst maintaining substantially less
queueing overhead, the Proportional Scheduler achieves maximum throughput
stability.Comment: 28 page
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
Throughput-Optimal Multihop Broadcast on Directed Acyclic Wireless Networks
We study the problem of efficiently broadcasting packets in multi-hop
wireless networks. At each time slot the network controller activates a set of
non-interfering links and forwards selected copies of packets on each activated
link. A packet is considered jointly received only when all nodes in the
network have obtained a copy of it. The maximum rate of jointly received
packets is referred to as the broadcast capacity of the network. Existing
policies achieve the broadcast capacity by balancing traffic over a set of
spanning trees, which are difficult to maintain in a large and time-varying
wireless network. We propose a new dynamic algorithm that achieves the
broadcast capacity when the underlying network topology is a directed acyclic
graph (DAG). This algorithm is decentralized, utilizes local queue-length
information only and does not require the use of global topological structures
such as spanning trees. The principal technical challenge inherent in the
problem is the absence of work-conservation principle due to the duplication of
packets, which renders traditional queuing modelling inapplicable. We overcome
this difficulty by studying relative packet deficits and imposing in-order
delivery constraints to every node in the network. Although in-order packet
delivery, in general, leads to degraded throughput in graphs with cycles, we
show that it is throughput optimal in DAGs and can be exploited to simplify the
design and analysis of optimal algorithms. Our characterization leads to a
polynomial time algorithm for computing the broadcast capacity of any wireless
DAG under the primary interference constraints. Additionally, we propose an
extension of our algorithm which can be effectively used for broadcasting in
any network with arbitrary topology
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