Zikuan Liu

Delay-dependent stabilization of singularly perturbed jump linear systems

This paper considers the stability and stabilization problems of continuous-time singularly perturbed Markov jump linear systems. LMI-based sufficient conditions for the system to be stochastically stable are given, and using LMI approaches, two methods for designing state feedback stabilizing controllers are also derived. Numerical examples are worked out to illustrate the usefulness of the proposed results.

Approximating Lognormal Sum Distributions With Power Lognormal Distributions

In wireless communications, cochannel interference is usually characterized by a sum of lognormal random variables. Since the characteristic function of a lognormal distribution lacks explicit expression, and numerical calculation of a lognormal sum distribution is very challenging, lognormal distributions are often used to approximate lognormal sum distributions. However, it has been shown that a lognormal distribution can only capture a certain part of the body of a lognormal sum distribution. To improve the accuracy of approximation of lognormal sum distributions, one must resort to non-lognormal approximations. In this paper, we propose the use of power lognormal distributions to approximate lognormal sum distributions. To illustrate the superiority of the proposed model, some numerical experimental results are provided.

Production and maintenance control for manufacturing systems

This paper addresses the production and maintenance control problem of a failure prone manufacturing system consisting of one machine and producing one part type. The machine is assumed to have three working states: good, average and bad, and a failure state. In the three working states, the machine can produce parts and some of these parts are rejected with a rate depending on the machine state. In the failure state, no part is produced. The state transition of the machine is governed by a continuous-time Markov process. The jump rates from average and bad states to the good state are the preventive maintenance rates and the one from failure state to good state is the corrective maintenance rate. The production rate and the maintenance rates are optimized.

Online EM algorithm for mixture with application to internet traffic modeling

Since histograms of many real network traces show strong evidence of mixture, this paper uses mixture distributions to model Internet traffic and applies the EM algorithm to fit the models. Making use of the fact that at each iteration of the EM algorithm the parameter increment has a positive projection on the gradient of the likelihood function, this paper proposes an online EM algorithm to fit the models and the Bayesian Information Criterion is applied to select the best model. Experimental results on real traces are provided to illustrate the efficiency of the proposed algorithm.

Mixture Lognormal Approximations to Lognormal Sum Distributions

In wireless communication, co-channel interference is usually characterized by a sum of lognormal random variables. Since calculating the exact distribution of a lognormal sum has a lot of challenges, lognormal distributions are often used to approximate lognormal sum distributions. However, it has been shown that lognormal approximations can only capture a certain part of the body of a lognormal sum distribution, which implies that to accurately approximate a lognormal sum distribution, one has to resort to non-lognormal approximations. In this paper we propose to use a two-component mixture lognormal model to approximate lognormal sum distributions. Numerical examples are provided to compare the proposed mixture lognormal approximation with the existing ones.

Traffic Estimation and Power Saving Mechanism Optimization of IEEE 802.16e Networks

In order to save power to prolong battery life of subscriber stations (SSs) in IEEE 802.16e networks, the standard defines a sleep mode for SS. When there is no traffic for an SS to transmit or to receive, the SS switches to sleep mode periodically. The sleep interval is doubled each time until a maximum sleep interval threshold Tmax is reached. Obviously, the performance of this power saving mechanism depends on the idle period distribution, which is user-specific. In network traffic modeling, it is commonly accepted that frame interarrival times have heavy-tailed distributions. Since heavy-tailed distributions make analysis and design challenging, in this paper we propose to use mixtures of exponentials to approximate heavy-tailed idle times. With a mixture of exponentials approximating the idle times, performance can be explicitly derived and optimized. An online EM algorithm is proposed to fit the mixture of exponential distributions to the idle times. Numerical examples show the effectiveness of the proposed procedures.

A long-range dependent model for Internet traffic with power transformation

Internet traffic has been shown to have long-range dependence, and is often modeled by using the fractional Gaussian noise model. The fractional Gaussian noise model can capture the autocorrelation of a real trace, but cannot fit the marginal distribution when the trace has a non-Gaussian marginal distribution. In this letter, we use the inverted Box-Cox transformation to establish a long-range dependent Internet traffic model that can simultaneously capture both the long-range dependence parameter and the marginal distribution of a real trace

Adaptive Traffic Light Control using VANET: A case study

Rapid urbanization has put increasingly pressure on traffic management in urban areas. Conventional traffic signal with fixed or pre-defined variable cycles setting can slightly alleviate the increasing traffic problem, but cannot deal with continuously growing vehicular traffic in rapidly growing urban areas. VANET technology offers a promising solution for better vehicular traffic management in urban area to reduce traffic jam and improve transportation safety. Adaptive Traffic Light Control (ATLC) using VANET has attracted considerable attention from academic community. Unfortunately, most of these existing works used simulated traffic flow and hypothetical intersection architectures which may not reflect the reality of urban area. In this paper, we present a case study based on a specific intersection in the city of Moncton with real traffic data, and propose a new adaptive traffic light control algorithm. Our results show a substantial improvement of traffic throughput and average waiting time in comparison with fixed optimal cycles time currently used by the city of Moncton and with existing adaptive solutions.

A Traffic Modeling Based Power Saving Mechanism for Mobile Devices in Wireless Systems

In wireless communication networks, power saving is a critical issue. Sleep mode is usually applied to save power in mobile devices; when there is no data to transmit or receive, a mobile device can switch to sleep mode periodically. Evidently, there is a trade-off between power saving and response delay, and the performance of a power saving mechanism depends on user traffic characteristics and how well the power saving mechanism can predict the termination time of an idle period. In the literature, it is commonly accepted that traffic on a highspeed network is self-similar, resulting from heavy-tailed on-off periods. In this paper, we model the on-off durations by generalized Pareto distributions and apply the Xp inspection policy of operational research to power saving mechanism design for wireless communication devices. Numerical examples are provided to show the usefulness of the proposed scheme.

Dynamical mobile terminal location registration in wireless PCS networks

In this paper, we propose a mobile terminal (MT) location registration/update model. In this model, the registration decision is based on two factors-the time elapsed since last call arrival and the distance the MT has traveled since last registration. It is established that the optimal registration strategy can be represented by a curve. Only when the state of the system reaches this curve is a registration performed. In order for an MT to calculate its traveled distance, an interactive implementation scheme and a distance calculation algorithm are developed. When the call interarrival times are independent and geometrically distributed, the proposed model becomes a distance-based model and, in this case, the optimal registration strategy is of threshold structure. For the distance-based model, a single sample path-based ordinal optimization algorithm is devised. In this algorithm, without any knowledge about the system parameters, the MT observes the system state transitions, estimates the ordinal of a set of strategies, and updates the registration strategy adaptively. Since only a single sample path is used, this algorithm can be implemented online. Several numerical examples are provided to compare the proposed model and the existing ones.