355 research outputs found
The effective bandwidth problem revisited
The paper studies a single-server queueing system with autonomous service and
priority classes. Arrival and departure processes are governed by marked
point processes. There are buffers corresponding to priority classes,
and upon arrival a unit of the th priority class occupies a place in the
th buffer. Let , denote the quota for the total
th buffer content. The values are assumed to be large, and
queueing systems both with finite and infinite buffers are studied. In the case
of a system with finite buffers, the values characterize buffer
capacities.
The paper discusses a circle of problems related to optimization of
performance measures associated with overflowing the quota of buffer contents
in particular buffers models. Our approach to this problem is new, and the
presentation of our results is simple and clear for real applications.Comment: 29 pages, 11pt, Final version, that will be published as is in
Stochastic Model
Hyper-Scalable JSQ with Sparse Feedback
Load balancing algorithms play a vital role in enhancing performance in data
centers and cloud networks. Due to the massive size of these systems,
scalability challenges, and especially the communication overhead associated
with load balancing mechanisms, have emerged as major concerns. Motivated by
these issues, we introduce and analyze a novel class of load balancing schemes
where the various servers provide occasional queue updates to guide the load
assignment.
We show that the proposed schemes strongly outperform JSQ() strategies
with comparable communication overhead per job, and can achieve a vanishing
waiting time in the many-server limit with just one message per job, just like
the popular JIQ scheme. The proposed schemes are particularly geared however
towards the sparse feedback regime with less than one message per job, where
they outperform corresponding sparsified JIQ versions.
We investigate fluid limits for synchronous updates as well as asynchronous
exponential update intervals. The fixed point of the fluid limit is identified
in the latter case, and used to derive the queue length distribution. We also
demonstrate that in the ultra-low feedback regime the mean stationary waiting
time tends to a constant in the synchronous case, but grows without bound in
the asynchronous case
Fixed points for multi-class queues
Burke's theorem can be seen as a fixed-point result for an exponential
single-server queue; when the arrival process is Poisson, the departure process
has the same distribution as the arrival process. We consider extensions of
this result to multi-type queues, in which different types of customer have
different levels of priority. We work with a model of a queueing server which
includes discrete-time and continuous-time M/M/1 queues as well as queues with
exponential or geometric service batches occurring in discrete time or at
points of a Poisson process. The fixed-point results are proved using
interchangeability properties for queues in tandem, which have previously been
established for one-type M/M/1 systems. Some of the fixed-point results have
previously been derived as a consequence of the construction of stationary
distributions for multi-type interacting particle systems, and we explain the
links between the two frameworks. The fixed points have interesting
"clustering" properties for lower-priority customers. An extreme case is an
example of a Brownian queue, in which lower-priority work only occurs at a set
of times of measure 0 (and corresponds to a local time process for the
queue-length process of higher priority work).Comment: 25 page
A Large Closed Queueing Network Containing Two Types of Node and Multiple Customer Classes: One Bottleneck Station
The paper studies a closed queueing network containing two types of node. The
first type (server station) is an infinite server queueing system, and the
second type (client station) is a single server queueing system with autonomous
service, i.e. every client station serves customers (units) only at random
instants generated by strictly stationary and ergodic sequence of random
variables. It is assumed that there are server stations. At the initial
time moment all units are distributed in the server stations, and the th
server station contains units, , where all the values
are large numbers of the same order. The total number of client stations is
equal to . The expected times between departures in the client stations are
small values of the order ~ . After service
completion in the th server station a unit is transmitted to the th
client station with probability ~ (), and being served
in the th client station the unit returns to the th server station. Under
the assumption that only one of the client stations is a bottleneck node, i.e.
the expected number of arrivals per time unit to the node is greater than the
expected number of departures from that node, the paper derives the
representation for non-stationary queue-length distributions in non-bottleneck
client stations.Comment: 39 pages, 5 figure
EUROPEAN CONFERENCE ON QUEUEING THEORY 2016
International audienceThis booklet contains the proceedings of the second European Conference in Queueing Theory (ECQT) that was held from the 18th to the 20th of July 2016 at the engineering school ENSEEIHT, Toulouse, France. ECQT is a biannual event where scientists and technicians in queueing theory and related areas get together to promote research, encourage interaction and exchange ideas. The spirit of the conference is to be a queueing event organized from within Europe, but open to participants from all over the world. The technical program of the 2016 edition consisted of 112 presentations organized in 29 sessions covering all trends in queueing theory, including the development of the theory, methodology advances, computational aspects and applications. Another exciting feature of ECQT2016 was the institution of the TakĂĄcs Award for outstanding PhD thesis on "Queueing Theory and its Applications"
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