Power line communication (PLC) networks play an important role in home networks and in next generation hybrid networks, which provide higher data rates (Gbps) and easier connectivity. The standard medium access control (MAC) protocol of PLC networks, IEEE 1901, uses a special carrier sense multiple access with collision avoidance (CSMA/CA) mechanism, in which the deferral counter technology is introduced to avoid unnecessary collisions. Although PLC networks have achieved great commercial success, MAC layer analysis for IEEE 1901 PLC networks received limited attention. Until now, a few studies used renewal theory and strong law of large number (SLLN) to analyze the MAC performance of IEEE 1901 protocol. These studies focus on saturated conditions and neglect the impacts of buffer size and traffic rate. Additionally, they are valid only for homogeneous traffic. Motivated by these limitations, we develop a unified and scalable analytical model for IEEE 1901 protocol in unsaturated conditions, which comprehensively considers the impacts of traffic rate, buffer size, and traffic types (homogeneous or heterogeneous traffic). In the modeling process, a multi-layer discrete Markov chain model is constructed to depict the basic working principle of IEEE 1901 protocol. The queueing process of the station buffer is captured by using Queueing theory. Furthermore, we present a detailed analysis for IEEE 1901 protocol under heterogeneous traffic conditions. Finally, we conduct extensive simulations to verify the analytical model and evaluate the MAC performance of IEEE 1901 protocol in PLC networks.

Using a matrix approach based on a Markov process, we investigate the reliability of a circular connected-(1,2)-or-(2,1)-out-of-(m,n):F lattice system for the i.i.d. case. We develop a modified linear lattice system that is equivalent to this circular system, and propose a methodology that allows the systematic calculation of the reliability. It is based on ideas presented by Fu and Hu [6]. A partial transition probability matrix is used to reduce the computational complexity of the calculations, and closed formulas are derived for special cases.

This paper presents a new, accurate multi-service model of a queueing system with state-dependent distribution of resources for each class of calls. The analysis of the considered queueing system was carried out at both the microstate and macrostate levels. The proposed model makes it possible to evaluate averaged parameters of queues for individual classes of calls that are offered to the system. In addition, the paper proposes a new algorithm for a determination of the occupancy distribution in the queueing system at the microstate level. The results of the calculations are compared with the results of a digital simulation for multi-service queueing systems with state-independent distribution of resources.

Network survivability is defined as the ability of a network keeping connected under failures and/or attacks. In this paper, we propose two stochastic models; binomial model and negative binomial model, to quantify the network survivability and compare them with the existing Poisson model. We give mathematical formulae of approximate network survivability for respective models and use them to carry out the sensitivity analysis on model parameters. Throughout numerical examples it is shown that the network survivability can change drastically when the number of network nodes is relatively small under a severe attack mode which is called the Black hole attack.

In this paper, we discuss the stochastic modeling for operational software reliability measurement, assuming that the testing environment is originally different from the user operation one. In particular, we introduce the concept of systemability which is defined as the reliability characteristic subject to the uncertainty of the field operational environment into the model. First we introduce the environmental factor to consistently bridge the gap between the software failure-occurrence characteristics during the testing and the operation phases. Then we consider the randomness of the environmental factor, i.e., the environmental factor is treated as a random-distributed variable. We use the Markovian imperfect debugging model to describe the software reliability growth phenomena in the testing and the operation phases. We derive the analytical solutions of the several operational software reliability assessment measures which are given as the functions of time and the number of debuggings. Finally, we show several numerical illustrations to investigate the impacts of the consideration of systemability on the field software reliability evaluation.

More and more mobile devices adopt multi-battery and dynamic voltage scaling policy (DVS) to reduce the energy consumption and extend the battery runtime. However, since the nonlinear characteristics of the multi-battery are not considered, the practical efficiency is not good enough. In order to reduce the energy consumption and extend the battery runtime, this paper proposes an approach based on the battery characteristics to implement the co-optimization of the multi-battery scheduling and dynamic voltage scaling on multi-battery powered systems. In this work, considering the nonlinear discharging characteristics of the existing batteries, we use the Markov process to depict the multi-battery discharging behavior, and build a multi-objective optimal model to denote the energy consumption and battery states, then propose a binary tree based algorithm to solve this model. By means of this method, we get an optimal and applicable scheme about multi-battery scheduling and dynamic voltage scaling. Experimental results show that this approach achieves an average improvement in battery runtime of 17.5% over the current methods in physical implementation.

We propose a call admission control scheme in cellular and wireless local area networks (WLANs) integration: integrated service-based admission control with load-balancing capability (ISACL). The novel aspects of the ISACL scheme include that load transfer in the cellular/WLAN overlapping areas is allowed for the admission of originating data calls from the area with cellular access only and vertical handoff requests to the cellular network. Packet-level quality of service (QoS) constraints in the WLANs and other-cell interference in the code division multiple access (CDMA) cellular network are taken into account to derive the WLANs and cellular capacity. We model the integrated networks using a multi-dimensional Markov chain and the important performance measures are derived for effective optimization of the admission parameters. The analytical model is validated by a computer simulation. The variation of admission parameters with traffic load and the dependence of resource utilization on admission parameters are investigated. It is shown that optimal balancing of the traffic load between the cellular network and WLANs results in the maximum resource utilization. Numerical results demonstrate that substantial performance improvements can be achieved by applying the proposed ISACL scheme.

Ultrasonic imaging is useful in seabed or lakebed observations. We can roughly estimate the sea depth by hearing the echo generated by the boundary of water and rocks or sand. However, the estimation quality is usually not sufficient to draw seabed landscape since the echo signal includes serious distortion caused by autointerference. This paper proposes a novel method to visualize the shape of distant boundaries, such as the seawater-rock/sand boundary, based on the complex-valued Markov random field (CMRF) model. Our method realizes adaptive compensation of distortion without changing the global features in the measurement data, and obtains higher-quality landscape with less computational cost than conventional methods.

We propose two vertical handoff schemes for cellular network and wireless local area network (WLAN) integration: integrated service-based handoff (ISH) and integrated service-based handoff with queue capabilities (ISHQ). Compared with existing handoff schemes in integrated cellular/WLAN networks, the proposed schemes consider a more comprehensive set of system characteristics such as different features of voice and data services, dynamic information about the admitted calls, user mobility and vertical handoffs in two directions. The code division multiple access (CDMA) cellular network and IEEE 802.11e WLAN are taken into account in the proposed schemes. We model the integrated networks by using multi-dimensional Markov chains and the major performance measures are derived for voice and data services. The important system parameters such as thresholds to prioritize handoff voice calls and queue sizes are optimized. Numerical results demonstrate that the proposed ISHQ scheme can maximize the utilization of overall bandwidth resources with the best quality of service (QoS) provisioning for voice and data services.

We point out that the interval algorithm can be expressed in the form of a shift on the sequence space. Then we clarify that, by using a Bernoulli process, the interval algorithm can generate only a block of Markov chains or a sequence of independent blocks of Markov chains but not a stationary Markov process. By virtue of the finitary coding constructed by Hamachi and Keane, we obtain the procedure, called the finitary interval algorithm, to generate a Markov process by using the interval algorithm. The finitary interval algorithm also gives maps, defined almost everywhere, which transform a Markov measure to a Bernoulli measure.

The call-level performance modelling is a challenge in the highly heterogeneous environment of modern telecom networks, due to the presence of elastic traffic. In this paper, we review existing teletraffic loss models and propose a model for elastic traffic of service-classes with finite population (quasi-random call arrival process). Upon arrival, calls have contingency alternative bandwidth requirements that depend on thresholds which indicate the available/occupied link bandwidth (state dependent model). Calls are admitted under the complete sharing policy, and can tolerate bandwidth compression, while in-service. We prove a recurrent formula for the efficient calculation of the link occupancy distribution and consequently the call blocking probabilities and link utilization. The accuracy of the proposed model is verified by simulation and is found to be quite satisfactory. Comparative results with other existing models show the necessity and the effectiveness of the proposed model. Its potential applications are mainly in the environment of wireless networks.

This paper presents the characteristics and modeling of VoIP traffic for a real network. The new model, based on measured data, shows a significant difference from the previously proposed models in terms of parameters and their effects. It is found that the effects of background noise and ringing tones have essential influences on the model. The observed distributions of talkspurt and silent durations have long-tail characteristics and considerably differ from the existing models. An additional state called "Long burst", which represents the background noise at the talker's place, is added into the continuous-time Markov process model. The other three states, "Talk", "Short silence" and "Long silence", represent the normal behavior of the VoIP user. Models for conversational speech containing the communication during the dialogue are presented. In the case of the VoIP traffic aggregation, the simplified models, which neglect the conversation's interaction, are proposed. Depending on the occurrences of background noise during the speech, the model is classified as "noisy speech" or "noiseless speech". The measured data shows that the background noise typically increases the data rate by 60%. Simulation results of aggregated VoIP traffic indicate the self-similarity, which is analogous to the measured data. Results from the measurements support the fact that except the ringing duration the conversations from both the directions can be modeled in identical manner.

The problem of optimal placement of pilot symbols is considered for single carrier packet-based transmission over time varying channels. Both flat and frequency-selective fading channels are considered, and the time variation of the channel is modeled by Gauss-Markov process. The semi-blind linear minimum mean-square error (LMMSE) channel estimation is used. Two different performance criteria, namely the maximum mean square error (MSE) of the channel tap state over a packet and the cumulative channel MSE over a packet, are used to compare different placement schemes. The pilot symbols are assumed to be placed in clusters of length (2L+1) where L is the channel order, and only one non-zero training symbols is placed at the center of each cluster. It is shown that, at high SNR, either performance metric is minimized by distributing the pilot clusters throughout the packet periodically. It is shown that at low SNR, the placement is in fact not optimal. Finally, the performance under the periodic placement is compared with that obtained with superimposed pilots.

Wireless LANs have been used for realizing fully-distributed users in a multimedia environment that has the ability to provide real-time bursty traffic (such as voice or video) and data traffic. In this paper, we present a new realistic and detailed system model and a new effective analysis for the performance of wireless LANs which support multimedia communication with non-persistent carrier sense multiple access with collision avoidance (CSMA/CA) protocol. In this CSMA/CA model, a user with a packet ready to transmit initially sends some pulse signals with random intervals within a collision avoidance period before transmitting the packet to verify a clear channel. The system model consists of a finite number of users to efficiently share a common channel. Each user can be a source of both voice traffic and data traffic. The time axis is slotted, and a frame has a large number of slots and includes two parts: the collision avoidance period and the packet transmission period. A discrete-time Markov process is used to model the system operation. The number of slots in a frame can be arbitrary, dependent on the chosen lengths of the collision avoidance period and packet transmission period. Numerical results are shown in terms of channel utilization and average packet delay for different packet generation rates. They indicate that the network performance can be improved by adequate choice of ratios between the collision avoidance period and transmission period, and the pulse transmission probability.

With a view to virtual studio applications, we design an optimal grid pattern such that the observed image of a small portion of it can be matched to its corresponding position in the pattern easily. The grid shape is so determined that the cross ratio of adjacent intervals is different everywhere. The cross ratios are generated by an optimal Markov process that maximizes the accuracy of matching. We test our camera calibration system using the resulting grid pattern in a realistic setting and show that the performance is greatly improved by applying techniques derived from the designed properties of the pattern.

This paper presents an efficient method to derive the first passage time of an extended stochastic Petri net by simple algebraic operations. The reachability graph is derived from an extended stochastic Petri net, and then converted to a timed stochastic state machine which is a semi-Markov process. The mean and the variance of the first passage time are derived by algebraic manipulations with the mean and the variance of the transition time, and the transition probability for each transition in the state machine model. For the derivation, three reduction rules are introduced on the transition trajectories in a well-formed regular expression. An efficient algorithm is provided to automate the suggested method.

We determine the optimum time TOPT to order a spare part for a system before the part in operation has failed. TOPT is a function of the part's failure-time distribution, the lead (delivery) time of the part, its inventory cost, and the cost of downtime while waiting delivery. The probabilities of the system's up and down states are obtained from a non-regenerative stochastic Petri net. TOPT is found by minimizing E[cost], the expected cost of inventory and downtime. Three cases are compared: 1) Exponential order and lead times, 2) Deterministic order time and exponential lead time, and 3) Deterministic order and lead times. In Case 1, it is shown analytically that, depending on the ratio of inventory to downtime costs, the optimum policy is one of three: order a spare part immediately at t = 0, wait until the part in operation fails, or order before failure at TOPT > 0. Numerical examples illustrate the three cases.

In this paper, we construct a software availability model considering the number of restoration actions. We correlate the failure and restoration characteristics of the software system with the cumulative number of corrected faults. Furthermore, we consider an imperfect debugging environment where the detected faults are not always corrected and removed from the system. The time-dependent behavior of the system alternating between up and down states is described by a Markov process. From this model, we can derive quantitative measures for software availability assessment considering the number of restoration actions. Finally, we show numerical examples of software availability analysis.

This paper analyzes first-order full-digital coherent and noncoherent PN code tracking loops for bandlimited baseband direct-sequence spread-spectrum signals under AWGN. The considered loop structures which employ a decimator to control the PN code phase have implementation advantages over loops employing higher-order interpolators. Analytic expressions are derived for the steady-state timing mean squared error, mean pull-in time, mean time to lose lock and the steady-state uncoded and coded bit error rates by employing appropriate Markov chain models. The analytical results are verified to be very accurate via computer simulations. Results are presented for BPSK spreading but extension to QPSK spreading is straightforward.

We develop a software availability model incorporating software failure-occurrence and fault-correction times, under the assumption that the hazard rate for software failure-occurrence decreases geometrically with the progress in fault-removal process. Considering that the software system alternates two states, i.e. the operational state that a system is operating and the maintenance state that a system is inoperable due to the fault-correction activity, we model the time-dependent behavior of the system with a Markov process. Expressions for several quantities of software system perfomance are derived from this model. Finally, numerical examples are presented for illustration of software availability measurement.