Computationally efficient method for analyzing guard channel schemes

Abstract

Call admission control (CAC) is important for cellular wireless networks in order to provide quality of service (QoS) requirements to users. Guard channel scheme is one of the CAC schemes. There are different computational models for analyzing the guard channel scheme which make unrealistic assumption of exponential distribution for both call holding duration and cell residence time for computational tractability. On the other hand, there are some more realistic models for guard channel schemes which capture general distributions of call holding duration and cell residence time by phase type distributions but are computationally cumbersome to implement. The state-spaces of the Markov chains for those models make the computation intractable. In this paper, we develop a tractable computational model to analyze guard channel scheme with general cell residence time and call holding duration captured by phase type distributions. We make our mathematical model computationally tractable by keeping track of the number of calls in different phases of the channel holding time instead of the phase of the channel holding time of individual calls.

Cell Dwell Time and Channel Holding Time Relationship in Mobile Cellular Networks

“…Most of the previously published papers that have developed mathematical models for the performance analysis of mobile cellular systems considering general probability distribution for cell dwell time have either only presented numerical results for the Erlang (Wang & Fan, 2007;Rahman & Alfa, 2009;Kim & Choi, 2009) or Gamma distributions with shape parameter greater than one 1 (Yeo & Jun, 2002;, and/or only for the CHTh 2 (Fang, 2001;, or have not presented numerical results at all Alfa & Li, 2002;Soong & Barria, 2000). Thus, numerical results both for values of the coefficient of variation (CoV) of CDT greater than one and/or for the CHTn have been largely ignored.…”

“…First, the unencumbered service time per call x s (also known as the requested call holding time (Alfa and Li, 2002) or call holding duration (Rahman & Alfa, 2009)) is the amount of time that the call would remain in progress if it experiences no forced termination. It has been widely accepted in the literature that the unencumbered service time can adequately be modeled by a negative exponentially distributed random variable (RV) (Lin et al, 1994;Hong & Rappaport, 1986).…”

“…The random variables (RVs) used to represent this time are X d (j) (for j = 0, 1, …) and are assumed to be independent and identically generally phasetype distributed. For homogeneous cellular systems, this assumption has been widely accepted in the literature (Lin et al, 1994;Hong & Rappaport, 1986;Alfa & Li, 2002;Rahman & Alfa, 2009).…”

“…However, a plenty of evidences showed that these assumptions are not longer valid (Wang & Fan, 2007;Christensen et al, 2004, Fang, 2001Alfa & 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, 2001Rahman & Alfa, 2009;Pattaramalai et al, 2007Pattaramalai et al, , 2009Hidata 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.…”