Peer-to-Peer (P2P) storage systems are a prevalent and important
mode for implementing cost-efficient, large-scale distributed
storage. Considering the random departure feature of the peers and
the diverse popularity of the data objects, a proper number of
replicas needs to be maintained, and a reasonable trigger threshold
of replica repair needs to be set for high data availability and
low system overhead. In this paper, based on the working principle
of the lazy replica repair policy in a P2P storage system, a
three-dimensional Markov chain model is constructed, and the model
is analyzed in steady-state by using a matrix-geometric method.
Then, the performance measures in terms of the availability of one
data object, the average access latency, and the replication rate
are given. Moreover, numerical results with analysis are provided
to demonstrate how system parameters such as the replica number and
the replica repair instant influence the system performance.
Finally, we develop benefit functions to optimize the replica number
and the repair trigger threshold.
In this paper, we consider a cognitive radio network with multiple Secondary Users (SUs). The SU packets generated from the SUs are divided into SU1 packets and SU2 packets, and the SU1 packets have higher priority than the SU2 packets. Different from the conventional preemptive priority scheme (called Scheme Ⅰ), we propose a non-preemptive priority scheme for the SU1 packets (called Scheme Ⅱ) to guarantee the transmission continuity of the SU2 packets. By constructing a three-dimensional Markov chain, we give the transition probability matrix of the Markov chain, and obtain the steady-state distribution of the system model. Accordingly, we derive some performance measures, such as the channel utilization, the blocking probability of the SU1 packets, the interruption probability of the SU1 packets and the SU2 packets, the normalized throughput of the SU1 packets, and the average latency of the SU2 packets. Moreover, we provide numerical experiments to compare different performance measures between the two priority schemes. Finally, we show and compare the Nash equilibrium strategy and the socially optimal strategy for the SU2 packets between Scheme Ⅰ and Scheme Ⅱ.
In this paper, we consider a cognitive radio network with multiple secondary users (SUs). The SU packets in the system can be divided into two categories: SU1 packets and SU2 packets, where SU1 packets have transmission priority over SU2 packets. Considering the absolute priority of the primary users (PUs), the PU packets have the highest priority in the system to transmit. In order to guarantee the Quality of Service (QoS) of the network users, as well as reduce the average delay of the SU2 packets, we propose an adjustable access control scheme for the SU2 packets. A newly arriving SU2 packet can access the system with an access probability related to the total number of packets in the system. A variable factor is also introduced to adjust the access probability dynamically. Based on the working principle of the adjustable access control scheme, we build a discrete-time queueing model with a finite waiting room and an adjustable joining rate. With a steady-state analysis of the queueing model, using a three-dimensional Markov chain, we derive some performance measures, such as the total channel utilization, the interruption rate, the throughput, and the average delay of the SU2 packets. Moreover, we show the influence of the adjustment factor on different system performance measures by using numerical results. Finally, considering the trade-off between the throughput and the average delay of the SU2 packets with respect to the adjustment factor, we build a net benefit function and show an optimal algorithm to optimize the adjustment factor.
In order to enhance the Quality of Service (QoS) for the secondary
users (SUs) in Cognitive Radio (CR) networks reasonably, in this
paper, we propose an adjustable admission control scheme considering
an access threshold under a centralized architecture. We assume that
a buffer is set for all the SUs. On the arrival instant of an SU
packet, if the number of SU packets already in the buffer is equal
to or greater than the access threshold that is set in advance, this
SU packet will be admitted to join the system with an adjustable
access probability, which is inversely proportional to the total
number of packets in the system. Based on the adjustable admission
control scheme proposed in this paper, considering the priority of
the primary users (PUs) in CR networks, we build a preemptive
priority queueing model. Aiming to comply with the digital nature of
modern networks, we establish a two-dimensional discrete-time Markov
chain (DTMC) and construct the transition probability matrix of the
Markov chain. Accordingly, we provide the formulas for several
performance measures, such as the blocking rate, the throughput and
the average latency of the SU packets. With numerical results, we show the
influence of the access threshold on different performance measures
for the SU packets. Finally, taking into account the trade-off between
different performance measures, we build a net benefit function to
find the optimal access threshold with an optimization algorithm.
We consider a mathematical model that describes the interactions of
the HIV virus, CD4 cells and CTLs within host, which is a
modification of some existing models by incorporating (i) two
distributed kernels reflecting the variance of time for virus to
invade into cells and the variance of time for invaded virions to
reproduce within cells; (ii) a nonlinear incidence function $f$ for
virus infections, and (iii) a nonlinear removal rate function $h$
for infected cells. By constructing Lyapunov functionals and subtle
estimates of the derivatives of these Lyapunov functionals, we shown
that the model has the threshold dynamics: if the basic
reproduction number (BRN) is less than or equal to one, then the
infection free equilibrium is globally asymptotically stable,
meaning that HIV virus will be cleared; whereas if the BRN is larger
than one, then there exist an infected equilibrium which is globally
asymptotically stable, implying that the HIV-1 infection will
persist in the host and the viral concentration will approach a
positive constant level. This together with the
dependence/independence of the BRN on $f$ and $h$ reveals the effect
of the adoption of these nonlinear functions.
This paper studies the problem of optimal output tracking control for networked control system with uncertain time delays and packet dropouts. Active time-varying sampling period strategy is proposed to ensure the random variable time delays always shorter than one sampling period. Hybrid driven modes are adopted by sensor to solve the issues of long time delay and packet dropout. By using augmentation approach, the tracking problem of this formulated within-one-step delayed discrete-time system is transformed into a general problem of non-delayed state linear quadratic regulator. A “gridding” approach is introduced to guarantee the realization of optimal output feedback control law by the solution of a series of Riccati matrix equations from an offline database that is constructed by different combination of time delays and packet dropouts. Simulation results demonstrate the effectiveness of the optimal tracking control law.
In the present paper, using the
Leray-Schauder degree theory, we proved the existence of
nontrivial solutions for p-Laplacian with a crossing nonlinearity.