On a Stein method based approximation for a two-dimensional Markov chain

This paper aims to investigate the impacts of sensing energy and data availability on the secondary throughput of energy harvesting cognitive radio networks (EH-CRNs), where secondary transmitters (STs) are powered by the energy harvested from primary radio frequency (RF) signals. To reach the aim, we consider two extreme cases by employing two data arrival processes: heavy data arrival and general data arrival. In the heavy data arrival case, we consider STs always have data to transmit, and study the impacts of sensing energy on the secondary throughput. In the general data arrival case, we consider the data arrives with a certain probability, and study the impacts of data availability (i.e., data arrival probability and data buffer capacity) on the secondary throughput. Moreover, to compare the secondary throughput under non-cooperative spectrum sensing (NCSS) and cooperative spectrum sensing (CSS), we further study two CRN scenarios for each data arrival case: <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Scenario 1</i> with one pair of secondary users (SUs) conducting NCSS, and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Scenario 2</i> with multiple pairs of SUs conducting CSS. As the harvest-then-transmit protocol is employed by STs, it is essential to balance energy harvesting and data transmission to achieve high secondary throughput. We thus utilize an energy threshold approach to determine the actions of each ST. Specifically, under the heavy data arrival, we derive the average secondary throughput for each scenario by taking the sensing energy as an energy unit and modeling the energy states of each ST as a Markov chain. Under the general data arrival, we derive the secondary throughput for each scenario by modeling the energy and data states of each ST as a two-dimensional Markov chain. Simulation results show that: (1) both the secondary throughput and the optimal energy threshold decrease with the sensing energy; (2) the secondary throughput increases with the data availability, while the optimal energy threshold decreases with the data availability; (3) from the normalized secondary throughput perspective, CSS is not always better than NCSS.

Coexistence between networks is an emerging challenge in the 60 GHz unlicensed band. An approximate analytical formulation of the saturated throughput of a cognitive IEEE 802.15.3c MAC in the directional contention access period (D-CAP) in the presence of contention time allocation period (CTAP) is presented in this paper. The analytical framework is formulated for N devices, including the pico-net controller (PNC). The state transition diagram is modeled by a two-dimensional discrete-time Markov chain. One dimension of the Markov chain is for the backoff stage and the second dimension is for the value of the backoff counter. The saturated throughput is approximated by the product of a weighted ratio of the throughput of the regular sub-CAP (RS-CAP) and the throughput of the RS-CAP minus the period necessary to transmit a packet before the end of the current RS-CAP, the probability of the number of devices in a beam sector, the number of beam sectors and the probability of false alarm. Numerical results of the saturated throughput corresponding to typical parameter values are presented. These results show the advantage of the cognitive IEEE 802.15.3c MAC in the D-CAP using the single carrier mode when the number of devices in the WPAN is large.

An analytical formulation of the saturated throughput enhancement of IEEE 802.11e using double increment plus one/ minus one half decrement (DIPO/MOHD) backoff mechanism for multiclass traffic is presented The analytical framework is formulated for N classes. The state transition diagram for the ith priority class is modeled by a two-dimensional discrete-time Markov chain One dimension of the Markov chain is for the backoff stage, and the second dimension is for the value of the backoff counter. The backoff stage moves to its previous backoff stage after a successful packet transmission and not back to the backoff stage 0 as in IEEE 802. lie. The advantages of this backoff mechanism are that it is easy to be implemented and can enhance the saturated throughputs. Numerical results of the saturated throughput corresponding to typical parameter values are presented The results show that the total saturated throughput using DIPO/MOHD can be better than that of IEEE 802. lie by up to 19%.

A stochastic ordering approach is applied with Stein's method for approximation by the equilibrium distribution of a birth-death process. The usual stochastic order and the more general s-convex orders are discussed. Attention is focused on Poisson and translated Poisson approximations of a sum of dependent Bernoulli random variables, for example, k-runs in independent and identically distributed Bernoulli trials. Other applications include approximation by polynomial birth-death distributions.

Adaptive lead time quotation in a pull production system with lead time responsive demand

Time-sensitive networking (TSN), a cutting-edge technology enabling efficient real-time communication and control, provides strong support for traditional Ethernet in terms of real-time performance, reliability, and deterministic transmission. In TSN systems, although time-triggered (TT) flows enjoy deterministic delay guarantees, audio video bridging (AVB) and best effort (BE) traffic still share link bandwidth through statistical multiplexing, a process that remains nondeterministic. This competition in shared memory switches adversely affects data transmission performance. In this paper, a priority queue threshold control policy is proposed and analyzed for mixed-critical traffic in time-sensitive networks. The core of this policy is to set independent queues for different types of traffic in the shared memory queuing system. To prevent low-priority traffic from monopolizing the shared buffer, its entry into the queue is blocked when buffer usage exceeds a preset threshold. A two-dimensional Markov chain is introduced to accurately construct the system’s queuing model. Through detailed analysis of the queuing model, the truncated chain method is used to decompose the two-dimensional state space into solvable one-dimensional sub-problems, and the approximate solution of the system’s steady-state distribution is derived. Based on this, the blocking probability, average queue length, and average queuing delay of different priority queues are accurately calculated. Finally, according to the optimization goal of the overall blocking probability of the system, the optimal threshold value is determined to achieve better system performance. Numerical results show that this strategy can effectively allocate the shared buffer space in multi-priority traffic scenarios. Compared with the conventional schemes, the queue blocking probability is reduced by approximately 40% to 60%.

Dynamic spectrum access (DSA) is important for spectrum management in the future. DSA with prioritization for two types of radio systems are presented through analytical formulation. The DSA with prioritization model is solved numerically using a two-dimensional Markov chain. Grades of service (GoSs) like system airtime and blocking probabilities are considered. The performance of these GoS measures and the effect of the size of the number of frequency channels for DSA with prioritization are evaluated. Numerical results illustrate that the advantages of DSA with prioritization for one type radio system over another type of radio system.

In this paper, we propose a direct-sequence spread spectrum multiple access (DS/SSMA) unslotted ALOHA system with two user classes and analyze the throughput of the proposed system. Mobile stations (MSs) are divided into two classes according to priority or traffic characteristics such as delay-intolerant and delay-tolerant. Different permission probabilities are assigned to each class so that the appropriate quality of service can be provided. We assume that the generation of class 1 and 2 messages are Poisson distributed and the message is divided into several packets before transmission. The system is modeled as a two-dimensional Markov chain under the assumption that the number of packets transmitted immediately by both user classes is geometrically distributed and the packet length is constant. We calculate the packet success probability and the throughput as a function of the signal-to-noise ratio (SNR) during packet transmission, considering the number of overlapped class 1 and 2 messages and the amount of their time overlap. Moreover, we show that the proposed system differentiates user messages according to class and maintains a high throughput even under heavy traffic conditions using access control based on the channel load.

In a cognitive wireless network, sudden arrival of a primary user could force one or more secondary users to terminate their ongoing communication. This situation leads us to propose a cognitive wireless network which dynamically assigns service rates to the secondary users depending on the available network spectral resource. Our analysis is based on a two-dimensional Markov chain with three state variables. Performance metrics for the secondary users such as dropping probability, blocking probability and completion probability are derived. Our numerical result demonstrates that, depending on the network condition, the proposed dynamic spectrum assignment scheme is capable of reducing the dropping probability substantially and yielding higher throughput via increasing the maximum allowable service rate. Analysis of blocking probability implies that higher value of the maximum allowable service rate may or may not make the network more selective in terms of admitting new secondary users.

Changes in the process mean (μ) or in the process standard deviation (σ) ought to be regarded as an indication that a production process is out of control. This paper considers the problem of the joint monitoring of these two parameters — when the quality characteristic follows a normal distribution —, using a combined Exponentially Weighted Moving Average (CEWMA) scheme. Three performance measures of this joint control scheme are investigated under shifts in the process mean or inflations of the process standard deviation, and under the adoption of head starts: the average run length, the run length percentage points and the probability of a misleading signal. Approximations to these three performance indicators will be obtained considering a two-dimensional Markov chain. The independence between the horizontal and vertical transitions of this approximating two-dimensional Markov chain plays an important role in providing simple expressions to those performance measures which avoid the computation of a probability transition matrix with unusual dimensions. A numerical comparison between these three performance measures and the corresponding ones of the matched combined Shewhart (CShewhart) scheme will be also presented, leading to the conclusion that the substituition of this combined scheme by the CEWMA scheme can improve the joint monitoring of the process mean and standard deviation.

In this paper we analyze the medium access control (MAC) of fixed WiMAX with respect to best effort (BE) traffic. WiMAX employs a contention based method with exponential backoff to facilitate multiple access. A two-dimensional Markov chain can be used to accurately model the backoff procedure. From this we derived expressions for channel access probability, access delay, system throughput and resource usage. The accuracy of the model and its results are validated by simulations carried out on an IEEE 802.16d simulator. Constraints and limitations of the model are also discussed. Insight from this model can be used to optimize bandwidth usage and channel partitioning.

The IEEE 802.11 protocols are used by millions of smartphone and tablet devices to access the Internet via Wi-Fi wireless networks or communicate with one another directly in a peer-to-peer mode. Insider attacks are those originating from a trusted node that had initially passed all the authentication steps to access the network and then got compromised. A trusted node that has turned rogue can easily perform Denial-of-Service (DoS) attacks on the Media Access Control (MAC) layer by illegally capturing the channel and preventing other legitimate nodes from communicating with one another. Insider attackers can alter the implementation of the IEEE 802.11 Distributed Coordination Function (DCF) protocol residing in the Network Interface Card (NIC) to illegally increase the probability of successful packet transmissions into the channel at the expenses of nodes that follow the protocol standards. The attacker fools the NIC to upgrade its firmware and forces in a version containing the malicious code. In this paper, we present a distributed solution to detect and isolate the attacker in order to minimize the impact of the DoS attacks on the network. Our detection algorithm enhances the DCF firmware to enable honest nodes to monitor each other's traffic and compare their observations against honest communication patterns derived from a two-dimensional Markov chain. A channel hopping scheme is then used on the physical layer (PHY) to evade the attacker. To facilitate communication among the honest member stations and minimize network downtime, we introduce two isolation algorithms, one based on identity-based encryption and another based on broadcast encryption. Our simulation results show that the latter enjoys quicker recovery time and faster network convergence.

This paper proposes a novel call admission control (CAC) algorithm and develops a two-dimensional markov chain processes (MCP) analytical model to evaluate its performance for heterogeneous wireless network. Within the context of this paper, a hybrid UMTS-WLAN network is investigated. The designed threshold-based CAC algorithm is launched basing on the user’s classification and channel allocation policy. In this approach, channels are assigned dynamically in accordance with user class differentiation. The two-dimensional MCP mathematical analytic method reflects the system performance by appraising the dropping likelihood of handover traffics. The results show that the new CAC algorithm increases the admission probability of handover traffics, while guarantees the system quality of service (QoS) requirement.KeywordsCall admission controlhandovertwo-dimension markov chainheterogeneous networksdropping probability

A receiver-based protocol for spread-spectrum multiple-access networks is proposed and analyzed. This scheme is based on a handshake procedure before any formal transmission of data packets. The protocol is collision-free during data transmission and can limit the number of simultaneous transmissions. The system is modeled as a two-dimensional Markov chain from which the throughput can be determined. Numerical results are presented and compared with those for other protocols. With a minislotted channel, the handshaking time is reasonably short, and it is shown that the performance can be significantly improved when the average packet length is not too small. Moreover, very high throughput can still be maintained, even when the offered traffic is high. The proposed protocol can be applied in multipoint to point situations as well as in multihop radio networks with a central station in each hop. >

Modeling and analysis of a supply–assembly–store chain