6,182 research outputs found
The upper bound of packet transmission capacity in local static routings
We propose a universal analysis for static routings on networks and describe
the congestion characteristics by the theory. The relation between average
transmission time and transmission capacity is described by inequality
T0Rc0<=1. For large scale sparse networks, the non-trivial upper bond of
transmission capacity Rc0 is limited by Rc0 in some approximate
conditions. the theoretical results agree with simulations on BA Networks.Comment: 7pages,4figure
Stationary analysis of the Shortest Queue First service policy
We analyze the so-called Shortest Queue First (SQF) queueing discipline
whereby a unique server addresses queues in parallel by serving at any time
that queue with the smallest workload. Considering a stationary system composed
of two parallel queues and assuming Poisson arrivals and general service time
distributions, we first establish the functional equations satisfied by the
Laplace transforms of the workloads in each queue. We further specialize these
equations to the so-called "symmetric case", with same arrival rates and
identical exponential service time distributions at each queue; we then obtain
a functional equation for unknown
function , where given functions , and are related to one branch
of a cubic polynomial equation. We study the analyticity domain of function
and express it by a series expansion involving all iterates of function .
This allows us to determine empty queue probabilities along with the tail of
the workload distribution in each queue. This tail appears to be identical to
that of the Head-of-Line preemptive priority system, which is the key feature
desired for the SQF discipline
The stability of join-the-shortest-queue models with general input and output processes
The paper establishes necessary and sufficient conditions for stability of
different join-the-shortest-queue models including load-balanced networks with
general input and output processes. It is shown, that the necessary and
sufficient condition for stability of load-balanced networks is associated with
the solution of a linear programming problem precisely formulated in the paper.
It is proved, that if the minimum of the objective function of that linear
programming problem is less than 1, then the associated load-balanced network
is stable.Comment: 22 pages, typos cor
Load balancing with heterogeneous schedulers
Load balancing is a common approach in web server farms or inventory routing
problems. An important issue in such systems is to determine the server to
which an incoming request should be routed to optimize a given performance
criteria. In this paper, we assume the server's scheduling disciplines to be
heterogeneous. More precisely, a server implements a scheduling discipline
which belongs to the class of limited processor sharing (LPS-) scheduling
disciplines. Under LPS-, up to jobs can be served simultaneously, and
hence, includes as special cases First Come First Served () and Processor
Sharing ().
In order to obtain efficient heuristics, we model the above load-balancing
framework as a multi-armed restless bandit problem. Using the relaxation
technique, as first developed in the seminal work of Whittle, we derive
Whittle's index policy for general cost functions and obtain a closed-form
expression for Whittle's index in terms of the steady-state distribution.
Through numerical computations, we investigate the performance of Whittle's
index with two different performance criteria: linear cost criterion and a cost
criterion that depends on the first and second moment of the throughput. Our
results show that \emph{(i)} the structure of Whittle's index policy can
strongly depend on the scheduling discipline implemented in the server, i.e.,
on , and that \emph{(ii)} Whittle's index policy significantly outperforms
standard dispatching rules such as Join the Shortest Queue (JSQ), Join the
Shortest Expected Workload (JSEW), and Random Server allocation (RSA)
Stability of Parallel Server Systems
The fundamental problem in the study of parallel-server systems is that of
finding and analyzing `good' routing policies of arriving jobs to the servers.
It is well known that, if full information regarding the workload process is
available to a central dispatcher, then the {\em join the shortest workload}
(JSW) policy, which assigns jobs to the server with the least workload, is the
optimal assignment policy, in that it maximizes server utilization, and thus
minimizes sojourn times. The {\em join the shortest queue} (JSQ) policy is an
efficient dispatching policy when information is available only on the number
of jobs with each of the servers, but not on their service requirements. If
information on the state of the system is not available, other dispatching
policies need to be employed, such as the power-of- routing policy, in which
each arriving job joins the shortest among queues sampled uniformly
at random. (Under this latter policy, the system is known as {\em the
supermarket model}.) In this paper we study the stability question of parallel
server systems assuming that routing errors occur, so that arrivals may be
routed to the `wrong' (not to the smallest) queue with a positive probability.
We show that, even if a `non-idling' dispatching policy is employed, under
which new arrivals are always routed to an idle server, if any is available,
the performance of the system can be much worse than under the policy that
chooses one of the servers uniformly at random. More specifically, we prove
that the usual traffic intensity does not guarantee that the system
is stable
Blocking Avoidance in Transportation Systems
The blocking problem naturally arises in transportation systems as multiple
vehicles with different itineraries share available resources. In this paper,
we investigate the impact of the blocking problem to the waiting time at the
intersections of transportation systems. We assume that different vehicles,
depending on their Internet connection capabilities, may communicate their
intentions (e.g., whether they will turn left or right or continue straight) to
intersections (specifically to devices attached to traffic lights). We consider
that information collected by these devices are transmitted to and processed in
a cloud-based traffic control system. Thus, a cloud-based system, based on the
intention information, can calculate average waiting times at intersections. We
consider this problem as a queuing model, and we characterize average waiting
times by taking into account (i) blocking probability, and (ii) vehicles'
ability to communicate their intentions. Then, by using average waiting times
at intersection, we develop a shortest delay algorithm that calculates the
routes with shortest delays between two points in a transportation network. Our
simulation results confirm our analysis, and demonstrate that our shortest
delay algorithm significantly improves over baselines that are unaware of the
blocking problem
Mean Field Approximations to a Queueing System with Threshold-Based Workload Control Scheme
In this paper, motivated by considerations of server utilization and energy
consumptions in cloud computing, we investigate a homogeneous queueing system
with a threshold-based workload control scheme. In this system, a virtual
machine will be turned off when there are no tasks in its buffer upon the
completion of a service by the machine, and turned on when the number of tasks
in its buffer reaches a pre-set threshold value. Due to complexity of this
system, we propose approximations to system performance measures by mean field
limits. An iterative algorithm is suggested for the solution to the mean field
limit equations. In addition, numerical and simulation results are presented to
justify the proposed approximation method and to provide a numerical analysis
on the impact of the system performances by system parameters.Comment: Revised version, 26 pages, 5 figure
Scalable Load Balancing in Networked Systems: Universality Properties and Stochastic Coupling Methods
We present an overview of scalable load balancing algorithms which provide
favorable delay performance in large-scale systems, and yet only require
minimal implementation overhead. Aimed at a broad audience, the paper starts
with an introduction to the basic load balancing scenario, consisting of a
single dispatcher where tasks arrive that must immediately be forwarded to one
of single-server queues.
A popular class of load balancing algorithms are so-called power-of- or
JSQ() policies, where an incoming task is assigned to a server with the
shortest queue among servers selected uniformly at random. This class
includes the Join-the-Shortest-Queue (JSQ) policy as a special case (),
which has strong stochastic optimality properties and yields a mean waiting
time that vanishes as grows large for any fixed subcritical load. However,
a nominal implementation of the JSQ policy involves a prohibitive communication
burden in large-scale deployments. In contrast, a random assignment policy () does not entail any communication overhead, but the mean waiting time
remains constant as grows large for any fixed positive load.
In order to examine the fundamental trade-off between performance and
implementation overhead, we consider an asymptotic regime where depends
on . We investigate what growth rate of is required to match the
performance of the JSQ policy on fluid and diffusion scale. The results
demonstrate that the asymptotics for the JSQ() policy are insensitive to
the exact growth rate of , as long as the latter is sufficiently fast,
implying that the optimality of the JSQ policy can asymptotically be preserved
while dramatically reducing the communication overhead. We additionally show
how the communication overhead can be reduced yet further by the so-called
Join-the-Idle-Queue scheme, leveraging memory at the dispatcher.Comment: Survey paper. Contribution to the Proceedings of the ICM 201
Transform Methods for Heavy-Traffic Analysis
The drift method was recently developed to study queueing systems in
steady-state. It was successfully used to obtain bounds on the moments of the
scaled queue lengths, that are asymptotically tight in heavy-traffic, in a wide
variety of systems including generalized switches, input-queued switches,
bandwidth sharing networks, etc. In this paper we develop the use of transform
techniques for heavy-traffic analysis, with a special focus on the use of
moment generating functions. This approach simplifies the proofs of the drift
method, and provides a new perspective on the drift method. We present a
general framework and then use the MGF method to obtain the stationary
distribution of queue lengths in heavy-traffic in queueing systems that satisfy
the Complete Resource Pooling condition. In particular, we study load balancing
systems and generalized switches under general settings
A Simple Steady-State Analysis of Load Balancing Algorithms in the Sub-Halfin-Whitt Regime
This paper studies a class of load balancing algorithms for many-server (
servers) systems assuming finite buffer with size (i.e. a server can have
at most one job in service and jobs in queue). We focus on steady-state
performance of load balancing algorithms in the heavy traffic regime such that
the load of system is for which we
call sub-Halfin-Whitt regime ( is the so-called the Halfin-Whitt
regime). We establish a sufficient condition under which the probability that
an incoming job is routed to an idle server is one asymptotically. The class of
load balancing algorithms that satisfy the condition includes
join-the-shortest-queue (JSQ), idle-one-first (I1F), join-the-idle-queue (JIQ),
and power-of--choices (Po) with . The proof of the main
result is based on the framework of Stein's method. A key contribution is to
use a simple generator approximation based on state space collapse
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