Inter-arrival time distribution for channel arrivals in cellular telephony (original) (raw)

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 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.

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...

Channel Holding Time Distribution in Public Cellular Telephony

Modeling Cellular Wireless Networks Under Gamma Inter-Arrival and General Service Time Distributions

2010

In this paper, an analytical traffic model with gamma inter-arrival time and general service time distributions is developed to evaluate the system performance, in terms of the blocking probabilities, in cellular wireless networks. The performance is evaluated with guard channels and compared with that obtained from classical Erlang model. Keywords—Cellular wireless networks, traffic model, performance analysis, handoff, guard channel, gamma inter-arrival distribution.

Modeling VoIP Call Holding Times for Telecommunications

IEEE Network, 2007

Voice over IP is one of the most popular applications in broadband access networks. It is anticipated that the characteristics of call holding times (CHTs) for VoIP calls will be quite different from traditional phone calls. This article analyzes the CHTs for mobile VoIP calls based on measured data collected from commercial operation. Previous approaches directly used the Kolmogorov-Smirnov (K-S) test to derive the CHT distributions, which may cause inaccuracy. In this article we propose a new approach to derive the CHT distributions for mobile VoIP calls and other call types. Specifically, our approach uses hazard rate to select an appropriate distribution, and then utilizes the K-S test to validate our selection. We show that the mobile VoIP CHT distribution can be accurately approximated by a mix of two lognormal distributions. Based on the derived distributions, we compare the mobile VoIP CHTs with those for non-VoIP calls and fixed-network VoIP calls. Our study indicates that the characteristics for mobile VoIP calls are quite different from those of the non-VoIP mobile phone calls and are more close to those of fixed-network phone calls.

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

1997

In this paper the statistics of the message arrivals to a PAMR trunked system are investigated. The tools used to perform the statistical analysis have been previously used in similar works and are extremely simple. First, probability density functions are fitted to the channel idle time (time between the end of a message and the beginning of the next one on the same channel). To characterise the population that generates the offered traffic it is more important the time between call attempts. This is a difficult measure as it needs to be induced from other measures: attempts are not seen when they really occur, but when the system allocates a radio-channel to them. Two methods to obtain the coefficient of variation of the time between call attempts are presented. Based on the proposed procedures we show that in our system the infinite population assumption is far from the true situation. The measures presented in this paper show that the time between call attempts follows a probability distribution smoother than the exponential and that models such as finite population or unbalanced multipopulation should be considered.

Inter-arrival time distribution for channel arrivals in cellular telephony (original) (raw)

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