1,646 research outputs found
A functional central limit theorem for a Markov-modulated infinite-server queue
The production of molecules in a chemical reaction network is modelled as a
Poisson process with a Markov-modulated arrival rate and an exponential decay
rate. We analyze the distributional properties of , the number of molecules,
under specific time-scaling; the background process is sped up by ,
the arrival rates are scaled by , for large. A functional central limit
theorem is derived for , which after centering and scaling, converges to an
Ornstein-Uhlenbeck process. A dichotomy depending on is observed. For
the parameters of the limiting process contain the deviation
matrix associated with the background process.Comment: 4 figure
Optimal Cooperative Cognitive Relaying and Spectrum Access for an Energy Harvesting Cognitive Radio: Reinforcement Learning Approach
In this paper, we consider a cognitive setting under the context of
cooperative communications, where the cognitive radio (CR) user is assumed to
be a self-organized relay for the network. The CR user and the PU are assumed
to be energy harvesters. The CR user cooperatively relays some of the
undelivered packets of the primary user (PU). Specifically, the CR user stores
a fraction of the undelivered primary packets in a relaying queue (buffer). It
manages the flow of the undelivered primary packets to its relaying queue using
the appropriate actions over time slots. Moreover, it has the decision of
choosing the used queue for channel accessing at idle time slots (slots where
the PU's queue is empty). It is assumed that one data packet transmission
dissipates one energy packet. The optimal policy changes according to the
primary and CR users arrival rates to the data and energy queues as well as the
channels connectivity. The CR user saves energy for the PU by taking the
responsibility of relaying the undelivered primary packets. It optimally
organizes its own energy packets to maximize its payoff as time progresses
Analysis of Markov-modulated infinite-server queues in the central-limit regime
This paper focuses on an infinite-server queue modulated by an independently
evolving finite-state Markovian background process, with transition rate matrix
. Both arrival rates and service rates are depending
on the state of the background process. The main contribution concerns the
derivation of central limit theorems for the number of customers in the system
at time , in the asymptotic regime in which the arrival rates
are scaled by a factor , and the transition rates by a
factor , with . The specific value of
has a crucial impact on the result: (i) for the system
essentially behaves as an M/M/ queue, and in the central limit theorem
the centered process has to be normalized by ; (ii) for ,
the centered process has to be normalized by , with the
deviation matrix appearing in the expression for the variance
Large deviations of an infinite-server system with a linearly scaled background process
This paper studies an infinite-server queue in a Markov environment, that is, an infinite-server queue with arrival rates and service times depending on the state of a Markovian background process. We focus on the probability that the number of jobs in the system attains an unusually high value. Scaling the arrival rates ¿i¿i by a factor NN and the transition rates ¿ij¿ij of the background process as well, a large-deviations based approach is used to examine such tail probabilities (where NN tends to 88). The paper also presents qualitative properties of the system’s behavior conditional on the rare event under consideration happening. Keywords: Queues; Infinite-server systems; Markov modulation; Large deviation
Sample path large deviations for queues with many inputs
This paper presents a large deviations principle for the average of real-valued processes indexed by the positive integers, one which is particularly suited to queueing systems with many traffic flows. Examples are given of how it may be applied to standard queues with finite and infinite buffers, to priority queues and to finding most likely paths to overflow
The single server semi-markov queue
A general model for the single server semi-Markov queue is studied. Its solution is reduced to a matrix factorization problem. Given this factorization, results are obtained for the distributions of actual and virtual waiting times, queue lengths both at arrival epochs and in continuous time, the number of customers during a busy period, its length and the length of a busy cycle. Two examples are discussed for which explicit factorizations have been obtained
Scaling limits for infinite-server systems in a random environment
This paper studies the effect of an overdispersed arrival process on the
performance of an infinite-server system. In our setup, a random environment is
modeled by drawing an arrival rate from a given distribution every
time units, yielding an i.i.d. sequence of arrival rates
. Applying a martingale central limit theorem, we
obtain a functional central limit theorem for the scaled queue length process.
We proceed to large deviations and derive the logarithmic asymptotics of the
queue length's tail probabilities. As it turns out, in a rapidly changing
environment (i.e., is small relative to ) the overdispersion
of the arrival process hardly affects system behavior, whereas in a slowly
changing random environment it is fundamentally different; this general finding
applies to both the central limit and the large deviations regime. We extend
our results to the setting where each arrival creates a job in multiple
infinite-server queues
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