Handoff Dwell Time Distribution Effect on Mobile Network Performance

Phase-type (PH) distributions are being used to model a wide range of phenomena in performance and dependability evaluation. The resulting models may be employed in analytical as well as in simulation-driven approaches. Simulations require the efficient generation of random variates from PH distributions. PH distributions have different representations and different associated computational costs for pseudo random-variate generation (PRVG). In this paper we study the problem of efficient representation and efficient generation of PH distributed variates. We introduce various PH representations of different sizes and optimize them according to different cost functions associated with PRVG.

This paper studies a series repairable system with a single repair facility in which the component lifetime and repair time are subject to general distribution that can be represented as Phase-type (PH) distribution. Based on the basic assumption, the proposed model is more suitable to characterize the real situation. The process of solving system steady-state probability is provided, and the analytical expressions for system stationary availability, mean time between failures (MTBF), mean down time (MDT), reliability and failure rate functions are expressed. Finally, the validity and applicability of the model are illustrated with a numerical example.

Employing a cross-layer approach, the explicit relationships between the fading channel characteristics and the significant teletraffic variables as well as the performance metrics in wireless network evaluation are formulated. In particular, the channel holding time, handoff probability, handoff call arrival rate, call blocking probability, call completion probability, and forced termination probability are developed, taking into account the carrier frequency (or equivalently wavelength), maximum Doppler frequency, and fade margin. In addition, the set of formulas are derived with the generalized assumptions for the call holding time and cell residence time. The analytical model has been validated by the simulation with the conventional exponential model and, additionally, the relaxed models for call holding time and cell residence time, e.g., Erlang and hyper-Erlang. The comparison demonstrates that the traditional result without considering the fading channel characteristics leads to substantially overestimated call blocking probability and call completion probability. The methodology presented in this paper provides a feasible manner for the wireless network cross-layer design and optimization

The paper presents a method of performance estimation of IEEE 802.11 wireless networks with linear topology using markovian arrival processes (MAP) for traffic modelling and phase-type (PH) distributions for service time approximation. PH -distribution is reconstructed from the data obtained from the simulation measurements. Markov processes space reduction methods are used to overcome the state-space explosion problem appearing in large-scaled networks analysis. Both tasks of reconstructing PH -distribution and MAP reduction are defined as optimization problems. The performance of the proposed methods is illustrated with numerical examples.

Effective and efficient emergency medical services (EMS) are a critical part of a national healthcare system. This paper describes research to model EMS by better capturing ambulance service times using Coxian phase-type (PH) distributions. Distributions are fitted to both the overall cycle time for different classes of patient priorities, as well as to sub-cycles. Sub-cycles are the distinct identifiable parts of the ambulance cycle time, such as travel times, time on scene and turnaround time at the hospital. The Coxian PH fits have then been used within a priority simulation model to provide guidance on the number of ambulances required to meet response time targets. Results from using various numbers of phases from the fitted Coxian distributions are compared. The proposed benefit of using sub-cycle fits is that it more readily permits scenario modelling within the simulation, such as evaluating the impact of reducing the turnaround time on the overall response times in the ambulance system.

In this paper, we investigate a wear and mixed shock model in which the system can fail due to internal aging or external shocks. The lifetime of the system, due to internal wear, follows continuous phase-type (PH) distributions. The external random shocks arrive at the system according to a PH renewal process. The system will fail when the internal failure occurs or k1 consecutive external shocks, the size of at least d1 or k2 consecutive external shocks the size of at least d2 occur, where d1<d2, k1>k2. The failed system can be repaired immediately, and the repair times of the system are governed by continuous PH distributions. The system can be replaced by a new and identical one based on a bivariate replacement policy (L,N). The long-run average profit rate for the system is obtained by employing the closure property of the PH distribution. Finally, a numerical example is also given to determine the optimal replacement policy.

Considering maintenance resources assignments of the large-scale complex equipment, the policy that single repairman has multiple vacations is utilized to analyze a warm standby repairable system. The former models that the known conditions are usually assumed to follow exponential distribution or other typical distributions have many constraint conditions. It is assumed that the online component lifetime, standby components lifetime, repair time and repairman vacation time are subject to different continuous Phase-type (PH) distribution, respectively. The reliability model with high versatile is acquired. The reliability features, such as system reliability function, system stationary availability, stationary failure frequency and mean time between failures (MTBF), are provided by the model. Finally, the applicability of the model is implemented by numerical application, and the influences of standby components counts and vacations or non-vacation of a repairman on the system reliability laws are demonstrated.

In this paper, we study a multi-server queueing system with retrials and an infinite orbit. The arrival of primary customers is described by a batch Markovian arrival process (BMAP), and the service times have a phase-type (PH) distribution. Previously, in the literature, such a system was mainly considered under the strict assumption that the intervals between the repeated attempts from the orbit have an exponential distribution. Only a few publications dealt with retrial queueing systems with non-exponential inter-retrial times. These publications assumed either the rate of retrials is constant regardless of the number of customers in the orbit or this rate is constant when the number of orbital customers exceeds a certain threshold. Such assumptions essentially simplify the mathematical analysis of the system, but do not reflect the nature of the majority of real-life retrial processes. The main feature of the model under study is that we considered the classical retrial strategy under which the retrial rate is proportional to the number of orbital customers. However, in this case, the assumption of the non-exponential distribution of inter-retrial times leads to insurmountable computational difficulties. To overcome these difficulties, we supposed that inter-retrial times have a phase-type distribution if the number of customers in the orbit is less than or equal to some non-negative integer (threshold) and have an exponential distribution in the contrary case. By appropriately choosing the threshold, one can obtain a sufficiently accurate approximation of the system with a PH distribution of the inter-retrial times. Thus, the model under study takes into account the realistic nature of the retrial process and, at the same time, does not resort to restrictions such as a constant retrial rate or to rough truncation methods often applied to the analysis of retrial queueing systems with an infinite orbit. We describe the behavior of the system by a multi-dimensional Markov chain, derive the stability condition, and calculate the steady-state distribution and the main performance indicators of the system. We made sure numerically that there was a reasonable value of the threshold under which our model can be served as a good approximation of the BMAP/PH/N queueing system with the PH distribution of inter-retrial times. We also numerically compared the system under consideration with the corresponding queueing system having exponentially distributed inter-retrial times and saw that the latter is a poor approximation of the system with the PH distribution of inter-retrial times. We present a number of illustrative numerical examples to analyze the behavior of the system performance indicators depending on the system parameters, the variance of inter-retrial times, and the correlation in the input flow.

Efficient and accurate methods are indispensible in the evaluation of complex systems. Methods of various abstraction levels may be applied, ranging from measurements in test-beds over simulation to analytical approaches. These methods vary in their efficiency and accuracy. In order to obtain realistic results, methods from all abstraction levels should be applied. Furthermore, real-world phenomena must be represented in a suitable way at all abstraction levels. This approach requires the use of stochastic models for the faults that may affect a system. This thesis explores several important issues of system evaluation using stochastic fault models. The first part of the thesis provides a survey of stochastic fault-models for system evaluation. We survey a broad range of existing fault-models and provide a new classification scheme for fault models in service-oriented systems. In the second part of the thesis we address the use of phase-type (PH) distributions as fault models in system evaluation. We study algorithms for random-variate generation and discuss their computational costs. An optimisation method for reducing the cost of random-variate generation by transformation of the representation is presented and an optimality result for the sub-class of acyclic phase-type distributions is derived. We then develop a new algorithm for efficient and user-friendly fitting of PH distributions to data sets using clustering. The algorithm is implemented as part of the HyperStar tool. We additionally illustrate application of HyperStar as a graphical user interface for prototype algorithms using a new algorithm for fitting general PH distributions. The third part illustrates application of the results from the first and second parts. We first study the application of stochastic fault models for IP packet loss in fault-injection and investigate the interaction between fault models and traffic arrival streams and its impact on evaluation results. We then describe a library for random-variate generation from phase-type distributions and show its use in two case-studies.

Phase-type (PH) fitting is a technique to approximate any general distribution as a PH distribution, which is a probability distribution representing an absorbing time of a Markov chain. Since the PH distribution is described as a discrete- or continuous-time Markov chain (CTMC), the PH fitting can provide approximate Markov models to any non-exponential stochastic models. Thus, the PH fitting is helpful for model-based performance evaluation. On the other hand, from the statistical point of view, the PH fitting is categorized as parameter estimation from data. Some efficient PH fitting techniques are based on the maximum-likelihood principle. Therefore, it is crucial to evaluate statistical errors, i.e., the variance and covariance of estimators. In maximum-likelihood estimation, the Fisher information matrix is a well-known method to compute the variance and covariance of estimators, and is obtained as the second derivative of the log-likelihood function (LLF). In this article, we propose an algorithm for efficiently computing the Fisher information matrix in PH fitting. By applying the uniformization technique to a CTMC, we design the algorithm for computing the second derivatives of LLF in PH fitting.

In this paper, the waiting time analysis for an OFDMA wireless cellular system with finite buffering and Adaptive Modulation and Coding (AMC) is addressed. When AMC is considered, several concentric regions within cells serving users with different data rates are differentiated. Phase type (PHT) distribution functions are used to model the conditional cumulative distribution function of the waiting time for users in the different coverage regions. The representation of the conditional waiting time distribution through PHT distributions allows expressing cumulative distribution function (CDF) as a linear combination of negative exponential distributions. The analytical method proposed here captures the exact behavior of the waiting time and the obtained solution is based on matrix analytic derivation, which allows evaluating system performance for any size of buffer and any number of coverage regions.

In this paper authors propose the approach for investigation of photonic switches performance metrics in modern all-optical networks. The approach includes photonic switches analytical and simulation modeling. The analytical model of the $$4\times 4$$ -photonic switch is based on the M/M/1/4 queuing model using so-called probability translation matrix method that allows to investigate functioning of the system in transient mode. The analytical expressions of such performance metrics as a loss probability, a buffer size and a transient time are obtained. A comparison of analytical and simulation modeling results was carried out. The analysis show that the steady-state loss probability obtained in results of analytical modeling is greater than the analogous parameter obtained in results of simulation modelling by 8%. The study of simulation models of $$4\times 4$$ and $$16\times 16$$ -photonic switches show that the buffer size of these systems does not exceed one packet. Analysis of the $$16\times 16$$ -photonic switch buffer show that the buffer size of the first cascade is four times larger than the buffer of the second cascade. The results of the investigation show that the proposed type of photonic switches can be used in the high-performance all-optical network designed to transmit information from the ground module to tethered high-altitude unmanned module and vice versa.

This study presents models for management of voice and data traffic and new algorithms, which use call admission control as well as buffer management to optimise the performance of single channel systems such as wireless local area networks in the presence of mobile stations. Unlike existing studies, the new approach queues incoming voice packets as well as data packets, and uses a new pre-emption algorithm in order to keep the response time of voice requests at certain levels while the blocking of data requests is minimised. A new performance metric is introduced to provide uncorrelated handling of integrated services. Queueing related issues such as overall queue capacity, individual capacities for voice and data requests, the probability of blocking, and effects of waiting time on overall quality of service are considered in detail. Analytical models are presented and the results obtained from the analytical models were validated using discrete event simulations.

Downlink throughput performance in Long Term Evolution - Advanced (LTE-A) networks has been widely investigated by many simulation studies. However, these studies generally assume that users are uniformly distributed in regularly arranged hexagonal cells. Analytical models and methods of stochastic geometry have been applied to wireless networks to consider the effects of spatial configuration of nodes and base stations on network performance by abstracting away many details of the systems. As such, comprehensive studies of the effects of spatial factors on throughput performance using standard-compliant, open-source software that simulates many details of LTE-A networks are still scarce. In this paper, we use the Vienna LTE-A Downlink System Level Simulator to re-evaluate the validity of usual throughput performance metrics under various spatial deployment scenarios and employ statistical methods to determine the significance of performance observations. Our primary aim is to show that clustered user deployments around a base station exhibit significantly different throughput performance compared to the case of uniformly distributed users throughout the cell. This is important since in practice, base stations are deployed in areas of high user density. In addition, we show that the most widely used scheduling scheme in cellular networks, namely the proportional fair scheduling, may lose its performance advantage over round robin scheduling when users are clustered around the base station. These findings are expected to have implications on the design and deployment of next generation cellular networks.

For a continuous-time phase-type (PH) distribution, starting with its Laplace–Stieltjes transform, we obtain a necessary and sufficient condition for its minimal PH representation to have the same order as its algebraic degree. To facilitate finding this minimal representation, we transform this condition equivalently into a non-convex optimization problem, which can be effectively addressed using an alternating minimization algorithm. The algorithm convergence is also proved. Moreover, the method we develop for the continuous-time PH distributions can be used directly for the discrete-time PH distributions after establishing an equivalence between the minimal representation problems for continuous-time and discrete-time PH distributions.