1,900 research outputs found
Many Server Scaling of the N-System Under FCFS-ALIS
The N-System with independent Poisson arrivals and exponential
server-dependent service times under first come first served and assign to
longest idle server policy has explicit steady state distribution. We scale the
arrival and the number of servers simultaneously, and obtain the fluid and
central limit approximation for the steady state. This is the first step
towards exploring the many server scaling limit behavior of general parallel
service systems
Stabilizing Queuing Networks with Model Data-Independent Control
Classical queuing network control strategies typically rely on accurate
knowledge of model data, i.e., arrival and service rates. However, such data
are not always available and may be time-variant. To address this challenge, we
consider a class of model data-independent (MDI) control policies that only
rely on traffic state observation and network topology. Specifically, we focus
on the MDI control policies that can stabilize multi-class Markovian queuing
networks under centralized and decentralized policies. Control actions include
routing, sequencing, and holding. By expanding the routes and constructing
piecewise-linear test functions, we derive an easy-to-use criterion to check
the stability of a multi-class network under a given MDI policy. For
stabilizable multi-class networks, we show that a centralized, stabilizing MDI
policy exists. For stabilizable single-class networks, we further show that a
decentralized, stabilizing MDI policy exists. In addition, for both settings,
we construct explicit policies that attain maximal throughput and present
numerical examples to illustrate the results.Comment: Accepted by IEEE Transactions on Control of Network System
An Optimal Medium Access Control with Partial Observations for Sensor Networks
We consider medium access control (MAC) in multihop sensor networks, where only partial information about the shared medium is available to the transmitter. We model our setting as a queuing problem in which the service rate of a queue is a function of a partially observed Markov chain representing the available bandwidth, and in which the arrivals are controlled based on the partial observations so as to keep the system in a desirable mildly unstable regime. The optimal controller for this problem satisfies a separation property: we first compute a probability measure on the state space of the chain, namely the information state, then use this measure as the new state on which the control decisions are based. We give a formal description of the system considered and of its dynamics, we formalize and solve an optimal control problem, and we show numerical simulations to illustrate with concrete examples properties of the optimal control law. We show how the ergodic behavior of our queuing model is characterized by an invariant measure over all possible information states, and we construct that measure. Our results can be specifically applied for designing efficient and stable algorithms for medium access control in multiple-accessed systems, in particular for sensor networks
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