20,075 research outputs found
Loss systems in a random environment
We consider a single server system with infinite waiting room in a random
environment. The service system and the environment interact in both
directions. Whenever the environment enters a prespecified subset of its state
space the service process is completely blocked: Service is interrupted and
newly arriving customers are lost. We prove an if-and-only-if-condition for a
product form steady state distribution of the joint queueing-environment
process. A consequence is a strong insensitivity property for such systems.
We discuss several applications, e.g. from inventory theory and reliability
theory, and show that our result extends and generalizes several theorems found
in the literature, e.g. of queueing-inventory processes.
We investigate further classical loss systems, where due to finite waiting
room loss of customers occurs. In connection with loss of customers due to
blocking by the environment and service interruptions new phenomena arise.
We further investigate the embedded Markov chains at departure epochs and
show that the behaviour of the embedded Markov chain is often considerably
different from that of the continuous time Markov process. This is different
from the behaviour of the standard M/G/1, where the steady state of the
embedded Markov chain and the continuous time process coincide.
For exponential queueing systems we show that there is a product form
equilibrium of the embedded Markov chain under rather general conditions. For
systems with non-exponential service times more restrictive constraints are
needed, which we prove by a counter example where the environment represents an
inventory attached to an M/D/1 queue. Such integrated queueing-inventory
systems are dealt with in the literature previously, and are revisited here in
detail
Bits Through Bufferless Queues
This paper investigates the capacity of a channel in which information is
conveyed by the timing of consecutive packets passing through a queue with
independent and identically distributed service times. Such timing channels are
commonly studied under the assumption of a work-conserving queue. In contrast,
this paper studies the case of a bufferless queue that drops arriving packets
while a packet is in service. Under this bufferless model, the paper provides
upper bounds on the capacity of timing channels and establishes achievable
rates for the case of bufferless M/M/1 and M/G/1 queues. In particular, it is
shown that a bufferless M/M/1 queue at worst suffers less than 10% reduction in
capacity when compared to an M/M/1 work-conserving queue.Comment: 8 pages, 3 figures, accepted in 51st Annual Allerton Conference on
Communication, Control, and Computing, University of Illinois, Monticello,
Illinois, Oct 2-4, 201
Defective and Clustered Choosability of Sparse Graphs
An (improper) graph colouring has "defect" if each monochromatic subgraph
has maximum degree at most , and has "clustering" if each monochromatic
component has at most vertices. This paper studies defective and clustered
list-colourings for graphs with given maximum average degree. We prove that
every graph with maximum average degree less than is
-choosable with defect . This improves upon a similar result by Havet and
Sereni [J. Graph Theory, 2006]. For clustered choosability of graphs with
maximum average degree , no bound on the number of colours
was previously known. The above result with solves this problem. It
implies that every graph with maximum average degree is
-choosable with clustering 2. This extends a
result of Kopreski and Yu [Discrete Math., 2017] to the setting of
choosability. We then prove two results about clustered choosability that
explore the trade-off between the number of colours and the clustering. In
particular, we prove that every graph with maximum average degree is
-choosable with clustering , and is
-choosable with clustering . As an
example, the later result implies that every biplanar graph is 8-choosable with
bounded clustering. This is the best known result for the clustered version of
the earth-moon problem. The results extend to the setting where we only
consider the maximum average degree of subgraphs with at least some number of
vertices. Several applications are presented
Discrete-time queues with zero-regenerative arrivals: moments and examples
In this paper we investigate a single-server discrete-time queueing system with single-slot service times. The stationary ergodic arrival process this queueing system is subject to, satisfies a regeneration property when there are no arrivals during a slot. Expressions for the mean and the variance of the queue content in steady state are obtained for this broad class which includes among others autoregressive arrival processes and M/G/infinity-input or train arrival processes. To illustrate our results, we then consider a number of numerical examples
Greedy Algorithms for Optimal Distribution Approximation
The approximation of a discrete probability distribution by an
-type distribution is considered. The approximation error is
measured by the informational divergence
, which is an appropriate measure, e.g.,
in the context of data compression. Properties of the optimal approximation are
derived and bounds on the approximation error are presented, which are
asymptotically tight. It is shown that -type approximations that minimize
either , or
, or the variational distance
can all be found by using specific
instances of the same general greedy algorithm.Comment: 5 page
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