Cell Residence Time Distribution Research Articles

Modeling and Cost Analysis of Movement-Based Location Management for PCS Networks With HLR/VLR Architecture, General Location Area and Cell Residence Time Distributions

Location management plays a central role in guaranteeing the effective operation of personal communication service (PCS) networks. In current PCS networks, a two-tier system of home location register (HLR) and visitor location register (VLR) databases is commonly used for location management. To improve the performance of PCS networks, several dynamic location management schemes have been proposed. Among the existing dynamic schemes, the movement-based location management may be the most practical due to its effectiveness and easy implementation under the framework of current PCS networks. To implement location management in PCS networks, cost analysis is a crucial aspect. However, most of the existing cost analyses for the movement-based scheme are too simple and not available for PCS networks with the HLR/VLR architecture. One reason for this is the complexity and the difficulty associated with the problem. Li et al. and Rodriguez-Dagnino et al. challenged this task by considering the HLR/VLR architecture. However, the cost analysis developed by Li et al. was carried out under the assumption that the cell and location area (LA) residence times are exponentially distributed. Rodriguez-Dagnino et al. furthered Li et al.'s work by assuming that the LA residence time follows a hyperexponential distribution and that the cell residence time is generally distributed. However, Li et al. and Rodriguez-Dagnino et al. failed to consider VLR location updates that are caused by terminal movements between LAs. In this paper, we relax the restrictions imposed on the distributions of the cell and LA residence times and propose an analytical model to study the movement-based scheme with HLR/VLR architecture. The issue of VLR location updates that are caused by movements between LAs is addressed carefully and successfully. Analytical formulas for the costs of HLR and VLR location updates are derived using a unified approach. Numerical study suggests that the total cost is a convex function of the movement threshold and is sensitive to the variances of the cell and LA residence times. The result presented in this paper can serve as a guideline for the system design and the implementation of the movement-based scheme for PCS networks.

Optimization of Distance-Based Location Management for PCS Networks

Location management (LM) is an important function in a personal communication network to track movements of mobile terminals (MTs) for call delivery. It is well-known that the total signaling cost of a distance-based LM scheme is the lowest among dynamic location management schemes for PCS networks. In this paper, we derive the joint probability distribution of two random variables: the moving distance of an MT and the number of location updates resulting from the moving distances exceeding the distance threshold. As special cases, the probability distributions of an MT's moving distances and the number of location updates during an LM interval are obtained. These statistics are generally applicable to irregular cell topologies and general cell residence time distributions. Based on the derived statistics, the optimal distance thresholds for distance based LM schemes with blanket paging and sequential paging are solved analytically. Numeric results show that our optimized distance-based LM scheme outperforms some well-known LM schemes in total LM cost.

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.

Modeling channel assignment of small-scale cellular networks

In a cellular telecommunications network, the call blocking, forced termination, and call incompletion probabilities are major output measures of system performance. Most previous analytic studies assumed that the handover traffic to a cell is a fixed-rate Poisson process. Such assumption may cause significant inaccuracy in modeling. This paper shows that the handover traffic to a cell depends on the workloads of the neighboring cells. Based on this observation, we derive the exact equation for the handover force-termination probability when the mobile station (MS) cell residence times are exponentially distributed. Then, we propose an approximate model with general MS cell residence time distributions. The results are compared with a previously proposed model. Our comparison study indicates that the new model can capture the handover behavior much better than the old one for small-scale cellular networks.

Author Index

This paper proposes a new analytical model for the performance evaluation of cellular communication systems. Our model allows more general cases of the distributions of the call time and the cell residence time. Based on the characterization of the call time by a hyper-Erlang distribution, the Laplace transform of the channel occupancy time distribution is derived as a function of the Laplace transform of the cell residence time distribution. In particular, the essential quality of service measure such as the forced termination probability is exactly obtained by using a delayed renewal process. From numerical results, it is shown that the non-exponential model has an obvious difference in performance as compared to exponential models.

Teletraffic analysis of cellular communication systems with general mobility based on hyper-Erlang characterization

This paper proposes a new analytical model for the performance evaluation of cellular communication systems. Our model allows more general cases of the distributions of the call time and the cell residence time. Based on the characterization of the call time by a hyper-Erlang distribution, the Laplace transform of the channel occupancy time distribution is derived as a function of the Laplace transform of the cell residence time distribution. In particular, the essential quality of service measure such as the forced termination probability is exactly obtained by using a delayed renewal process. From numerical results, it is shown that the non-exponential model has an obvious difference in performance as compared to exponential models.

Modeling PCS networks under general call holding time and cell residence 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.

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.

A Novel Modelling Technique for Tracing Mobile Users in a Cellular Mobile Communication System

Mobility of users in a cellular mobile communication system has been formulated mathematically under generalized conditions. Based on this model a computer simulation has been developed. This mobility model is used to examine cell residence time distribution in cellular environments defined by different cell sizes and mobility parameters. It is shown that cell residence time can be described by the generalized gamma distribution.