2,643 research outputs found
Block-Structured Supermarket Models
Supermarket models are a class of parallel queueing networks with an adaptive
control scheme that play a key role in the study of resource management of,
such as, computer networks, manufacturing systems and transportation networks.
When the arrival processes are non-Poisson and the service times are
non-exponential, analysis of such a supermarket model is always limited,
interesting, and challenging.
This paper describes a supermarket model with non-Poisson inputs: Markovian
Arrival Processes (MAPs) and with non-exponential service times: Phase-type
(PH) distributions, and provides a generalized matrix-analytic method which is
first combined with the operator semigroup and the mean-field limit. When
discussing such a more general supermarket model, this paper makes some new
results and advances as follows: (1) Providing a detailed probability analysis
for setting up an infinite-dimensional system of differential vector equations
satisfied by the expected fraction vector, where "the invariance of environment
factors" is given as an important result. (2) Introducing the phase-type
structure to the operator semigroup and to the mean-field limit, and a
Lipschitz condition can be obtained by means of a unified matrix-differential
algorithm. (3) The matrix-analytic method is used to compute the fixed point
which leads to performance computation of this system. Finally, we use some
numerical examples to illustrate how the performance measures of this
supermarket model depend on the non-Poisson inputs and on the non-exponential
service times. Thus the results of this paper give new highlight on
understanding influence of non-Poisson inputs and of non-exponential service
times on performance measures of more general supermarket models.Comment: 65 pages; 7 figure
Throughput and Delay Scaling in Supportive Two-Tier Networks
Consider a wireless network that has two tiers with different priorities: a
primary tier vs. a secondary tier, which is an emerging network scenario with
the advancement of cognitive radio technologies. The primary tier consists of
randomly distributed legacy nodes of density , which have an absolute
priority to access the spectrum. The secondary tier consists of randomly
distributed cognitive nodes of density with , which
can only access the spectrum opportunistically to limit the interference to the
primary tier. Based on the assumption that the secondary tier is allowed to
route the packets for the primary tier, we investigate the throughput and delay
scaling laws of the two tiers in the following two scenarios: i) the primary
and secondary nodes are all static; ii) the primary nodes are static while the
secondary nodes are mobile. With the proposed protocols for the two tiers, we
show that the primary tier can achieve a per-node throughput scaling of
in the above two scenarios. In the associated
delay analysis for the first scenario, we show that the primary tier can
achieve a delay scaling of
with . In the second scenario, with two mobility
models considered for the secondary nodes: an i.i.d. mobility model and a
random walk model, we show that the primary tier can achieve delay scaling laws
of and , respectively, where is the random walk
step size. The throughput and delay scaling laws for the secondary tier are
also established, which are the same as those for a stand-alone network.Comment: 13 pages, double-column, 6 figures, accepted for publication in JSAC
201
From Packet to Power Switching: Digital Direct Load Scheduling
At present, the power grid has tight control over its dispatchable generation
capacity but a very coarse control on the demand. Energy consumers are shielded
from making price-aware decisions, which degrades the efficiency of the market.
This state of affairs tends to favor fossil fuel generation over renewable
sources. Because of the technological difficulties of storing electric energy,
the quest for mechanisms that would make the demand for electricity
controllable on a day-to-day basis is gaining prominence. The goal of this
paper is to provide one such mechanisms, which we call Digital Direct Load
Scheduling (DDLS). DDLS is a direct load control mechanism in which we unbundle
individual requests for energy and digitize them so that they can be
automatically scheduled in a cellular architecture. Specifically, rather than
storing energy or interrupting the job of appliances, we choose to hold
requests for energy in queues and optimize the service time of individual
appliances belonging to a broad class which we refer to as "deferrable loads".
The function of each neighborhood scheduler is to optimize the time at which
these appliances start to function. This process is intended to shape the
aggregate load profile of the neighborhood so as to optimize an objective
function which incorporates the spot price of energy, and also allows
distributed energy resources to supply part of the generation dynamically.Comment: Accepted by the IEEE journal of Selected Areas in Communications
(JSAC): Smart Grid Communications series, to appea
ATD-2 Integrated Arrival/Departure/Surface (IADS) System Specification - Phase 2
The purpose of this document is to capture the core capabilities developed in ATD-2 Phase 2
The effect of workload dependence in systems: Experimental evaluation, analytic models, and policy development
This dissertation presents an analysis of performance effects of burstiness (formalized by the autocorrelation function) in multi-tiered systems via a 3-pronged approach, i.e., experimental measurements, analytic models, and policy development. This analysis considers (a) systems with finite buffers (e.g., systems with admission control that effectively operate as closed systems) and (b) systems with infinite buffers (i.e., systems that operate as open systems).;For multi-tiered systems with a finite buffer size, experimental measurements show that if autocorrelation exists in any of the tiers in a multi-tiered system, then autocorrelation propagates to all tiers of the system. The presence of autocorrelated flows in all tiers significantly degrades performance. Workload characterization in a real experimental environment driven by the TPC-W benchmark confirms the existence of autocorrelated flows, which originate from the autocorrelated service process of one of the tiers. A simple model is devised that captures the observed behavior. The model is in excellent agreement with experimental measurements and captures the propagation of autocorrelation in the multi-tiered system as well as the resulting performance trends.;For systems with an infinite buffer size, this study focuses on analytic models by proposing and comparing two families of approximations for the departure process of a BMAP/MAP/1 queue that admits batch correlated flows, and whose service time process may be autocorrelated. One approximation is based on the ETAQA methodology for the solution of M/G/1-type processes and the other arises from lumpability rules. Formal proofs are provided: both approximations preserve the marginal distribution of the inter-departure times and their initial correlation structures.;This dissertation also demonstrates how the knowledge of autocorrelation can be used to effectively improve system performance, D_EQAL, a new load balancing policy for clusters with dependent arrivals is proposed. D_EQAL separates jobs to servers according to their sizes as traditional load balancing policies do, but this separation is biased by the effort to reduce performance loss due to autocorrelation in the streams of jobs that are directed to each server. as a result of this, not all servers are equally utilized (i.e., the load in the system becomes unbalanced) but performance benefits of this load unbalancing are significant
Analysis and Computation of the Joint Queue Length Distribution in a FIFO Single-Server Queue with Multiple Batch Markovian Arrival Streams
This paper considers a work-conserving FIFO single-server queue with multiple
batch Markovian arrival streams governed by a continuous-time finite-state
Markov chain. A particular feature of this queue is that service time
distributions of customers may be different for different arrival streams.
After briefly discussing the actual waiting time distributions of customers
from respective arrival streams, we derive a formula for the vector generating
function of the time-average joint queue length distribution in terms of the
virtual waiting time distribution. Further assuming the discrete phase-type
batch size distributions, we develop a numerically feasible procedure to
compute the joint queue length distribution. Some numerical examples are
provided also
- …