1,389 research outputs found
Some analysis results associated with the optimization problem for a discrete-time finite-buffer NT-policy queue
The prime objective of this paperis to give some analysis results concerning
the discrete-time finite-buffer NT-policy queue, which can be utilized to
determine the optimal threshold values. By recording the waiting time of the leading
customer in server’s vacation period, the model is successfully described as a
vector-valued Markov chain. Meanwhile, depending on the special block structure
of the one-step transition probability matrix, the equilibrium queue length distribution
is calculated through a more effective UL-type RG-factorization. Due to the
number of customers served in the busy period does not have the structure of a
Galton-Watson branching process, analysis of the regeneration cycle is regarded as
a difficult problem in establishing the cost structure of the queueing system.
However, employing the concept of i-busy period and some difference equation
solving skills, the explicit expression for the expected length of the regeneration
cycle is easily derived, and the stochastic decomposition structure of the busy period
is also demonstrated. Finally, numerical results are offered to illustrate how the
direct search method can be implemented to obtain the optimal management policy.This research was partially supported by grant from NSERC DAS programs, National Natural Science Foundation of China (Nos. 71301111,71171138, 71402072) and the FSUSE (No.2012RC23).http://link.springer.com/journal/123512017-07-30hb201
A Mean Field Approach for Optimization in Particles Systems and Applications
This paper investigates the limit behavior of Markov Decision Processes
(MDPs) made of independent particles evolving in a common environment, when the
number of particles goes to infinity. In the finite horizon case or with a
discounted cost and an infinite horizon, we show that when the number of
particles becomes large, the optimal cost of the system converges almost surely
to the optimal cost of a discrete deterministic system (the ``optimal mean
field''). Convergence also holds for optimal policies. We further provide
insights on the speed of convergence by proving several central limits theorems
for the cost and the state of the Markov decision process with explicit
formulas for the variance of the limit Gaussian laws. Then, our framework is
applied to a brokering problem in grid computing. The optimal policy for the
limit deterministic system is computed explicitly. Several simulations with
growing numbers of processors are reported. They compare the performance of the
optimal policy of the limit system used in the finite case with classical
policies (such as Join the Shortest Queue) by measuring its asymptotic gain as
well as the threshold above which it starts outperforming classical policies
Cross-Layer Optimization of Network Performance over MIMO Wireless Mobile Channels
In the information theory, the channel capacity states the maximum amount of information which can be reliably transmitted over the communication channel. In the specific case of multiple-input multiple-output (MIMO) wireless systems, it is well recognized that the instantaneous capacity of MIMO systems is a random Gaussian process. Time variation of the capacity leads to the outages at instances when it falls below the transmission rate. The frequency of such events is known as outage probability. The cross-layer approach proposed in this work focuses on the effects of MIMO capacity outages on the network performance, providing a joint optimization of the MIMO communication system. For a constant rate transmission, the outage probability sensibly affects the amount of information correctly received at destination. Theoretically, the limit of the ergodic capacity in MIMO time-variant channels can be achieved by adapting the transmission rate to the capacity variation. With an accurate channel state information, the capacity evolution can be predicted by a suitable autoregressive model based on the capacity time correlation. Taking into consideration the joint effects of channel outage at the physical layer and buffer overflow at the medium access control (MAC) layer, the optimal transmission strategy is derived analytically through the Markov decision processes (MDP) theory. The adaptive policy obtained by MDP is optimal and maximizes the amount of information correctly received at the destination MAC layer (throughput of the system). Analytical results demonstrate the significant improvements of the optimal variable rate strategy compared to a constant transmission rate strategy, in terms of both system throughput and probability of data loss
Reliable Transmission of Short Packets through Queues and Noisy Channels under Latency and Peak-Age Violation Guarantees
This work investigates the probability that the delay and the peak-age of
information exceed a desired threshold in a point-to-point communication system
with short information packets. The packets are generated according to a
stationary memoryless Bernoulli process, placed in a single-server queue and
then transmitted over a wireless channel. A variable-length stop-feedback
coding scheme---a general strategy that encompasses simple automatic repetition
request (ARQ) and more sophisticated hybrid ARQ techniques as special
cases---is used by the transmitter to convey the information packets to the
receiver. By leveraging finite-blocklength results, the delay violation and the
peak-age violation probabilities are characterized without resorting to
approximations based on large-deviation theory as in previous literature.
Numerical results illuminate the dependence of delay and peak-age violation
probability on system parameters such as the frame size and the undetected
error probability, and on the chosen packet-management policy. The guidelines
provided by our analysis are particularly useful for the design of low-latency
ultra-reliable communication systems.Comment: To appear in IEEE journal on selected areas of communication (IEEE
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