Two-dimensional Continuous-time Markov Chain Research Articles

Stability and performance analysis of wireless powered communication networks

In RF-based wireless powered communication networks (WPCNs), the wireless charging rate at a device is usually low or unstable because of health concerns or time-varying characteristics of wireless channels. Under a low charging rate, the data backlog at a wireless device may be continuously increasing, leading to system performance degradation and data loss. To keep a wireless powered device stable and preserve a finite data backlog, the upper limit of data arrival/acquisition rate at a wireless powered device must be solved under the given data transmission rate and wireless charging rate. Hence, in this paper a novel two-dimensional continuous-time Markov chain model was proposed for analyzing the stability condition of a wireless powered device with a finite energy storage buffer. The average number of data packets, average packet delay, and energy shortage probability at a wireless powered device were analyzed as well. Additionally, simulations were conducted to validate the analytic results and demonstrate that the obtained stability condition is necessary and sufficient for the wireless device.

A polling system with ‘Join the shortest - serve the longest’ policy

This paper studies a Markovian single-server non-symmetric two-queue polling system, operating simultaneously under a combination of two well-known queueing regimes: (i) ‘Join the Shortest Queue’ and (ii) ‘Serve the Longest Queue’. The system is defined as a two-dimensional continuous-time Markov chain, and analyzed via both probability generating functions approach and matrix geometric method. Although both queues are unbounded, by applying a non-conventional representation and without resorting to involved boundary-value problem analysis, we derive the joint steady-state probability distribution of the system’s states, and consequently calculate its performance measures and derive its stability condition. Numerical results are presented, as well as a comparison with a corresponding M/G/1 queue.

An Energy Efficient Task Scheduling Strategy in a Cloud Computing System and its Performance Evaluation using a Two-Dimensional Continuous Time Markov Chain Model

With ongoing energy shortages and rises in greenhouse emissions worldwide, increasing academic attention is being turned towards ways to improve the efficiency and sustainability of cloud computing. In this paper, we present a performance analysis and a system optimization of a cloud computing system with an energy efficient task scheduling strategy directed towards satisfying the service level agreement of cloud users while at the same time improving the energy efficiency in cloud computing system. In this paper, we propose a novel energy-aware task scheduling strategy based on a sleep-delay timer and a waking-up threshold. To capture the stochastic behavior of tasks with the proposed strategy, we establish a synchronous vacation queueing system combining vacation-delay and N-policy. Taking into account the total number of tasks and the state of the physical machine (PM), we construct a two-dimensional continuous-time Markov chain (CTMC), and produce an infinitesimal generator. Moreover, by using the geometric-matrix solution method, we analyze the queueing model in the steady state, and then, we derive the system performance measures in terms of the average sojourn time and the energy conservation level. Furthermore, we conduct system experiments to investigate the proposed strategy and validate the system model according to performance measures. Statistical results show that there is a compromise between the different performance measures when setting strategy parameters. By combining different performance measures, we develop a cost function for the system optimization. Finally, by dynamically adjusting the crossover probability and the mutation probability, and initializing the individuals with chaotic equations, we present an improved genetic algorithm to jointly optimize the sleep parameter, the sleep-delay parameter and the waking-up threshold.

Delay performance of data-center queue with setup policy and abandonment

This paper considers a finite capacity multiserver queue for performance modeling of data centers. One of the most important issues in data centers is to save energy of servers. To this end, a natural policy is to turn off a server immediately once it has no job to process. In this policy, which is called ON–OFF policy, the server must be setup upon the arrival of a new job. During the setup time, the server cannot process jobs but consumes energy. To mitigate the drawback, this paper considers a setup policy, where the number of setup servers at a time is limited. We also consider an extension of the setup policy in which some of servers, but not all of them, are allowed to remain idle for a random amount of time. The main purpose of this paper is to analyze the delay distribution of the multiserver queue with the setup policies. We assume that jobs may abandon the queue without receiving their services. We formulate the queue length process using a two-dimensional continuous-time Markov chain. It can be shown that we cannot apply the distributional Little’s law to obtain the waiting time distribution via the queue length distribution. Therefore, we construct a three-dimensional absorbing Markov chain which describes the virtual waiting time process. We then obtain a phase-type expression of the stationary waiting time distribution. We evaluate the performance of the multiserver queue with the setup policy, and then discuss the optimal control parameters of the policy based on the delay performance as well as the mean power consumption.

Simultaneous Two-Dimensional Continuous-Time Markov Chain Approximation of Two-Dimensional Fully Coupled Markov Diffusion Processes

In this paper, we propose a novel simultaneous two-dimensional continuous-time Markov chain (CTMC) approximation method, in contrast to the existing double-layer approach, to approximate the general fully coupled Markov diffusion processes which cover all the classical models. Extensive simulation studies on different kinds of financial option pricing problems in the European, American, and barrier settings, confirm that the proposed methodology has superior accuracy and outperforms the widely applicable Monte Carlo (MC) simulation approach consistently.

An energy-saving strategy based on multi-server vacation queuing theory in cloud data center

Energy consumption is a growing concern in cloud data centers because underutilization of servers results in significant wasted power. Thus, improving server utilization for optimal energy use is now an urgent issue. We propose an energy-saving strategy based on multi-server vacation queuing theory that switches servers between on and sleep in groups. The strategy incorporates both synchronous and asynchronous strategies. When the number of idle servers reaches to a given threshold, idle servers enter sleep mode synchronously as a group. Varying workloads cause groups of servers to sleep asynchronously. We model the data center with our strategy as an M/M/H vacation queuing system and construct a two-dimensional continuous-time Markov chain to formulate the queuing system. Using a powerful matrix-geometric method, we obtain the stationary probability distribution for the system states. We use results from theoretical and simulated experiments to estimate the performance of our approach. The results are valuable for studying the power-performance trade-off in cloud data centers.

An adaptive base stock policy for repairable item inventory control

Abstract This paper presents an adaptive base stock policy for a repairable item inventory control problem. Base stock level of a repairable item is updated based on the work-in-process (WIP) inventory level in repair facility with update frequency modeled as a separate tactical control parameter together with a standard base stock level. Stock-out situations are handled by emergency shipments, and priority shipments are used when updating the base stock level. A single-item single-location problem is considered, with repair facility having a limited capacity, and the problem is modeled by a two-dimensional continuous-time Markov chain, which is then solved explicitly by using matrix geometric methods. Numerical results are provided that show, for a given downtime target, the new policy achieves substantial reduction in inventory on-hand and significant saving in total cost.

Performance Evaluation of Routing Schemes for the Energy-Constrained DTN with Selfish Nodes

Due to the lack of end-to-end paths between the communication source and destination, the routing of Delay Tolerant Networks (DTN) exploits the store-carry-and-forward mechanism. This mechanism requires nodes with sufficient energy to relay and forward messages in a cooperative and selfless way. However, in the real world, the energy is constrained and most of the nodes exhibit selfish behaviors. In this paper, we investigate the performance of DTN routing schemes considering both the energy constraint and selfish behaviors of nodes. First, we model the two-hop relay and epidemic routing based on a two-dimensional continuous time Markov chain. Then, we obtain the system performance of message delivery delay and delivery cost by explicit expressions. Numerical results show that both the energy constraint and node selfishness reduce the message delivery cost at the expense of increasing the message delivery delay. Furthermore, we demonstrate that the energy constraint plays a more important role in the performance of epidemic routing than that of two-hop relay.

An analytical model for SMAC protocol in multi-hop wireless sensor networks

Considering the active/sleep dynamics and the contention backoff scheme of SMAC protocol in multi-hop wireless sensor networks (WSNs), we model each node as a finite single server queue with server shutdown, and model each node’s states as a two-dimensional continuous-time Markov chain. Based on the model, we derive the network performance in terms of average packet loss ratio, network throughput, average packet delay and average power consumption. Experiment comparisons show that the analytical results match well with the simulation results, which validates the accuracy of the analytical model. Furthermore, using the analytical model can enable us to investigate the performance tradeoff between energy efficiency and QoS requirement, and give us theoretical insight into the optimal parameters such as duty cycle, mean active period and buffer size in multi-hop wireless sensor networks.

A New Fair Call Admission Control for Integrated Voice and Data Traffic in Wireless Mobile Networks

It is essential to guarantee a handoff dropping probability below a predetermined threshold for wireless mobile networks. Previous studies have proposed admission control policies for integrated voice/data traffic in wireless mobile networks. However, since QoS has been considered only in terms of CDP (Call Dropping Probability), the result has been a serious CBP (Call Blocking Probability) unfairness problem between voice and data traffic. In this paper, we suggest a new admission control policy that treats integrated voice and data traffic fairly while maintaining the CDP constraint. For underprivileged data traffic, which requires more bandwidth units than voice traffic, the packet is placed in a queue when there are no available resources in the base station, instead of being immediately rejected. Furthermore, we have adapted the biased coin method concept to adjust unfairness in terms of CBP. We analyzed the system model of a cell using both a two-dimensional continuous-time Markov chain and the Gauss-Seidel method. Numerical results demonstrate that our CAC (Call Admission Control) scheme successfully achieves CBP fairness for voice and data traffic.

Determination of Optimal Cell Capacity for Initial Cell Planning in Wireless Cellular Networks

In wireless cellular networks, previous researches on admission control policies and resource allocation algorithm considered the QoS (Quality of Service) in terms of CDP (Call Dropping Probability) and CBP (Call Blocking Probability). However, since the QoS was considered only within a predetermined cell capacity, the results indicated a serious overload problem of systems not guaranteeing both CDP and CBP constraints, especially in the hotspot cell. That is why a close interrelationship between CDP, CBP and cell capacity exists. Thus, it is indispensable to consider optimal cell capacity guaranteeing multiple QoS (CDP and CBP) at the time of initial cell planning for networks deployment. In this paper, we will suggest a distributed determination scheme of optimal cell capacity guaranteeing both CDP and CBP from a long-term perspective for initial cell planning. The cell-provisioning scheme is performed by using both the two-dimensional continuous-time Markov chain and an iterative method called the Gauss-Seidel method. Finally, numerical and simulation results will demonstrate that our scheme successfully determines an optimal cell capacity guaranteeing both CDP and CBP constraints for initial cell planning.

A Light Call Admission Control with Inter-Cell and Inter-Service Fairness in Heterogeneous Packet Radio Networks

In this paper, we propose a new measurement-based fair call admission control policy for heterogeneous packet radio networks. The objectives of the new admission policy are to 1) reduce computation overhead and rapidly re-allocate resources to keep desired Quality of Service (QoS) demands, 2) relieve hot-spot cell by reducing the number of handoff calls from neighboring cells, 3) fairly admit voice and data traffic to prevent declined service degradation. With numerical analysis, we evaluate QoS constraints and inter-cell as well as inter-service fairness by using queuing model, which is described by a two-dimensional continuous-time Markov chain. Finally, we validate our model's accuracy by comparing results of analytical model with ones of event-driven simulation.

Performance analysis of dynamic packet assignment in cellular systems with OFDMA

The authors present a performance analysis of orthogonal frequency division multiple access (OFDMA) based cellular systems with dynamic packet assignment (DPA). Most approaches in the current literature for analysing wireless data networks do not take into account the interference conditions on the radio channel. An analytical model based on a two-dimensional continuous-time Markov chain (CTMC), that takes into account the interference conditions on the OFDM subcarriers in addition to the traffic conditions, is proposed. The authors derive expressions for the mean delay and the average system throughput on the uplink and the downlink in OFDMA based cellular systems with data traffic.

Novel group-based spreading code protocol: hierarchy schedule sensing protocol for CDMA wireless networks

An efficient hierarchy schedule sensing (HSS) spreading code protocol is proposed for wireless DS/CDMA networks. It uses a central pilot frame to schedule request transmissions to avoid collisions. To reduce the scheduling time, hierarchical group-based spreading codes are employed. A two-dimensional continuous time Markov chain is used to model the behaviour of the HSS protocol. The performance is evaluated under various channel traffic loads. The results show that the HSS protocol offers a robust performance without much extra hardware cost if compared with conventional receiver-based spreading code protocols.

Triple-receiver-based code protocol for unslotted DS/SSMA packet-radio networks and its performance analysis

An unslotted DS/SSMA packet-radio protocol (the triple-receiver-based code (R/sup 3/) protocol) suitable for code-division multiple-access (CDMA) wireless data networks is proposed. The communication between two data terminals is initiated by hand-shaking (request and acknowledgement stages) followed by data-packet transmission (pair-up stage), using the receiver-based signature codes for multiple-accessing. The two-dimensional continuous-time Markov chain was used to model and analyse the behaviour of the network. The analytical results show that a respectable improvement in throughput-delay performance can be achieved, applying the proposed protocol to unslotted DS/SSMA packet-radio networks, when compared to other reported code protocols.

A two-echelon multi-server markovian queueing system with a limited intermediate buffer

We consider a two-echelon multi-server tandem queueing system fed by a Poissonian stream of arrivals. There are S k servers at stage k where service times are exponentially distributed with parameter µ k (k = 1,2). The first stage has an unlimited waiting capacity, while the second stage has a finite buffer of size M–S2. Upon service completion at the first stage, a customer leaves the system with probability q, or moves on to request additional service at the second stage. If the intermediate buffer is full, the customer leaves the system with probability 1. Such a model describes, for example, a telephone information system where a customer, after being served by a regular operator, may request a higher-echelon-service from a supervisor. We formulate the problem as a two-dimensional continuous-time Markov chain and derive a set of linear equations, , where is an M + 1-dimensional vector of unknown partial generating functions which determine the steady-state probabilities of the system. The tridiagonal matrix A(z), which contains the parameters, is transformed into an Hessenberg matrix whose determinants yield polynomials with interesting interlacing properties. These properties are exploited to obtain a set of equations in "boundary" probabilities that are required for the complete specification of the generating functions. An example and numerical results are presented.