2,178 research outputs found
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
Delay Optimal Server Assignment to Symmetric Parallel Queues with Random Connectivities
In this paper, we investigate the problem of assignment of identical
servers to a set of parallel queues in a time slotted queueing system. The
connectivity of each queue to each server is randomly changing with time; each
server can serve at most one queue and each queue can be served by at most one
server per time slot. Such queueing systems were widely applied in modeling the
scheduling (or resource allocation) problem in wireless networks. It has been
previously proven that Maximum Weighted Matching (MWM) is a throughput optimal
server assignment policy for such queueing systems. In this paper, we prove
that for a symmetric system with i.i.d. Bernoulli packet arrivals and
connectivities, MWM minimizes, in stochastic ordering sense, a broad range of
cost functions of the queue lengths including total queue occupancy (or
equivalently average queueing delay).Comment: 6 pages, 4 figures, Proc. IEEE CDC-ECC 201
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
Variable frame based Max-Weight algorithms for networks with switchover delay
This paper considers the scheduling problem for networks with interference constraints and switchover delays, where it takes a nonzero time to reconfigure each service schedule. Switchover delay occurs in many telecommunication applications such as satellite, optical or delay tolerant networks (DTNs). Under zero switchover delay it is well known that the Max-Weight algorithm is throughput-optimal without requiring knowledge of the arrival rates. However, we show that this property of Max-Weight no longer holds when there is a nonzero switchover delay. We propose a class of variable frame based Max-Weight (VFMW) algorithms which employ the Max-Weight schedule corresponding to the beginning of the frame during an interval of duration dependent on the queue sizes. The VFMW algorithms dynamically adapt the frame sizes to the stochastic arrivals and provide throughput-optimality without requiring knowledge of the arrival rates. Numerical results regarding the application of the VFMW algorithms to DTN and optical networks demonstrate a good delay performance.National Science Foundation (U.S.) (NSF grant CNS-0626781)National Science Foundation (U.S.) (NSF grant CNS-0915988)United States. Army Research Office (ARO Muri grant number W911NF-08-1-0238
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
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