Nan-Fu Peng

Modeling Credit Reservation Procedure for UMTS Online Charging System

The IP multimedia core network subsystem (IMS) provides real-time multimedia services for Universal Mobile Telecommunications System (UMTS). Through recharge threshold-based credit reservation (RTCR) mechanism, prepaid IMS services can be supported by the online charging system (OCS) in UMTS. In RTCR, when the remaining amount of prepaid credit is below a threshold, the OCS reminds the user to recharge the prepaid account. It is essential to choose an appropriate recharge threshold to reduce the probability that the in-progress service sessions are forced-terminated. An analytic model is developed to investigate the performance of RTCR for the OCS. Based on our study, the network operator can select the appropriate parameter values for various traffic conditions.

Resolving mobile database overflow with most idle replacement

In a personal communications service (PCS) network, mobility databases called visitor location registers (VLRs) are utilized to temporarily store the subscription data and the location information for the roaming users. Because of user mobility, it is possible that the VLR is full when a mobile user arrives. Under such a circumstance, the incoming user has no VLR record and thus cannot receive PCS services. This issue is called VLR overflow. To resolve the VLR overflow problem, a VLR record can be selected for replacement when the VLR is full and then the reclaimed storage is used to hold the record of the requesting user. This paper considers the most idle replacement policy to provide services to mobile users without VLR records. In this policy, the record with the longest idle time is selected for replacement. We propose an analytic model to investigate the performance of this replacement policy. The analytic results are validated against simulation experiments. The results indicate that our approach effectively resolves the VLR overflow problem.

Repacking on demand for two-tier wireless local loop

This paper proposes a radio channel assignment scheme called repacking on demand (RoD) for two-tier wireless local loop (WLL) networks. A two-tier WLL overlays a macrocell with several microcells. When a new call arrives at a two-tier WLL with RoD, if no idle channel is available in both the microcell and the macrocell, repacking is performed (i.e., a call in the macrocell is moved to its corresponding microcell), and then the reclaimed macrocell channel is used to serve the new call. An analytic model is proposed to compute the call blocking probability of the two-tier WLL with repacking. This analytic model is validated against simulation experiments. We prove that the blocking probability is not affected by the call holding time distributions, but is only dependent on the mean of the call holding times. Compared with some previous proposed schemes, RoD has low blocking probability and significantly reduces repacking rate.

Testing process precision for truncated normal distributions

Abstract Process precision index C p has been widely used in the manufacturing industry to provide numerical measures of process precision, which essentially reflects product quality consistency. Precision measures using C p for normal processes, contaminated normal processes, have been investigated extensively, but are neglected for truncated normal processes. Truncated normal processes are common in the manufacturing industry, particularly, for factories equipped with automatic machines handling fully inspections, and scrap/rework products falling outside the specification limits. If the processes follow the normal distribution, then the inspected products (processes) must follow the truncated normal distribution. In this note, we consider the precision measure for truncated normal processes. We investigate the analytically intractable sampling distribution of the estimated C p , and obtain a rather accurate approximation. Using the results, we develop a practical testing procedure for practitioners to use in their in-plant applications.

A statistic approach for deriving the short message transmission delay distributions

Short Message Service (SMS) is one of the most popular mobile data services. This paper develops a Web-based short message system and analyzes the short message transmission delays based on 40 000 measured data collected from commercial operation. We investigate the distributions of SMS round-trip transmission delays. These distributions are roughly approximated by truncated normal, gamma, log-normal, and Weibull distributions with various parameters, which can be utilized in theoretical analysis. Furthermore, with the nonparametric fitting approach, we use the rejection method to develop random number generators for these delays, which can be used in any simulation models that employ SMS transmission delays.

On weak lumpability of a finite Markov chain

An irreducible and homogeneous Markov chain with finite state space is considered. Under a mild condition [Gamma] on the transition probability matrix, a necessary and sufficient condition for weak lumpability, and the characterization of the set of initial starting vectors which make it lumpable are obtained. A similar result is obtained for those transition probability matrices without the restriction of condition [Gamma].

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.

Linear birth and death processes under the influence of disasters with time-dependent killing probabilities

Supercritical linear birth-and-death processes are considered under the influence of disasters that arrive as a renewal process independently of the population size. The novelty of this paper lies in assuming that the killing probability in a disaster is a function of the time that has elapsed since the last disaster. A necessary and sufficient condition for a.s. extinction is found. When catastrophes form a Poisson process, formulas for the Laplace transforms of the expectation and variance of the population size as a function of time as well as moments of the odds of extinction are derived (these odds are random since they depend on the intercatastrophe times). Finally, we study numerical techniques leading to plots of the density of the probability of extinction.

Spectral representations of the transition probability matrices for continuous time finite Markov chains

Using an easy linear-algebraic method, we obtain spectral representations, without the need for eigenvector determination, of the transition probability matrices for completely general continuous time Markov chains with finite state space. Comparing the proof presented here with that of Brown (1991), who provided a similar result for a special class of finite Markov chains, we observe that ours is more concise.

Deriving the Vehicle Speeds from a Mobile Telecommunications Network

Vehicle speeds are often measured by intelligent transportation systems (ITSs) by utilizing sensors or software solutions. Our previous work proposed the Lin-Chang-Huangfu (LCH) scheme to compute the cell residence times by the standard counter values in mobile telecommunications switches. In this paper, we use mathematical and statistical developments to investigate the accuracy of the LCH scheme by deriving the bias of the cell residence times computed in this scheme. Then, we extend the LCH scheme with some filtering and compensation techniques for vehicle speed estimation and validate our approach with vehicle detector (VD) measurements at National Highway 3, Longtan Township, Taoyuan County, Taiwan. Our study indicates that the LCH scheme is an effective approach to vehicle speed estimation.