JIMO
Performance analysis and evaluation for power saving class type III in IEEE 802.16e network
Shunfu Jin Wuyi Yue
Journal of Industrial & Management Optimization 2010, 6(3): 691-708 doi: 10.3934/jimo.2010.6.691
In this paper, we present an enhanced power saving class (PSC) type III by introducing a sleep-delay mechanism into the conventional PSC type III in the IEEE 802.16e network. Two multiple vacation queueing models: without sleep-delay and with sleep-delay, are built to capture the working principles of the conventional PSC type III and the enhanced PSC type III, respectively. Then, using the boundary state variable theory method, we analyze these queueing models and give the performance measures in terms of the switch ratio, the power saving ratio, the average response time and the system utility for both the conventional and the enhanced power saving schemes. Next, numerical results are given to demonstrate the dependency relationships between the performance measures and the sleep window size. Moreover, we compare the performance of the both systems without sleep-delay (the conventional PSC type III) and with sleep-delay (the enhanced PSC type III) to validate the effect of the sleep-delay mechanism in the enhanced PSC type III proposed in this paper. Finally, we also construct a cost function to determine the optimal time length of the sleep-delay timer for minimizing the cost function.
keywords: sleep mode power saving class type III IEEE 802.16e sleep-delay performance evaluation.
JIMO
Analysis of an M/M/1 queueing system with impatient customers and a variant of multiple vacation policy
Dequan Yue Wuyi Yue Zsolt Saffer Xiaohong Chen
Journal of Industrial & Management Optimization 2014, 10(1): 89-112 doi: 10.3934/jimo.2014.10.89
In this paper, we consider an M/M/1 queueing system with impatient customers and a variant of multiple vacation policy, where we examine the case that customer impatience is due to the servers' vacation. Whenever a system becomes empty, the server takes a vacation. However, the server is allowed to take a maximum number $K$ of vacations if the system remains empty after the end of a vacation. This vacation policy includes both a single vacation and multiple vacations as special cases. We derive the probability generating functions of the steady-state probabilities and obtain the closed-form expressions of the system sizes when the server is in different states. We further make comparisons between the mean system sizes under the variant vacation policy and the mean system sizes under the single vacation policy or the multiple vacation policy. In addition, we obtain the closed-form expressions for other important performance measures and discuss their monotonicity with respect $K$. Finally, we present some numerical results to show the effects of some parameters on some performance measures.
keywords: mean system size. probability generating function a variant of multiple vacation impatience Queue
JIMO
A novel active DRX mechanism in LTE technology and its performance evaluation
Shunfu Jin Wuyi Yue Chao Meng Zsolt Saffer
Journal of Industrial & Management Optimization 2015, 11(3): 849-866 doi: 10.3934/jimo.2015.11.849
With the development of communication technology, the functions of the mobile terminals are becoming ever more enhanced, and the energy requirements for the terminals become harder than before. In this paper we propose a novel Active Discontinuous Reception (DRX) mechanism with a sleep-delay strategy in the Long Term Evolution (LTE) technology in order to reduce the average latency while saving more energy in 4G networks. The key idea is to influence the control of the downlink transmission on that way that the system would go to sleep only when there is no data frame arrival within the sleep-delay timer. Considering several logical channels for one connection, we model the network using the novel Active DRX mechanism with a sleep-delay strategy as a multiple synchronous vacation queueing system with a wake-up period and a sleep-delay. We derive several performance measures, such as the energy saving ratio, the system blocking ratio and the average latency. We also provide numerical results by means of analysis and simulation to show the validity of the novel Active DRX mechanism. Finally by constructing a profit function, we optimize several system parameters in terms of the number of the logical channels for one connection, the time lengths of the sleep-delay timer and the sleep period.
keywords: performance evaluation active DRX synchronization vacation sleep-delay LTE multiple channels system optimization.
JIMO
Optimal execution strategy with an endogenously determined sales period
Guibin Lu Qiying Hu Youying Zhou Wuyi Yue
Journal of Industrial & Management Optimization 2005, 1(3): 289-304 doi: 10.3934/jimo.2005.1.289
We discuss the problem of the optimal liquidation of a financial product in which both the market risk of the asset and the market impact of the investor's own dealings are considered, and where the asset is liquidated over several sales periods with a constant sales interval. The investor chooses the sales volume in each period as well as the volume over the entire sales period in order to minimize the expected execution costs under a certain level of risk. We obtain an explicit solution for the optimal execution strategies and present four numerical examples to show that the proportion between market risk and liquidity risk exerts a major influence over the optimal execution strategy. We also show that to obtain the optimal result the investor should liquidate his holdings over a short sales period.
keywords: optimal execution strategy market impact dynamic programming. sales period market risk
JIMO
A dual tandem queueing system with GI service time at the first queue
Zsolt Saffer Wuyi Yue
Journal of Industrial & Management Optimization 2014, 10(1): 167-192 doi: 10.3934/jimo.2014.10.167
In this paper we consider the analysis of a tandem queueing model $M/G/1 -> ./M/1$. In contrast to the vast majority of the previous literature on tandem queuing models we consider the case with GI service time at the first queue and with infinite buffers. The system can be described by an M/G/1-type Markov process at the departure epochs of the first queue. The main result of the paper is the steady-state vector generating function at the embedded epochs, which characterizes the joint distribution of the number of customers at both queues. The steady-state Laplace-Stieljes transform and the mean of the sojourn time of the customers in the system are also obtained.
    We provide numerical examples and discuss the dependency of the steady-state mean of the sojourn time of the customers on several basic system parameters. Utilizing the structural characteristics of the model we discuss the interpretation of the results. This gives an insight into the behavior of this tandem queuing model and can be a base for developing approximations for it.
keywords: Queueing theory M/G/1-type Markov process tandem queueing model G/M/1-type Markov process.
JIMO
Performance evaluation and optimization of cognitive radio networks with adjustable access control for multiple secondary users
Yuan Zhao Wuyi Yue
Journal of Industrial & Management Optimization 2018, 13(5): 1-14 doi: 10.3934/jimo.2018029

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.

keywords: Cognitive radio networks multiple secondary users access control adjustment factor optimization
JIMO
Optimal control for resource allocation in discrete event systems
Qiying Hu Wuyi Yue
Journal of Industrial & Management Optimization 2006, 2(1): 63-80 doi: 10.3934/jimo.2006.2.63
Supervisory control for discrete event systems (DESs) belongs essentially to the logic level for control problems in DESs. Its corresponding control task is hard. In this paper, we study a new optimal control problem in DESs. The performance measure is to maximize the maximal discounted total reward among all possible strings (i.e., paths) of the controlled system. The condition we need for this is only that the performance measure is well defined. We then divide the problem into three sub-cases where the optimal values are respectively finite, positive infinite and negative infinite. We then show the optimality equation in the case with a finite optimal value. Also, we characterize the optimality equation together with its solutions and characterize the structure of the set of all optimal policies. All the results are still true when the performance measure is to maximize the minimal discounted total reward among all possible strings of the controlled system. Finally, we apply these equations and solutions to a resource allocation system. The system may be deadlocked and in order to avoid the deadlock we can either prohibit occurrence of some events or resolve the deadlock. It is shown that from the view of the maximal discounted total cost, it is better to resolve the deadlock if and only if the cost for resolving the deadlock is less than the threshold value.
keywords: resource allocation system. discrete event systems Optimal control
JIMO
Performance analysis of a P2P storage system with a lazy replica repair policy
Shunfu Jin Yuan Zhao Wuyi Yue Lingling Chen
Journal of Industrial & Management Optimization 2014, 10(1): 151-166 doi: 10.3934/jimo.2014.10.151
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.
keywords: three-dimensional Markov chain lazy replica repair benefit function. matrix-geometric method P2P storage system
DCDS-B
Optimal control for discrete event systems with arbitrary control pattern
Qiying Hu Wuyi Yue
Discrete & Continuous Dynamical Systems - B 2006, 6(3): 535-558 doi: 10.3934/dcdsb.2006.6.535
In this paper, we present a new model for optimal control of discrete event systems (DESs) with an arbitrary control pattern. Here, a discrete event system is defined as a collection of event sets that depend on strings. When the system generates a string, the next event that may occur should be in the corresponding event set. In the optimal control model, there are rewards for choosing control inputs at strings and the sets of available control inputs also depend on strings. The performance measure is to find a policy under the condition where the discounted total reward among strings from the initial state is maximized. By applying ideas from Markov decision processes, we divide the problem into three sub-cases where the optimal value is respectively finite, positive infinite and negative infinite. For the case with finite optimal values, the optimality equation is shown and further characterized with its solutions. We also characterize the structure of the set of all optimal policies. Moreover, we discuss invariance and closeness of several languages. We present a new supervisory control problem of DESs with the control pattern being dependent on strings. We study the problem in both the event feedback control and the state feedback control by generalizing concepts of invariant and closed languages/predicates. Finally, we apply the above model and results to a job-matching problem.
keywords: Markov decision processes. supervisory control problem Optimal control arbitrary control patterns optimality equation
JIMO
Two new optimal models for controlling discrete event systems
Qiying Hu Wuyi Yue
Journal of Industrial & Management Optimization 2005, 1(1): 65-80 doi: 10.3934/jimo.2005.1.65
Supervisory control belongs essentially to the logic level for control problems in discrete event systems (DESs) and its corresponding control task is hard. This is unlike many practical optimal control problems which belong to the performance level and whose control tasks are soft. In this paper, we present two new optimal control problems of DESs: one with cost functions for choosing control inputs, and the other for occurring events. Their performance measures are to minimize the maximal discounted total cost among all possible strings that the system generates. Since this is a nonlinear optimization problem, we model such systems by using Markov decision processes. We then present the optimality equations for both control problems and obtain their optimal solutions. When the cost functions are stationary, we show that both the optimality equations and their solutions are also stationary. We then use these equations and solutions to describe and solve uniformly the basic synthesizing problems in the two branches of the supervisory control area: those being the event feedback control and the state feedback control. Moreover, we show that the control invariant languages and the control invariant predicates with their permissive supervisors and state feedbacks not only have meanings in supervisory control of DESs, but are also the optimal solutions for some optimal control problems. This shows a link existing between the logic level and the performance level for the control of discrete event systems. Finally, a numerical example is given to illustrate some results for supervisory control of a DES.
keywords: Optimal control discrete event systems state feedback. supervisor

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