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     

Performance analysis of cognitive radio networks with generalized call holding time distribution of secondary user

In cognitive radio networks (CRNs), spectrum handoff probability and expected number of spectrum handoffs are important parameters in the evaluation of network performance and design. This paper presents an analytical model for spectrum handoff probability and spectrum handoff rate for CRNs under general distribution of call holding time of secondary users (SUs). The standardized analytical forms of spectrum handoff probability and handoff rate of secondary network under negotiated scenario are derived for a complete service call duration. The effect of mobility parameters: departure rate of SUs (\(\upmu )\) and departure rate of spectrum holes (\(\uplambda )\) on spectrum handoff are also reported in this paper. Extensive results for all the proposed analytical models are obtained and presented in this paper. Analytical results show that exponential and Erlangian distribution functions are not suitable for call holding time of SU in the analysis of spectrum handoff in CRNs. Moreover, the superiority of lognormal distribution function ascertains its use for call holding time of SU in spectrum handoff estimation for better CRN performances. The Monte-Carlo simulation is also performed for spectrum handoff probability to validate the analytical model.     

Actual call connection time characterization for wireless mobile networks under a general channel allocation scheme

Actual call connection time (ACCT) is the total time that a mobile user engages in communications over a wireless network during a call connection. Due to limited network resources of wireless mobile networks, a call connection may be prematurely disconnected and the ACCT for the call in general may not be the same as the requested call connection time (RCCT). The ACCT depends not only on the RCCT, but also on the network resource allocation scheme and network traffic. We characterize the ACCT and related performance metrics for wireless mobile networks under a newly proposed general channel allocation scheme. This scheme generalizes the nonprioritized scheme, the reserved channel scheme, the queueing priority scheme and the subrating scheme in such a way as to reduce the blocking probability of the handoff calls while keeping the ACCT as long as possible. Explicit formulae for the distribution and the expectation of the ACCT are obtained. The call completion probability, the call drop probability, and the average actual call connection times for both the complete calls and the incomplete calls are derived. The results can form the basis for designing better billing rate schemes by differentiating incomplete calls and complete calls.     

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.     

A teletraffic performance study of mobile LEO-Satellite cellular networks with gamma distributed call duration

In this paper, the authors develop an analytical model to study the performance of a mobile low earth orbiting (LEO) satellite cellular network. The model assumes that the call duration has a gamma distribution and considers the effect of system parameters such as the number of channels per cell, the number of channels reserved for the handoff, and the cell residence time, on the teletraffic performance of the system. The quality of service (QoS) measures studied in this paper include new call blocking probability, handoff failure probability, premature call-termination probability (CTP), and call dropping probability (CDP). Based on the causal central limit theorem, the authors use a two-parameter gamma distribution to approximate the distribution of the sum of the residence times in the cells. The analytical model presented in this paper may be used with any call-holding-time distribution. The analytical results are validated by a computer simulation.     

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.     

Effect of mobile terminal heterogeneity on call blocking/dropping probability in cooperative heterogeneous cellular networks

It is envisaged that next generation wireless networks (NGWN) will be heterogeneous, consisting of multiple radio access technologies (RATs) coexisting in the same geographical area. In these heterogeneous wireless networks, mobile terminals of different capabilities (heterogeneous terminals) will be used by subscribers to access network services. We investigate the effect of using heterogeneous mobile terminals (e.g. single-mode, dual-mode, triple-mode, etc.) on call blocking and call dropping probabilities in cooperative heterogeneous wireless networks. We develop analytical models for heterogeneous mobile terminals and joint radio resource management in heterogeneous wireless networks. Using a two-class three-RAT heterogeneous wireless network as an example, the effect of using heterogeneous terminals in the network is evaluated. Results show the overall call blocking/dropping probability experienced by subscribers in heterogeneous wireless networks depends on the capabilities of mobile terminals used by the subscribers. In the worst case scenario, when all subscribers use single-mode mobile terminals, each subscriber is confined to a single RAT and consequently, joint radio resource management in heterogeneous wireless network has no improvement on new call blocking and handoff call dropping probabilities. However, in the best case scenario, when all subscribers use three-mode terminals, new class-1 call blocking probability decreases from 0.37 (for 100% single-mode terminals) to 0.05, at the arrival rate of 6 calls per minute. New class-2 call blocking probability also decreases from 0.8 to 0.52. Similarly, handoff class-1 call dropping probability decreases from 0.14 to 0.003, and handoff class-2 call dropping probability decreases from 0.44 to 0.09.     

Modeling call holding time distributions for CCS network design andperformance analysis

The message traffic offered to the CCS signaling network depends on and is modulated by the traffic characteristics of the circuit switched calls supported by the CCS network. Most previous analyses of CCS network engineering, performance evaluation and congestion control protocols generally assume an exponential holding time of circuit switched calls. Analysis of actual holding time distributions in conversations, facsimile and voice mail connections revealed that these distributions radically differ from the exponential distribution. Especially significant is the large proportion of very short calls in real traffic in comparison with the exponential distribution model. The diversity of calls (partial dialing, subscriber busy, no answer) and services results in a multi-component call mix, with even larger proportion of short time intervals between message-generating events. Very short call holding times can have a significant impact on the traffic stream presented to the CCS network: for calls with short holding times, the different CCS messages arrive relatively close to each other, and this manifests as burstiness in the CCS traffic stream     

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.     

Network dimensioning at the call level for the always‐on network

It is becoming common for the network to provide always‐on access services, where subscribers are guaranteed that their call requests will never be blocked. This paper studies the call‐level link dimensioning for the always‐on network with single‐class traffic. The call‐level QoS requirement is expressed in terms of the probability of a poor‐quality call, which is the probability that a call experiences packet‐level QoS violation at any time during its duration, as opposed to the probability of blocking in the network with call admission control (CAC). The system is modelled as the M/M/infinite system with finite population and an analytic expression for the probability of a poor‐quality call is derived based on performability analysis. The effects of the call‐level traffic characteristics on the required link resources are studied. It is also shown that the call‐level link dimensioning for the always‐on network needs more link resources than the network with CAC, and the call‐level link dimensioning based on the analytic expression can be used to conservatively dimension the always‐on network with arbitrarily distributed call holding time and inter‐call time. The paper also studies the problem of estimating the call‐level traffic characteristics when the knowledge of call boundaries is not available. Copyright © 2004 John Wiley & Sons, Ltd.     

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.     

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.     

Call admission control for capacity-varying networks

Many networks, such as Non-Geostationary Orbit Satellite (NGOS) networks and networks providing multi-priority service using advance reservations, have capacities which vary over time for some or all types of calls carried on these networks. For connection-oriented networks, Call Admission Control (CAC) policies which only use current capacity information may lead to excessive and intolerable dropping of admitted calls whenever the network capacity decreases. Thus, novel CAC policies are required for these networks. Three such CAC policies are discussed, two for calls with exponentially distributed call holding times and one for calls whose holding time distributions have Increasing Failure Rate (IFR) functions. The Admission Limit Curve (ALC) is discussed and shown to be a constraint limiting the conditions under which any causal CAC policy may admit calls and still meet call dropping guarantees on an individual call basis. We demonstrate how these CAC policies and ALC represent progressive steps in developing optimal CAC policies for calls with exponentially distributed call holding times, and extend this process to the more general case of calls with IFR call holding times.     

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 evaluation of a reservation random access scheme for packetized wireless systems with call control and hand-off loading

We consider a packet switched wireless network where each cell's communication channel is shared among packet voice sources. In this paper, we present a method for the design and analysis of wireless cells using a reservation random access (RRA) scheme for packet access control. This scheme is integrated with a call admission control procedure. We model the state process of a single cell as a vector Markov chain. We compute the steady state distribution of the Markov chain. This result is used to calculate the packet dropping probability and the call blocking probability. By setting limits on maximum permissible levels for the call blocking probability and the packet dropping probability, we obtain the Erlang capacity of a single cell, with and without hand-off traffic. For an illustrative RRA scheme, the Erlang capacity of a single cell is shown to be about twice that attained by a comparable fixed assigned TDMA scheme. We show that a cellular network using this RRA scheme and which applies can be no blocking of hand-off calls, exhibits similar call capacity levels.This work is supported by a University of California MICRO and Pacific-Bell Grant No. 94-107.     

Dynamic call admission control in ATM networks

The authors present dynamic call admission control using the distribution of the number of cells arriving during the fixed interval. This distribution is estimated from the measured number of cells arriving at the output buffer during the fixed interval and traffic parameters specified by users. Call acceptance is decided on the basis of online evaluation of the upper bound of cell loss probability, derived from the estimated distribution of the number of calls arriving. QOS (quality of service) standards can be guaranteed using this control when there is no estimation error. The control mechanism is effective when the number of call classes is large. It tolerates loose bandwidth enforcement and loose policing control, and dispenses with modeling of the arrival processes. Numerical examples demonstrate the effectiveness of this control, and implementation is also discussed     

Genetic algorithms applied to cellular call admission: localpolicies

It is well known that if a stochastic service system (such as a cellular network) is shared by users with different characteristics (such as differing handoff rates or call holding times), the overall system performance can be improved by denial of service requests even when the success capacity exists. Such selective denial of service based on the system state is defined as the call admission. A previous paper suggested the use of genetic algorithms (GAs) to find near-optimal call admission policies for cellular networks. In this paper, we define local call admission policies that make admission decisions based on partial state information. We search for the best local call admission policies for one-dimensional (1-D) cellular networks using genetic algorithms and show that the performance of the best local policies is comparable to optima for small systems. We test our algorithm on larger systems and show that the local policies found outperform the maximum packing and best handoff reservation policies for the systems we have considered. We find that the local policies suggested by the genetic algorithm search in these cases are double threshold policies. We then find the best double threshold policies by exhaustive search for both 1-D and Manhattan model cellular networks and show that they almost always outperform the best trunk reservation policies for these 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     

Call performance for a PCS network

It is well known that, due to the mobility of a portable and limited channel availability, calls of portables may not be completed due to being blocked or terminated during the call initiation or the handover process. The characteristics of the call-completion and call-holding times for both a complete call and an incomplete call are of critical importance for establishing the actual billing process in the PCS network. We derive the call-completion probability (hence, call-dropping probability) and the effective call-holding time distributions for complete/incomplete calls with a general cell-residence time and a general call-holding time are analyzed, and general computable formulas are obtained. We show that when call-holding times are Erlang distributed, easy-to-compute formulas for the probability of a call completion and the expected effective call-holding times for both a complete call and an incomplete call can be derived     

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