Hyper-Erlang Distribution Model and its Application in Wireless Mobile Networks

This paper presents the study of the hyper-Erlang distribution model and its applications in wireless networks and mobile computing systems. We demonstrate that the hyper-Erlang model provides a very general model for users' mobility and may provide a viable approximation to fat-tailed distribution which leads to the self-similar traffic. The significant difference from the traditional approach in the self-similarity study is that we want to provide an approximation model which preserves the Markovian property of the resulting queueing systems. We also illustrate that the hyper-Erlang distribution is a natural model for the characterization of the systems with mixed types of traffics. As an application, we apply the hyper-Erlang distribution to model the cell residence time (for users' mobility) and demonstrate the effect on channel holding time. This research may open a new avenue for traffic modeling and performance evaluation for future wireless networks and mobile computing systems, over which multiple types of services (voice, data or multimedia) will be supported.     

Modeling PCS networks under general call holding time and cellresidence time distributions

In a personal communication service (PCS) network, the call completion probability and the effective call holding times for both complete and incomplete calls are central parameters in the network cost/performance evaluation. These quantities will depend on the distributions of call holding times and cell residence times. The classical assumptions made in the past that call holding times and cell residence times are exponentially distributed are not appropriate for the emerging PCS networks. This paper presents some systematic results on the probability of call completion and the effective call holding time distributions for complete and incomplete calls with general cell residence times and call holding times distributed with various distributions such as gamma, erlang, hyperexponential, hyper-erlang, and other staged distributions. These results provide a set of alternatives for PCS network modeling, which can be chosen to accommodate the measured data from PCS field trials. The application of these results in billing rate planning is also discussed     

Mobility modeling and analytical solution for spatial traffic distribution in wireless multimedia networks

In this paper, we propose a general mobility model suitable for wireless multimedia networks. Our model is based on splitting a region into subregions. Furthermore, we make an analogy between subregions as well as their inter-connections with a multi-class Jackson queueing network comprising of infinite-server nodes. The main attribute of such a network is due to its product-form stationary distribution. Using this model, we are able to obtain a closed analytical form for the spatial traffic distribution corresponding to a specific number of network-connected users with different classes of service and mobility in a typical region. Also, we show the flexibility obtained by the proposed mobility model in representing some general distributions such as sum-of-hyper-exponentials (SOHYP), hyper-Erlang and Cox which were previously suggested to model mobility-related statistical parameters, e.g., cell dwell time and channel holding time. Finally, we apply the proposed model to a few mobility scenarios and obtain the resultant active user's location density.     

Performance Analysis of Wireless Networks Over Rayleigh Fading Channel

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.     

Modeling and analysis of hierarchical cellular networks with general distributions of call and cell residence times

We present an analytic model for the performance evaluation of hierarchical cellular systems, which can provide multiple routes for calls through overflow from one cell layer to another. Our model allows the case where both the call time and the cell residence time are generally distributed. Based on the characterization of the call time by a hyper-Erlang distribution, the Laplace transform of channel occupancy time distribution for each call type (new call, handoff call, and overflow call) is derived as a function of the Laplace transform of cell residence time. In particular, overflow calls are modeled by using a renewal process. Performance measures are derived based on the product form solution of a loss system with capacity limitation. Numerical results show that the distribution type of call time and/or cell residence time has influence on the performance measure and that the exponential case may underestimate the system performance.     

A Mobility Model and Performance Analysis in Wireless Cellular Network with General Distribution and Multi-Cell Model

Multi-cell mobility model and performance analysis for wireless cellular networks are presented. The mobility model plays an important role in characterizing different mobility-related parameters such as handoff call arrival rate, blocking or dropping probability, and channel holding time. We present a novel tractable multi-cell mobility model for wireless cellular networks under the general assumptions that the cell dwell times induced by mobiles’ mobility and call holding times are modeled by using a general distribution instead of exponential distribution. We propose a novel generalized closed-form matrix formula to support the multi-cell mobility model and call holding time with general distributions. This allows us to develop a fixed point algorithm to compute loss probabilities, and handoff call arrival rate under the given assumptions. In order to reduce computational complexity of the fixed point algorithm, the channel holding time of each cell is down-modeled into an exponentially distributed one for purposes of simplification, since the service time is insensitive in computing loss probabilities of each cell due to Erlang insensitivity. The accuracy of the multi-cell analytic mobility model is supported by the comparison of the simulation results and the analytic ones.     

A Homogeneous PCS network with Markov Call Arrival Process and Phase Type Cell Residence Time

In this paper, the arrival of calls (i.e., new and handoff calls) in a personal communications services (PCS) network is modeled by a Markov arrival process (MAP) in which we allow correlation of the interarrival times among new calls, among handoff calls, as well as between these two kinds of calls. The PCS network consists of homogeneous cells and each cell consists of a finite number of channels. Under the conditions that both cell's residence time and the requested call holding time possess the general phase type (PH) distribution, we obtain the distribution of the channel holding times, the new call blocking probability and the handoff call failure probability. Furthermore, we prove that the cell residence time is PH distribution if and only if the new call channel holding time is PH distribution; or the handoff call channel holding time is PH distribution; or the call channel holding time is PH distribution;provided that the requested call holding time is a PH distribution and the total call arrival process is a MAP. Also, we prove that the actual call holding time of a non-blocked new call is a mixture of PH distributions. We then developed the Markov process for describing the system and found the complexity of this Markov process. Finally, two interesting measures for the network users, i.e., the duration of new call blocking period and the duration of handoff call blocking period, are introduced; their distributions and the expectations are then obtained explicitly.     

Call Blocking Performance Study for PCS Networks under More Realistic Mobility Assumptions

In the micro-cell-based PCS networks, due to the high user mobility, handoffs occur more frequently. Hence, the classical assumptions, such as the exponential assumptions for channel holding time and call inter-arrival time, may not be valid. In this paper, we investigate the call blocking performance for PCS networks using a semi-analytic and semi-simulation approach. We first construct a simulation model as the base for our performance study, using which the handoff traffic is studied. Then we present a few possible approximation models from which analytical results for call blocking performance metrics can be obtained and compared with the simulation results. We show that for a certain parameter range, such approximations may provide appropriate results for call blocking performance. Finally, using the simulation model, we investigate how various factors, such as the high moments, the variance of cell residence time, mobility factors and the new call traffic load affect the call blocking performance. Our study shows that all these factors may have a significant impact on call blocking performance metrics such as call blocking probability, call incompletion probability and call dropping probability. This research provides a strong motivation for the necessity of reexamining the validity of analytical results obtained from classical teletraffic theory when dealing with the emerging wireless systems.     

User mobility modeling and characterization of mobility patterns

A mathematical formulation is developed for systematic tracking of the random movement of a mobile station in a cellular environment. It incorporates mobility parameters under the most generalized conditions, so that the model can be tailored to be applicable in most cellular environments. This mobility model is used to characterize different mobility-related traffic parameters in cellular systems. These include the distribution of the cell residence time of both new and handover calls, channel holding time, and the average number of handovers. It is shown that the cell residence time can be described by the generalized gamma distribution. It is also shown that the negative exponential distribution is a good approximation for describing the channel holding time     

Channel reservation for handoff calls in a PCS network

Some new performance measures and channel reservation for handoff calls for maximizing the service provider's revenue in a personal communications service (PCS) network, with general cell residence time and general requested call holding time, are investigated. Here, each cell within the PCS network consists M channels, but only when at least m+1 (0⩽m<μ) channels are available will a new originating call be accepted. A handoff attempt is unsuccessful if no channel in the target cell is available. Some new performance measures of the system such as the modified offered load (MOL) approximations of the blocking probability of new and handoff calls, the distribution and the mean actual call holding time of a new call and related conditional distributions and the expectations, as well as the boundary of the mean of the actual call holding time of an incomplete call and a complete call are obtained. A necessary and sufficient condition for maximizing the provider's revenue is achieved for any general cost structure if it is an increasing function of the actual call holding time. In order to be fair to the customers with incomplete call and complete call, two different kinds of holding costs are considered for the different customers. In both situations, the optimal controlling value m of handoff priority is obtained by maximizing the service provider's revenue     

Modeling and performance analysis for wireless mobile networks: a new analytical approach

In wireless mobile networks, quantities such as call blocking probability, call dropping probability, handoff probability, handoff rate, and the actual call holding times for both complete and incomplete calls are very important performance parameters in the network performance evaluation and design. In the past, their analytical computations are given only when the classical exponential assumptions for all involved time variables are imposed. In this paper, we relax the exponential assumptions for the involved time variables and, under independence assumption on the cell residence times, derive analytical formulae for these parameters using a novel unifying analytical approach. It turns out that the computation of many performance parameters is boiled down to computing a certain type of probability, and the obtained analytical results can be easily applied when the Laplace transform of probability density function of call holding time is a rational function. Thus, easily computable results can be obtained when the call holding time is distributed with the mixed-Erlang distribution, a distribution model having universal approximation capability. More importantly, this paper develops a new analytical approach to performance evaluation for wireless networks and mobile computing systems.     

SWiMNet: A Scalable Parallel Simulation Testbed for Wireless and Mobile Networks

We present a framework, called SWiMNet, for parallel simulation of wireless and mobile PCS networks, which allows realistic and detailed modeling of mobility, call traffic, and PCS network deployment. SWiMNet is based upon event precomputation and a combination of optimistic and conservative synchronization mechanisms. Event precomputation is the result of model independence within the global PCS network. Low percentage of blocked calls typical for PCS networks is exploited in the channel allocation simulation of precomputed events by means of an optimistic approach.Various experiments were conducted to study the performance and scalability of SWiMNet using a realistic mobility model and executed on a cluster of workstations. Experimental results indicate that our parallel simulation model yields good speedup, and significantly reduces the execution time compared to a sequential implementation. Finally, an analytical study of our PCS simulation model is also presented and compared with the experimental results. Our model is found to be consistent with the analytical study.     

A Coxian model for channel holding time distribution forteletraffic mobility modeling

In this letter, we derive an algebraic set of equations that examines the relationships between the cell residence times and the handoff call's channel holding time. When the cell residence times have an Erlang or Hyper-Erlang distribution, the channel holding times can be represented by a Coxian model. An algorithm is presented to compute the parameters of the equivalent Coxian model. The analytical models proposed in this letter provide a flexible framework for further studies into the optimization and performance evaluation aspects of teletraffic mobile systems     

Modeling and analysis of hierarchical cellular networks with bidirectional overflow and take-back strategies under generally distributed cell residence times

The rapid growth of wireless services and mobile users drives a great interest in cellular networks with a hierarchical structure. Hierarchical cellular networks (HCNs) can provide high system capacity, efficient channel utilization and inherent load-balancing capability. In this paper, we develop an analytical model and a performance analysis method for a two-layer HCN with bidirectional overflow and take-back strategies. Mobile users are divided into two classes. The call requests (including new and handoff calls) of fast and slow users are preferably assigned to the macrolayer and microlayer, respectively. A call from a fast user or slow user can overflow to its non-preferable layer if there is no channel available. The successful overflow call can be taken back to its preferable layer if a channel becomes available. Since the commonly used exponentially distributed assumption for cell residence time and then the channel occupancy time does not hold for emerging mobile networks, we model various cell residence times by general distributions to adapt to more flexible mobility environments. The channel occupancy times are derived in terms of the Laplace transforms of various cell residence times. The handoff rates, overflow rates and take-back rates of each layer are also derived in terms of the new call arrival rates and related probabilities. The stationary probabilities (and then the performance measures) are determined on the basis of the theory of multi-dimensional loss systems.     

Modeling of the electrical characteristics of an organic field effect transistor in presence of the bending effects

An analytical model incorporating the density of trap states for a bendable organic field effect transistor (OFET) is presented in this paper. The aim of this work is to propose a novel modeling framework to quantitatively characterize the bending effects on the electrical properties of an OFET in the linear and saturation regimes. In this model, the exponentially distributed shallow trap states are introduced into the Poisson equation to describe the carrier transports in the channel. The carrier mobility takes into account the low field mobility enhancement under gradual channel approximation and high field degradation. As a result, the generalized current-voltage transistor equations are derived for the first time to reflect the transconductance relationships of the OFET with trap states. In addition, an electro-mechanical coupling relationship is established per the metaphorical analogy between inorganic and organic semiconductor energy band models to quantify the stress-induced variations of the carrier mobility, and the threshold voltage. It is revealed that the before- and after-bending transconductances, predicted from the derived analytical model, are in good agreement with the experimental data measured from DNTT-based OFET bending tests.     

Computationally efficient method for analyzing guard channel schemes

Call admission control (CAC) is important for cellular wireless networks in order to provide quality of service (QoS) requirements to users. Guard channel scheme is one of the CAC schemes. There are different computational models for analyzing the guard channel scheme which make unrealistic assumption of exponential distribution for both call holding duration and cell residence time for computational tractability. On the other hand, there are some more realistic models for guard channel schemes which capture general distributions of call holding duration and cell residence time by phase type distributions but are computationally cumbersome to implement. The state-spaces of the Markov chains for those models make the computation intractable. In this paper, we develop a tractable computational model to analyze guard channel scheme with general cell residence time and call holding duration captured by phase type distributions. We make our mathematical model computationally tractable by keeping track of the number of calls in different phases of the channel holding time instead of the phase of the channel holding time of individual calls.     

Modeling techniques for large-scale PCS networks

There has been rapid growth in the demand for mobile communications that has led to intensive research and development of complex PCS (personal communication services) networks. Capacity planning and performance modeling are necessary to maintain a high quality of service to the PCS subscriber while minimizing costs. Effective and practical performance models for large-scale PCS networks are available. Two new performance models are presented in this article which can be solved using analytical techniques. The first is the so-called portable population model, based on the flow equivalent assumption (the rate of portables into a cell equals the rate of portables out of the cell). The model provides the steady-state portable population distribution in a cell that is independent of the portable residual time distribution, which can be used by simulations to reduce the necessary execution time by reaching the steady state more rapidly. Additionally, this model can be used to study the blocking probability of a low (portable) mobility PCS network and the performance of portable deregistration strategies. The second model is the so-called portable movement model which can be used to study location tracking and handoff algorithms. The model assumes that the arriving calls to a portable form a Poisson process, and portable residual times have a general distribution. This model can be used to study location-tracking algorithms and handoff algorithms. It is shown that under some assumptions, the analytic techniques are consistent with the simulation model     

A Model with Generalized Holding and Cell Residence Times for Evaluating Handoff Rates and Channel Occupancy Times in PCS Networks

This paper presents a performance model for apersonal communications services (PCS) system whichgeneralizes results obtained by the authors, allowingfor a more realistic computation of basic PCS network parameters. In particular, this modelgeneralizes the call holding time and the cell residencetime distributions. On the basis of this model, wederive the handoff rates and the channel occupationtimes, and show how these can be applied to computethe call blocking probabilities in these networks. Asimplified numerical example is presented to demonstratethe application of the presented approach.     

Analytical generalized results for handoff probability in wirelessnetworks

We present analytical results for handoff probability for wireless networks under assumption that the call holding time and the cell residence time are all generally distributed. Easily computable formulas can be obtained for cases when the call holding time and cell residence time have rational Laplace transforms     

Crossing Over the Bounded Domain: From Exponential to Power-Law Intermeeting Time in Mobile Ad Hoc Networks

Intermeeting time between mobile nodes is one of the key metrics in a mobile ad hoc network (MANET) and central to the end-to-end delay of forwarding algorithms. It is typically assumed to be exponentially distributed in many performance studies of MANET or numerically shown to be exponentially distributed under most existing mobility models in the literature. However, recent empirical results show otherwise: The intermeeting time distribution, in fact, follows a power-law. This outright discrepancy potentially undermines our understanding of the performance tradeoffs in MANET obtained under the exponential distribution of the intermeeting time and, thus, calls for further study on the power-law intermeeting time including its fundamental cause, mobility modeling, and its effect. In this paper, we rigorously prove that a finite domain, on which most of the current mobility models are defined, plays an important role in creating the exponential tail of the intermeeting time. We also prove that by simply removing the boundary in a simple two-dimensional isotropic random walk model, we are able to obtain the empirically observed power-law decay of the intermeeting time. We then discuss the relationship between the size of the boundary and the relevant timescale of the network scenario under consideration. Our results thus provide guidelines on the mobility modeling with power-law intermeeting time distribution, new protocols including packet-forwarding algorithms, as well as their performance analysis.