**1. Introduction**

356 Wireless Communications and Networks – Recent Advances

Estelle (1989). Information Processing Systems - OSI: Estelle, A Formal Description

Gotzhein R., et al. (2009). Energy-Aware System Design with SDL, *Proceedings of the 14th* 

ISBN:3-642-04553-7 978-3-642-04553-0, September 22-24, Bochum, Germany Hall A. (1990), Seven Myths of Formal Methods, *IEEE Software*, Vol. 7, No. 5, Sept. 1990, pp.

Latkoski P. et al. (2010). Modeling and optimization of bandwidth request procedure in

Larsen K. G. et al. (1997). UPPAAL in a Nutshell, *International Journal on Software Tools for* 

Lopez J. et al., (2005). Security Protocols Analysis: A SDL-based Approach, *Computer* 

LOTOS (2000). Information technology Enhancements to LOTOS (E-LOTOS), *SO/IEC* 

Mitschele-Thiel A. (2001). *Systems Engineering with SDL: Developing Performance-Critical Communication Systems*, Wiley, ISBN: 978-0-471-49875-9, New York, USA MSC (2001). Series Z: Languages and General Software Aspects for Telecommunication Systems, Message Sequence Chart, *ITU-T Recommendation Z.120*, Geneva, Switzerland, 2001 Petri C. A. (1996), Nets, Time and Space, *Theoretical Computer Science, Special Volume on Petri* 

SDL (2011). Series Z: Languages and General Software Aspects for Telecommunication

Sherif M. H. & Sparrell D. K. (1992), Standards and Innovations in Telecommunications, *IEEE Communication Magazine*, Vol. 30, No. 7, July 1992, pp. 22–29, ISSN 0163-6804 Sherif M. H. (2001). A Framework for Standardization in Telecommunications and

Showk A., et al. (2009). Modeling LTE protocol for mobile terminals using a formal

TTCN (2006). ITU-T, Recommendation Z.140 Tree and Tabular Combined Notation (TTCN),

Wing J. M. (1990), A Specifier's Introduction to Formal Methods, *IEEE Computer*, Vol. 23, No.

WiMAX (2010). IEEE Std 802.16-2004, IEEE Standard for Local and metropolitan area networks, Part 16: Air Interface for Fixed Broadband Wireless Access Systems WiFi (2007) IEEE Std IEEE 802.11, IEEE Standard for Wireless LAN Medium Access Control and Physical Layer Specification. 3GPP. Available from http://www.3gpp.org

September 22-24, Bochum, Germany SPIN. Available from

Systems, Specification and Description Language, *ITU-T Recommendation Z.100*,

Information Technology, *IEEE Communications Magazine*, No.4, April 2001, pp. 94-

description technique, *Proceedings of the 14th international SDL conference on Design for motes and mobiles - SDL'09*, pp. 222-238, ISBN:3-642-04553-7 978-3-642-04553-0,

11–19, September 1990 IEEE. Available from http://www.ieee.org

ISBN: 978-1-4244-8017-3, September 26-30, 2010, Istanbul, Turkey.

*Technology Transfer (STTT)*, Volume 1, Numbers 1-2, pp.134-152

*Standards & Interfaces*, Vol. 27, No. 3, pp. 489-499, ISSN: 0920-5489

*JTC1/SC7, International Standard 15437*, July 2000

*Nets*, Vol. 153, No. 1-2, pp. 3-48

http://netlib.sandia.gov/spin/index.html

9, pp. 8-24, September 1990

100, ISSN 0163-6804

March 2006.

Geneva, Switzerland, Latest edition 2011

*9074*, June 1989 ETSI. Available from http://www.etsi.org

Chicago, USA, 10-12 April 2010

*Networking, Sensing and Control (ICNSC),* pp. 441 – 446, ISBN: 978-1-4244-6450-0,

Technique Based on an Extended State Transition Model, *International Standard* 

*international SDL conference on Design for motes and mobiles - SDL'09*, pp. 19-33,

IEEE 802.16 networks, *Proceedings of the IEEE 21st International Symposium on Personal Indoor and Mobile Radio Communications (PIMRC), 2010*, pp. 1469 – 1474,

> Channel holding time (CHT) is of paramount importance for the analysis and performance evaluation of mobile cellular networks. This time variable allows one to derive other key system parameters such as channel occupancy time, new call blocking probability, and handoff call dropping probability. CHT depends on cellular shape, cell size, user's mobility patterns, used handoff scheme, and traffic flow characteristics. Traffic flow characteristics are associated with unencumbered service time (UST), while the overall effects of cellular shape, users' mobility, and handoff scheme are related to cell dwell time (CDT).

> For convenience and analytical/computational tractability, the teletraffic analysis of mobile cellular networks has been commonly performed under the unrealistic assumption that CDT and/or CHT follow the negative exponential distribution (Lin et al., 1994; Hong & Rappaport, 1986). However, a plenty of evidences showed that these assumptions are not longer valid (Wang & Fan, 2007; Christensen et al., 2004, Fang, 2001, 2005; Orlik & Rappaport, 1998; Fang & Chlamtac, 1999; Fang et al., 1999; Alfa & Li, 2002; Rahman & Alfa, 2009; Soong & Barria, 2000; Yeo & Jun, 2002; Pattaramalai, et al., 2007). Recent papers have concluded that in order to capture the overall effects of users' mobility, one needs suitable models for CDT distribution (Lin, 1994; Hong & Rappaport, 1986). In specific, the use of general distributions for modeling this time variable has been highlighted. In this research direction, some authors have used Erlang, gamma, uniform, deterministic, hyper-Erlang, sum of hyper-exponentials, log-normal, Pareto, and Weibull distributions to model the pdf of CDT; see (Wang & Fan, 2007; Fang, 2001, 2005; Orlik & Rappaport, 1998; Fang & Chlamtac, 1999; Fang et al., 1997, 1999; Rahman & Alfa, 2009; Pattaramalai et al., 2007, 2009; Hidata et al., 2002; Thajchayapong & Toguz, 2005; Khan & Zeghlache, 1997; Zeng et al. 2002; Kim & Choi, 2009) and the references therein. Fang in (Fang, 2001)) emphasizes the use of phase-type (PH) distributions for modeling CDT. The reason is twofold. First, PH distributions provide accurate description of the distributions of different time variables in wireless cellular networks, while retaining the underlying Markovian properties of the distribution. Markovian properties are essential in generating tractable queuing models for cellular networks. Second, there have been major advances in fitting PH distributions to real data. Among the PH probability distributions, the use of either Coxian or Hyper-Erlang distributions are of

particular interest because their universality property (i.e, they can be used to approximate any non negative distribution arbitrarily close) (Soong & Barria, 2000; Fang, 2001).

Due to the discrepancy and the wide variety of proposed models, it appears mandatory to investigate the implications of the cell dwell time distribution on channel holding time characteristics in mobile wireless networks. This is the topic of research of the present chapter. Let us describe the related work reported in this research direction.
