Idle and inter-arrival time statistics in public access mobile radio (PAMR) systems (original) (raw)

Inter-arrival time distribution for channel arrivals in cellular telephony

1998

In this paper different probability density functions are fitted to the inter-arrival time in a channel of a Cellular Mobile Telephony system. The approach is entirely experimental: the data set to be fitted has been obtained on an actual system in operation. The Kolmogorov-Smirnov (K-S) goodness-of-fit test is used in order to establish a ranking of the best fitting probability density functions. From this study it can be concluded that the arrivals to a channel in a cell are according to a smooth process.

Elusive Statistical Property of Arrival Rate and Holding Time used in Mobile Communication Networks

International Journal of Computer Applications, 2012

This research work is aimed at the study of arrival rate and holding time used in mobile communication networks, also to determine the best suitable statistical probability distribution of both arrival rate and holding time or service time in mobile communication network. The most general acceptable assumption about arrival rate is Poisson distribution and the holding time is exponential distribution in traffic modeling of mobile communication networks. Exhaustive literature review is deployed for details explanation on discrete random variables of arrival rate and continuous holding time use in traffic modeling of mobile communication networks. From the research work, the arrival rate is explained using point process or counting process, which leads to two unique properties, they are orderly and memorylessness. These unique properties are possessed by Bernoulli process with is discrete time, having Geometric distribution function, also with Poisson process, which is continuous time and discrete space, having Exponential distribution function which is used to characterize arrival rate based on interarrival rate process. Therefore, from the research work, it is assumed that arrivals rate is Poisson distribution and service time or holding time is exponentially distributed in traffic situation in mobile communication networks. These statistical properties since to the best suitable in mobile communication networks because of their unique parameters and are simple to analyses.

An Empirical Study on Statistical Properties of GSM Telephone Call Arrivals

Globecom, 2006

We investigate the statistical properties of both originated and terminated call arrivals in sets of real GSM telephone traffic data (TIM, Italy), emphasizing results obtained by the Modified Allan Variance (MAVAR), a widely used timedomain quantity with excellent capability of discriminating power-law noise. The call arrival rate exhibits a diurnal trend, with peak hours in the morning and late afternoon. Besides this diurnal change, the number of call arrivals in a second is found perfectly uncorrelated to the number of arrivals in other seconds and Poisson distributed, with good consistency by χ 2-test evaluation. Uniform and accurate whiteness of call arrivals per second is verified in all hours, regardless the time of the day. In all series analyzed, the empirical statistics of both originated and terminated call arrivals proved excellent consistency with the ideal Poisson model with variable rate λ(t). This study may be valuable to researchers concerned about realistic modelling of traffic in planning and performance evaluation of cellular networks.

WLC09-1: An Empirical Study on Statistical Properties of GSM Telephone Call Arrivals

IEEE Globecom 2006, 2006

 We investigate the statistical properties of both originated and terminated call arrivals in sets of real GSM telephone traffic data (TIM, Italy), emphasizing results obtained by the Modified Allan Variance (MAVAR), a widely used timedomain quantity with excellent capability of discriminating power-law noise. The call arrival rate exhibits a diurnal trend, with peak hours in the morning and late afternoon. Besides this diurnal change, the number of call arrivals in a second is found perfectly uncorrelated to the number of arrivals in other seconds and Poisson distributed, with good consistency by χ 2 -test evaluation. Uniform and accurate whiteness of call arrivals per second is verified in all hours, regardless the time of the day. In all series analyzed, the empirical statistics of both originated and terminated call arrivals proved excellent consistency with the ideal Poisson model with variable rate λ(t). This study may be valuable to researchers concerned about realistic modelling of traffic in planning and performance evaluation of cellular networks.

Channel Holding Time Distribution in Public Cellular Telephony

This paper examines the channel holding time of public cellular telephony systems. This is the time that the Mobile Station (MS) remains in the same cell, a fraction of the call holding time. The study is based on actual data taken from a working system. The probability distribution that fits the empirical sample best when applying the Kolmogorov-Smirnov test is a mixture of lognormals. Combinations of memory-less stages are also tested in the paper.

Modeling Channel Occupancy Times for Voice Traffic in Cellular Networks

2007

Call holding times in telephony networks are commonly approximated by exponential distributions to facilitate traffic engineering. However, for traffic engineering of cellular networks, channel occupancy times need to be modeled instead to facilitate analytical modeling or to feed network simulations. In this paper, we classify channel occupancy times and present an empirical study based on data obtained from a real cellular network to determine which probability distribution functions can approximate them better. The results are environment dependent, but no assumptions that can be influential are made, as opposed to previous analytical and simulation studies which results are highly dependent on the assumptions made by the authors. We show that all types of channel occupancy times can be approximated by lognormal distribution. For stationary users, channel occupancy times are commonly approximated by exponential distribution due to its tractability, assuming that cell residence times are also exponentially distributed. However, we show that lognormal distribution fits much better to both channel occupancy and call holding times regardless of whether users are stationary or mobile.

Deriving Call Holding Time Distribution in Cellular Network from Empirical Data

Summary The call holding time distribution in cellular systems is one of the main parameters that are used to study and analyze several system performance measures. Several statistical distributions have been used in the literature to model the call holding time distribution in 3rd and 4th generations cellular systems, such as exponential, Erlang, Gamma, and generalized Gamma. In practice, the call holding time is affected by several factors such as the service plan, the class of the service area, and some of the system design parameters, however, the parameters of the distributions used to model the call holding time were assumed, and the effects of some factors on the call holding time are eliminated. In this paper, we derived the probability density function of the call holding time based on actual data taken at Tabouk city, Saudi Arabia, from the working Aljwal network which is a 3.5G cellular network operated by Saudi Telecommunications Company, then the probability density fun...

Handoff traffic characterization in cellular networks under nonclassical arrivals and service time distributions

IEEE Transactions on Vehicular Technology, 2001

The phenomenal growth in subscriber population has necessitated the accurate dimensioning and performance analysis of cellular networks. Classically, cellular networks have been analyzed using Poisson call arrivals and negative exponential channel holding times. However, these assumptions may not be valid for modern networks providing heterogeneous services and serving users with highly varied mobility. In this paper, we propose a moment-based approach for analyzing cellular networks under more generalized arrival processes and more generalized channel holding-time distributions. We present a model for accurately characterizing the handoff traffic offered by a cell to its neighbor in a simple two-cell scenario. We derive this handoff traffic for two different channel holding-time distributions. Our two-cell model easily lends itself to being used as building blocks for analyzing more general cellular network layouts. We illustrate the accuracy of our analysis using comparison with simulation results.

Empirical Modeling of Public Safety Voice Traffic in the Land Mobile Radio Band

Proceedings of the 7th International Conference on Cognitive Radio Oriented Wireless Networks, 2012

An RF measurement system with high time resolution is implemented to determine the statistical characteristics of various channels in the Land Mobile Radio bands. The applicability of simple statistical models to the observed data is investigated, as well as their validity over short and long periods of time. The results show that the statistics of the idle and holding times of communication on these channels vary significantly over time and demonstrate daily periodicity, requiring non-stationary models to accurately represent them. Over short durations of time however, conventional distributions such as the exponential and log-normal may adequately characterize the properties of these quantities, allowing convenient and compact representations of the data. Results based on empirical data are presented to quantify the probability of stationarity for voice traffic within a time span of given length. The findings are useful for network planning or streamlining, network simulation and modeling, and investigation of dynamic spectrum access.

CHANNEL HOLDING TIME DISTRIBUTION IN CELLULAR TELEPHONY

1998

This paper examines the channel holding time of public cellular telephony systems. This is the time that the Mobile Station (MS) remains in the same cell, a fraction of the call holding time. The study is based on actual data taken from a working system. The probability distribution that fits the empirical sample best when applying the Kolmogorov-Smirnov test is a mixture of lognormals. Combinations of memory-less stages are also tested in the paper. * This work was funded by Spanish CICYT Project TIC 94-0475.