73,117 research outputs found
Simple and explicit bounds for multi-server queues with (and sometimes better) scaling
We consider the FCFS queue, and prove the first simple and explicit
bounds that scale as (and sometimes better). Here
denotes the corresponding traffic intensity. Conceptually, our results can be
viewed as a multi-server analogue of Kingman's bound. Our main results are
bounds for the tail of the steady-state queue length and the steady-state
probability of delay. The strength of our bounds (e.g. in the form of tail
decay rate) is a function of how many moments of the inter-arrival and service
distributions are assumed finite. More formally, suppose that the inter-arrival
and service times (distributed as random variables and respectively)
have finite th moment for some Let (respectively )
denote (respectively ). Then
our bounds (also for higher moments) are simple and explicit functions of
, and
only. Our bounds scale gracefully even when the number of
servers grows large and the traffic intensity converges to unity
simultaneously, as in the Halfin-Whitt scaling regime. Some of our bounds scale
better than in certain asymptotic regimes. More precisely,
they scale as multiplied by an inverse polynomial in These results formalize the intuition that bounds should be tighter
in light traffic as well as certain heavy-traffic regimes (e.g. with
fixed and large). In these same asymptotic regimes we also prove bounds for
the tail of the steady-state number in service.
Our main proofs proceed by explicitly analyzing the bounding process which
arises in the stochastic comparison bounds of amarnik and Goldberg for
multi-server queues. Along the way we derive several novel results for suprema
of random walks and pooled renewal processes which may be of independent
interest. We also prove several additional bounds using drift arguments (which
have much smaller pre-factors), and make several conjectures which would imply
further related bounds and generalizations
Information Design for Congested Social Services: Optimal Need-Based Persuasion
We study the effectiveness of information design in reducing congestion in
social services catering to users with varied levels of need. In the absence of
price discrimination and centralized admission, the provider relies on sharing
information about wait times to improve welfare. We consider a stylized model
with heterogeneous users who differ in their private outside options: low-need
users have an acceptable outside option to the social service, whereas
high-need users have no viable outside option. Upon arrival, a user decides to
wait for the service by joining an unobservable first-come-first-serve queue,
or leave and seek her outside option. To reduce congestion and improve social
outcomes, the service provider seeks to persuade more low-need users to avail
their outside option, and thus better serve high-need users. We characterize
the Pareto-optimal signaling mechanisms and compare their welfare outcomes
against several benchmarks. We show that if either type is the overwhelming
majority of the population, information design does not provide improvement
over sharing full information or no information. On the other hand, when the
population is a mixture of the two types, information design not only Pareto
dominates full-information and no-information mechanisms, in some regimes it
also achieves the same welfare as the "first-best", i.e., the Pareto-optimal
centralized admission policy with knowledge of users' types.Comment: Accepted for publication in the 21st ACM Conference on Economics and
Computation (EC'20). 40 pages, 6 figure
Delay, memory, and messaging tradeoffs in distributed service systems
We consider the following distributed service model: jobs with unit mean,
exponentially distributed, and independent processing times arrive as a Poisson
process of rate , with , and are immediately dispatched
by a centralized dispatcher to one of First-In-First-Out queues associated
with identical servers. The dispatcher is endowed with a finite memory, and
with the ability to exchange messages with the servers.
We propose and study a resource-constrained "pull-based" dispatching policy
that involves two parameters: (i) the number of memory bits available at the
dispatcher, and (ii) the average rate at which servers communicate with the
dispatcher. We establish (using a fluid limit approach) that the asymptotic, as
, expected queueing delay is zero when either (i) the number of
memory bits grows logarithmically with and the message rate grows
superlinearly with , or (ii) the number of memory bits grows
superlogarithmically with and the message rate is at least .
Furthermore, when the number of memory bits grows only logarithmically with
and the message rate is proportional to , we obtain a closed-form expression
for the (now positive) asymptotic delay.
Finally, we demonstrate an interesting phase transition in the
resource-constrained regime where the asymptotic delay is non-zero. In
particular, we show that for any given (no matter how small), if our
policy only uses a linear message rate , the resulting asymptotic
delay is upper bounded, uniformly over all ; this is in sharp
contrast to the delay obtained when no messages are used (), which
grows as when , or when the popular
power-of--choices is used, in which the delay grows as
Towards Fast-Convergence, Low-Delay and Low-Complexity Network Optimization
Distributed network optimization has been studied for well over a decade.
However, we still do not have a good idea of how to design schemes that can
simultaneously provide good performance across the dimensions of utility
optimality, convergence speed, and delay. To address these challenges, in this
paper, we propose a new algorithmic framework with all these metrics
approaching optimality. The salient features of our new algorithm are
three-fold: (i) fast convergence: it converges with only
iterations that is the fastest speed among all the existing algorithms; (ii)
low delay: it guarantees optimal utility with finite queue length; (iii) simple
implementation: the control variables of this algorithm are based on virtual
queues that do not require maintaining per-flow information. The new technique
builds on a kind of inexact Uzawa method in the Alternating Directional Method
of Multiplier, and provides a new theoretical path to prove global and linear
convergence rate of such a method without requiring the full rank assumption of
the constraint matrix
Decentralized Delay Optimal Control for Interference Networks with Limited Renewable Energy Storage
In this paper, we consider delay minimization for interference networks with
renewable energy source, where the transmission power of a node comes from both
the conventional utility power (AC power) and the renewable energy source. We
assume the transmission power of each node is a function of the local channel
state, local data queue state and local energy queue state only. In turn, we
consider two delay optimization formulations, namely the decentralized
partially observable Markov decision process (DEC-POMDP) and Non-cooperative
partially observable stochastic game (POSG). In DEC-POMDP formulation, we
derive a decentralized online learning algorithm to determine the control
actions and Lagrangian multipliers (LMs) simultaneously, based on the policy
gradient approach. Under some mild technical conditions, the proposed
decentralized policy gradient algorithm converges almost surely to a local
optimal solution. On the other hand, in the non-cooperative POSG formulation,
the transmitter nodes are non-cooperative. We extend the decentralized policy
gradient solution and establish the technical proof for almost-sure convergence
of the learning algorithms. In both cases, the solutions are very robust to
model variations. Finally, the delay performance of the proposed solutions are
compared with conventional baseline schemes for interference networks and it is
illustrated that substantial delay performance gain and energy savings can be
achieved
Large deviations analysis for the queue in the Halfin-Whitt regime
We consider the FCFS queue in the Halfin-Whitt heavy traffic
regime. It is known that the normalized sequence of steady-state queue length
distributions is tight and converges weakly to a limiting random variable W.
However, those works only describe W implicitly as the invariant measure of a
complicated diffusion. Although it was proven by Gamarnik and Stolyar that the
tail of W is sub-Gaussian, the actual value of was left open. In subsequent work, Dai and He
conjectured an explicit form for this exponent, which was insensitive to the
higher moments of the service distribution.
We explicitly compute the true large deviations exponent for W when the
abandonment rate is less than the minimum service rate, the first such result
for non-Markovian queues with abandonments. Interestingly, our results resolve
the conjecture of Dai and He in the negative. Our main approach is to extend
the stochastic comparison framework of Gamarnik and Goldberg to the setting of
abandonments, requiring several novel and non-trivial contributions. Our
approach sheds light on several novel ways to think about multi-server queues
with abandonments in the Halfin-Whitt regime, which should hold in considerable
generality and provide new tools for analyzing these systems
Some Challenges of Specifying Concurrent Program Components
The purpose of this paper is to address some of the challenges of formally
specifying components of shared-memory concurrent programs. The focus is to
provide an abstract specification of a component that is suitable for use both
by clients of the component and as a starting point for refinement to an
implementation of the component. We present some approaches to devising
specifications, investigating different forms suitable for different contexts.
We examine handling atomicity of access to data structures, blocking operations
and progress properties, and transactional operations that may fail and need to
be retried.Comment: In Proceedings Refine 2018, arXiv:1810.0873
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