137 research outputs found
Heavy-traffic revenue maximization in parallel multiclass queues
Motivated by revenue maximization in server farms with admission control, we investigate the optimal scheduling in parallel processor-sharing queues. Incoming customers are distinguished in multiple classes and we define revenue as a weighted sum of class throughputs. Under these assumptions, we describe a heavy-traffic limit for the revenue maximization problem and study the asymptotic properties of the optimization model as the number of clients increases. Our main result is a simple heuristic that is able to provide tight guarantees on the optimality gap of its solutions. In the general case with M queues and R classes, we prove that our heuristic is (1+1M-1)-competitive in heavy-traffic. Experimental results indicate that the proposed heuristic is remarkably accurate, despite its negligible computational costs, both in random instances and using service rates of a web application measured on multiple cloud deployments
Stochastic bounds for two-layer loss systems
This paper studies multiclass loss systems with two layers of servers, where
each server at the first layer is dedicated to a certain customer class, while
the servers at the second layer can handle all customer classes. The routing of
customers follows an overflow scheme, where arriving customers are
preferentially directed to the first layer. Stochastic comparison and coupling
techniques are developed for studying how the system is affected by packing of
customers, altered service rates, and altered server configurations. This
analysis leads to easily computable upper and lower bounds for the performance
of the system.Comment: Revised conten
Detecting Markov Chain Instability: A Monte Carlo Approach
We devise a Monte Carlo based method for detecting whether a non-negative
Markov chain is stable for a given set of parameter values. More precisely, for
a given subset of the parameter space, we develop an algorithm that is capable
of deciding whether the set has a subset of positive Lebesgue measure for which
the Markov chain is unstable. The approach is based on a variant of simulated
annealing, and consequently only mild assumptions are needed to obtain
performance guarantees.
The theoretical underpinnings of our algorithm are based on a result stating
that the stability of a set of parameters can be phrased in terms of the
stability of a single Markov chain that searches the set for unstable
parameters. Our framework leads to a procedure that is capable of performing
statistically rigorous tests for instability, which has been extensively tested
using several examples of standard and non-standard queueing networks
A new approach to service provisioning in ATM networks
The authors formulate and solve a problem of allocating resources among competing services differentiated by user traffic characteristics and maximum end-to-end delay. The solution leads to an alternative approach to service provisioning in an ATM network, in which the network offers directly for rent its bandwidth and buffers and users purchase freely resources to meet their desired quality. Users make their decisions based on their own traffic parameters and delay requirements and the network sets prices for those resources. The procedure is iterative in that the network periodically adjusts prices based on monitored user demand, and is decentralized in that only local information is needed for individual users to determine resource requests. The authors derive the network's adjustment scheme and the users' decision rule and establish their optimality. Since the approach does not require the network to know user traffic and delay parameters, it does not require traffic policing on the part of the network
QD-AMVA: Evaluating Systems with Queue-Dependent Service Requirements
AbstractWorkload measurements in enterprise systems often lead to observe a dependence between the number of requests running at a resource and their mean service requirements. However, multiclass performance models that feature these dependences are challenging to analyze, a fact that discourages practitioners from characterizing workload dependences. We here focus on closed multiclass queueing networks and introduce QD-AMVA, the first approximate mean-value analysis (AMVA) algorithm that can efficiently and robustly analyze queue-dependent service times in a multiclass setting. A key feature of QD-AMVA is that it operates on mean values, avoiding the computation of state probabilities. This property is an innovative result for state-dependent models, which increases the computational efficiency and numerical robustness of their evaluation. Extensive validation on random examples, a cloud load-balancing case study and comparison with a fluid method and an existing AMVA approximation prove that QD-AMVA is efficient, robust and easy to apply, thus enhancing the tractability of queue-dependent models
Dynamic Assignment Control of a Closed Queueing Network under Complete Resource Pooling
We study the design of dynamic assignment control in networks with a fixed
number of circulating resources (supply units). Each time a demand arises, the
controller has (limited) flexibility in choosing the node from which to assign
a supply unit. If no supply units are available at any compatible node, the
demand is lost. If the demand is served, this causes to the supply unit to
relocate to the "destination" of the demand. We study how to minimize the
proportion of lost requests in steady state (or over a finite horizon) via a
large deviations analysis.
We propose a family of simple state-dependent policies called Scaled
MaxWeight (SMW) policies that dynamically manage the distribution of supply in
the network. We prove that under a complete resource pooling condition
(analogous to the condition in Hall's marriage theorem), any SMW policy leads
to exponential decay of demand-loss probability as the number of supply units
scales to infinity. Further, there is an SMW policy that achieves the
loss exponent among all assignment policies, and we
analytically specify this policy in terms of the demand arrival rates for all
origin-destination pairs. The optimal SMW policy maintains high supply levels
adjacent to structurally under-supplied nodes. We discuss two applications: (i)
Shared transportation platforms (like ride-hailing and bikesharing): We
incorporate travel delays in our model and show that SMW policies for
assignment control continue to have exponentially small loss. Simulations of
ride-hailing based on the NYC taxi dataset demonstrate excellent performance.
(ii) Service provider selection in scrip systems (like for babysitting or for
kidney exchange): With only cosmetic modifications to the setup, our results
translate fully to a model of scrip systems and lead to strong performance
guarantees for a "Scaled Minimum Scrip" service provider selection rule
A Survey on Delay-Aware Resource Control for Wireless Systems --- Large Deviation Theory, Stochastic Lyapunov Drift and Distributed Stochastic Learning
In this tutorial paper, a comprehensive survey is given on several major
systematic approaches in dealing with delay-aware control problems, namely the
equivalent rate constraint approach, the Lyapunov stability drift approach and
the approximate Markov Decision Process (MDP) approach using stochastic
learning. These approaches essentially embrace most of the existing literature
regarding delay-aware resource control in wireless systems. They have their
relative pros and cons in terms of performance, complexity and implementation
issues. For each of the approaches, the problem setup, the general solution and
the design methodology are discussed. Applications of these approaches to
delay-aware resource allocation are illustrated with examples in single-hop
wireless networks. Furthermore, recent results regarding delay-aware multi-hop
routing designs in general multi-hop networks are elaborated. Finally, the
delay performance of the various approaches are compared through simulations
using an example of the uplink OFDMA systems.Comment: 58 pages, 8 figures; IEEE Transactions on Information Theory, 201
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