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     

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.     

Performance of mobile networks with wireless channel unreliability and resource insufficiency

New closed-form formulas for the call complete probability and the probability density function (pdf) of the completed call holding time (CCHT) are developed under the concurrent impacts of the resource insufficiency as well as the wireless link unreliability in the wireless mobile networks performance evaluation. The results are obtained with the general scenario, i.e. general call holding time, general cell residence time and the generalized wireless channel model. The analysis result is validated by the simulation model under typical call holding time and cell residence time distributions, Gilbert-Elliott or Fritchman wireless channel model. The comparison indicates that the wireless networks performance will be greatly overestimated without taking into account the unreliable wireless link effect.     

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.     

Effects of Erlang call holding times on PCS call completion

This paper studies personal communications services (PCSs) channel allocation assuming the Erlang call holding time distribution (a generalization of the exponential distribution) to investigate the effect of the variance of the call holding times on the call completion probability. Our analysis indicates that the call completion probability decreases as the variance of the call holding times decreases. This effect becomes more pronounced as the variance of the cell residence times decreases     

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     

Channel holding time in hierarchical cellular systems

We study the characteristics of the channel holding time in the multitier cellular systems supporting overflow and underflow schemes with the general call holding time and the general cell residence time. Comparison between our results, together with previous results, and simulation shows that our result is more universal and more accurate.     

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.     

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.     

Call admission control for an adaptive heterogeneous multimedia mobile network

A novel call admission control (CAC) scheme for an adaptive heterogeneous multimedia mobile network with multiple classes of calls is investigated here. Different classes of calls may have different bandwidth requirement, different request call holding time and different cell residence time. At any time, each cell of the network has the capability to provide service to at least a given number of calls for each class of calls. Upon the arrival (or completion or hand off) of a call, a bandwidth degrade (or upgrade) algorithm is applied. An arriving call to a cell, finding insufficient bandwidth available in this cell, may either be disconnected from the network or push another call out of the cell toward a neighboring cell with enough bandwidth. We first prove that the stationary distribution of the number of calls in the network has a product form and then show how to apply this result in deriving explicit expressions of handoff rates for each class of calls, in obtaining the disconnecting probabilities for each class of new and handoff calls, and in finding the grade of service of this mobile network     

Performance analysis of a cellular network with multiple classes of calls

In this paper, we study a cellular mobile communications network with multiple cells and multiple classes of calls. The different classes of calls have different call holding times and residence time distributions. We consider a protocol mechanism under which a blocked call in a cell is either disconnected from the network or is deemed as a handoff call in a neighboring cell. Under this protocol, we prove that the stationary distribution of this cellular mobile network has a product form. This allows us to derive explicit expressions for handoff rates of each class of calls from one cell to another and the disconnecting probabilities for each class of new and handoff calls. Our numerical results show how these measures depend on the mobility of the mobile terminals in each cell and on the numbers of reserved channels.     

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.     

Teletraffic analysis and mobility modeling of PCS networks

Channel holding time is of primary importance in teletraffic analysis of PCS networks. This quantity depends on user's mobility which can be characterized by the cell residence time. We show that when the cell residence time is not exponentially distributed, the channel holding time is not exponentially distributed either, a fact also confirmed by available field data. In order to capture the essence of PCS network behaviour, including the characterization of channel holding time, a correct mobility model is therefore necessary. The new model must be good enough to fit field data, while at the same time resulting in a tractable queueing system. We propose a new mobility model, called the hyper-Erlang distribution model, which is consistent with these requirements. Under the new realistic operational assumption of this model, in which the cell residence time is generally distributed, we derive analytical results for the channel holding time distribution, which are readily applicable to the hyper-Erlang distribution models. Using the derived analytical results we demonstrate how the distribution of the cell residence time affects the channel holding time distribution. The results presented in this paper can provide guidelines for field data processing in PCS network design and performance evaluation     

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.     

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.     

Channel Holding Time in Wireless Cellular Communications with General Distributed Session Time and Dwell Time

Channel holding time is fundamental to teletraffic analysis of wireless cellular networks. This quantity depends on user's mobility which can be characterized by the dwell time, and the traffic model which is associated with the unencumbered session time. In this paper, under a general assumption on the distributions of unencumbered session time and dwell time, the characteristics of new call channel holding time and handoff call channel holding time are investigated. Analytical formulae for the distributions of new call channel holding time and handoff call channel holding time are derived     

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     

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     

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.     

Impact of PCS handoff response time

In a personal communications services (PCS) network, the network delay for a handoff request is limited by a timeout period. If the network fails to respond within the timeout period, the handoff call is forced terminated. We study the effect of the network response time on the performance (the call incompletion probability) of a PCS network. Our study indicates that at a small offered load, the network response time has a significant effect on the call incompletion probability. We also observe that the effect of the network response time is more significant if the mobile residence time distribution at a cell has a smaller variance