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Analysis of a class of distributed queues with application
Recently we have developed a class of media access control algorithms for different types of Local Area Networks. A common feature of these LAN algorithms is that they represent various strategies by which the processors in the LAN can simulate the availability of a centralized packet transport facility, but whose service incorporates a particular type of change over time known as 'moving sever' overhead. First we describe the operation of moving server systems in general, for both First-Come - First-Served and Head-of-the-Line orders of service, together with an approach for their delay analysis in which we transform the moving server queueing system into a conventional queueing system having proportional waiting times. Then we describe how the various LAN algorithms may be obtained from the ideal moving server system, and how a significant component of their performance characteristics is determined by the performance characteristics of that ideal system. Finally, we evaluate the compatibility of such LAN algorithms with separable queueing network models of distributed systems by computing the interdeparture time distribution for M/M/1 in the presence of moving server overhead. Although it is not exponential, except in the limits of low server utilization or low overhead, the interdeparture time distribution is a weighted sum of exponential terms with a coefficient of variation not much smaller than unity. Thus, we conjecture that a service centre with moving server overhead could be used to represent one of these LAN algorithms in a product form queueing network model of a distributed system without introducing significant approximation errors
Queuing with future information
We study an admissions control problem, where a queue with service rate
receives incoming jobs at rate , and the decision maker is
allowed to redirect away jobs up to a rate of , with the objective of
minimizing the time-average queue length. We show that the amount of
information about the future has a significant impact on system performance, in
the heavy-traffic regime. When the future is unknown, the optimal average queue
length diverges at rate , as . In sharp contrast, when all future arrival and service times are revealed
beforehand, the optimal average queue length converges to a finite constant,
, as . We further show that the finite limit of
can be achieved using only a finite lookahead window starting from the current
time frame, whose length scales as , as
. This leads to the conjecture of an interesting duality between
queuing delay and the amount of information about the future.Comment: Published in at http://dx.doi.org/10.1214/13-AAP973 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Datacenter Traffic Control: Understanding Techniques and Trade-offs
Datacenters provide cost-effective and flexible access to scalable compute
and storage resources necessary for today's cloud computing needs. A typical
datacenter is made up of thousands of servers connected with a large network
and usually managed by one operator. To provide quality access to the variety
of applications and services hosted on datacenters and maximize performance, it
deems necessary to use datacenter networks effectively and efficiently.
Datacenter traffic is often a mix of several classes with different priorities
and requirements. This includes user-generated interactive traffic, traffic
with deadlines, and long-running traffic. To this end, custom transport
protocols and traffic management techniques have been developed to improve
datacenter network performance.
In this tutorial paper, we review the general architecture of datacenter
networks, various topologies proposed for them, their traffic properties,
general traffic control challenges in datacenters and general traffic control
objectives. The purpose of this paper is to bring out the important
characteristics of traffic control in datacenters and not to survey all
existing solutions (as it is virtually impossible due to massive body of
existing research). We hope to provide readers with a wide range of options and
factors while considering a variety of traffic control mechanisms. We discuss
various characteristics of datacenter traffic control including management
schemes, transmission control, traffic shaping, prioritization, load balancing,
multipathing, and traffic scheduling. Next, we point to several open challenges
as well as new and interesting networking paradigms. At the end of this paper,
we briefly review inter-datacenter networks that connect geographically
dispersed datacenters which have been receiving increasing attention recently
and pose interesting and novel research problems.Comment: Accepted for Publication in IEEE Communications Surveys and Tutorial
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
Redundancy Scheduling with Locally Stable Compatibility Graphs
Redundancy scheduling is a popular concept to improve performance in
parallel-server systems. In the baseline scenario any job can be handled
equally well by any server, and is replicated to a fixed number of servers
selected uniformly at random. Quite often however, there may be heterogeneity
in job characteristics or server capabilities, and jobs can only be replicated
to specific servers because of affinity relations or compatibility constraints.
In order to capture such situations, we consider a scenario where jobs of
various types are replicated to different subsets of servers as prescribed by a
general compatibility graph. We exploit a product-form stationary distribution
and weak local stability conditions to establish a state space collapse in
heavy traffic. In this limiting regime, the parallel-server system with
graph-based redundancy scheduling operates as a multi-class single-server
system, achieving full resource pooling and exhibiting strong insensitivity to
the underlying compatibility constraints.Comment: 28 pages, 4 figure
Telemetry downlink interfaces and level-zero processing
The technical areas being investigated are as follows: (1) processing of space to ground data frames; (2) parallel architecture performance studies; and (3) parallel programming techniques. Additionally, the University administrative details and the technical liaison between New Mexico State University and Goddard Space Flight Center are addressed
On-board B-ISDN fast packet switching architectures. Phase 2: Development. Proof-of-concept architecture definition report
For the next-generation packet switched communications satellite system with onboard processing and spot-beam operation, a reliable onboard fast packet switch is essential to route packets from different uplink beams to different downlink beams. The rapid emergence of point-to-point services such as video distribution, and the large demand for video conference, distributed data processing, and network management makes the multicast function essential to a fast packet switch (FPS). The satellite's inherent broadcast features gives the satellite network an advantage over the terrestrial network in providing multicast services. This report evaluates alternate multicast FPS architectures for onboard baseband switching applications and selects a candidate for subsequent breadboard development. Architecture evaluation and selection will be based on the study performed in phase 1, 'Onboard B-ISDN Fast Packet Switching Architectures', and other switch architectures which have become commercially available as large scale integration (LSI) devices
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