692 research outputs found
Redundancy scheduling with scaled Bernoulli service requirements
Redundancy scheduling has emerged as a powerful strategy for improving
response times in parallel-server systems. The key feature in redundancy
scheduling is replication of a job upon arrival by dispatching replicas to
different servers. Redundant copies are abandoned as soon as the first of these
replicas finishes service. By creating multiple service opportunities,
redundancy scheduling increases the chance of a fast response from a server
that is quick to provide service, and mitigates the risk of a long delay
incurred when a single selected server turns out to be slow.
The diversity enabled by redundant requests has been found to strongly
improve the response time performance, especially in case of highly variable
service requirements. Analytical results for redundancy scheduling are
unfortunately scarce however, and even the stability condition has largely
remained elusive so far, except for exponentially distributed service
requirements. In order to gain further insight in the role of the service
requirement distribution, we explore the behavior of redundancy scheduling for
scaled Bernoulli service requirements. We establish a sufficient stability
condition for generally distributed service requirements and we show that, for
scaled Bernoulli service requirements, this condition is also asymptotically
nearly necessary. This stability condition differs drastically from the
exponential case, indicating that the stability condition depends on the
service requirements in a sensitive and intricate manner
Stability of Redundancy Systems with Processor Sharing
We investigate the stability condition for redundancy-d systems where each of
the servers follows a processor-sharing (PS) discipline. We allow for generally
distributed job sizes, with possible dependence among the d replica sizes being
governed by an arbitrary joint distribution. We establish that the stability
condition is characterized by the expectation of the minimum of d replica sizes
being less than the mean interarrival time per server. In the special case of
identical replicas, the stability condition is insensitive to the job size
distribution given its mean, and the stability condition is inversely
proportional to the number of replicas. In the special case of i.i.d. replicas,
the stability threshold decreases (increases) in the number of replicas for job
size distributions that are NBU (NWU). We also discuss extensions to scenarios
with heterogeneous servers.Comment: To appear in proceedings of ValueTools 202
Performance analysis of redundancy and mobility in multi-server systems
In this thesis, we studied how both redundancy and mobility impact the performance of computer systems and cellular networks, respectively. The general notion of redundancy is that upon arrival each job dispatches copies into multiple servers. This allows exploiting the variability of the queue lengths and server capacities in the system. We consider redundancy models with both identical and i.i.d. copies. When copies are i.i.d., we show that with PS and ROS, redundancy does not reduce the stability region. When copies are identical, we characterize the stability condition for systems where either FCFS, PS, or ROS is implemented in the servers. We observe that this condition strongly depends on the scheduling policy implemented in the system. We then investigate how redundancy impacts the performance by comparing it to a non-redundant system. We observe that both the stability and performance improve considerably under redundancy as the heterogeneity of the server capacities increases. Furthermore, for both i.i.d. and identical copies, we characterize redundancy-aware scheduling policies that improve both the stability and performance. Finally, we identify several open problems that might be of interest to the community. User mobility in wireless networks addresses the fact that users in a cellular network switch from cell to cell when geographically moving in the system. We control the mobility speed of the users among the servers and analyze how mobility impacts the performance at a user level. We observe that the performance of the system under fixed mobility speed strongly depends on the inherent parameters of the system
Approximations of the aggregated interference statistics for outage analysis in massive MTC
This paper presents several analytic closed-form approximations of the aggregated interference statistics within the framework of uplink massive machine-type-communications (mMTC), taking into account the random activity of the sensors. Given its discrete nature and the large number of devices involved, a continuous approximation based on the GramâCharlier series expansion of a truncated Gaussian kernel is proposed. We use this approximation to derive an analytic closed-form expression for the outage probability, corresponding to the event of the signal-to-interference-and-noise ratio being below a detection threshold. This metric is useful since it can be used for evaluating the performance of mMTC systems. We analyze, as an illustrative application of the previous approximation, a scenario with several multi-antenna collector nodes, each equipped with a set of predefined spatial beams. We consider two setups, namely single- and multiple-resource, in reference to the number of resources that are allocated to each beam. A graph-based approach that minimizes the average outage probability, and that is based on the statistics approximation, is used as allocation strategy. Finally, we describe an access protocol where the resource identifiers are broadcast (distributed) through the beams. Numerical simulations prove the accuracy of the approximations and the benefits of the allocation strategy.Peer ReviewedPostprint (published version
Near-Optimal Packet Scheduling in Multihop Networks with End-to-End Deadline Constraints
Scheduling packets with end-to-end deadline constraints in multihop networks
is an important problem that has been notoriously difficult to tackle.
Recently, there has been progress on this problem in the worst-case traffic
setting, with the objective of maximizing the number of packets delivered
within their deadlines. Specifically, the proposed algorithms were shown to
achieve fraction of the optimal objective value if the
minimum link capacity in the network is , where
is the maximum length of a packet's route in the network (which is bounded by
the packet's maximum deadline). However, such guarantees can be quite
pessimistic due to the strict worst-case traffic assumption and may not
accurately reflect real-world settings. In this work, we aim to address this
limitation by exploring whether it is possible to design algorithms that
achieve a constant fraction of the optimal value while relaxing the worst-case
traffic assumption.
We provide a positive answer by demonstrating that in stochastic traffic
settings, such as i.i.d. packet arrivals, near-optimal,
-approximation algorithms can be designed if . To the best of our
knowledge, this is the first result that shows this problem can be solved
near-optimally under nontrivial assumptions on traffic and link capacity. We
further present extended simulations using real network traces with
non-stationary traffic, which demonstrate that our algorithms outperform
worst-case-based algorithms in practical settings
Asymptotic performance of queue length based network control policies
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 199-204).In a communication network, asymptotic quality of service metrics specify the probability that the delay or buffer occupancy becomes large. An understanding of these metrics is essential for providing worst-case delay guarantees, provisioning buffer sizes in networks, and to estimate the frequency of packet-drops due to buffer overflow. Second, many network control tasks utilize queue length information to perform effectively, which inevitably adds to the control overheads in a network. Therefore, it is important to understand the role played by queue length information in network control, and its impact on various performance metrics. In this thesis, we study the interplay between the asymptotic behavior of buffer occupancy, queue length information, and traffic statistics in the context of scheduling, flow control, and resource allocation. First, we consider a single-server queue and deal with the question of how often control messages need to be sent in order to effectively control congestion in the queue. Our results show that arbitrarily infrequent queue length information is sufficient to ensure optimal asymptotic decay for the congestion probability, as long as the control information is accurately received. However, if the control messages are subject to errors, the congestion probability can increase drastically, even if the control messages are transmitted often. Next, we consider a system of parallel queues sharing a server, and fed by a statistically homogeneous traffic pattern. We obtain the large deviation exponent of the buffer overflow probability under the well known max-weight scheduling policy. We also show that the queue length based max-weight scheduling outperforms some well known queue-blind policies in terms of the buffer overflow probability. Finally, we study the asymptotic behavior of the queue length distributions when a mix of heavy-tailed and light-tailed traffic flows feeds a system of parallel queues. We obtain an exact asymptotic queue length characterization under generalized max-weight scheduling. In contrast to the statistically homogeneous traffic scenario, we show that max-weight scheduling leads to poor asymptotic behavior for the light-tailed traffic, whereas a queue-blind priority policy gives good asymptotic behavior.by Krishna Prasanna Jagannathan.Ph.D
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