Impact of the Busy-Line Effect on the Interservice Time Distribution and Modeling of Portable Movements in PCS Networks

The distribution of the interservice time, which is the interval between the end of a call served and the start of the succedent call served by a portable, is a crucial parameter for modeling and cost analysis for location management in personal communication service (PCS) networks. The interservice time differs from the interarrival time due to the busy-line effect. However, in the literature, most of the cost analyses for location management were carried out by ignoring the busy-line effect, i.e., by identifying the interservice time with the interarrival time, because, so far, there is no analytical result for the interservice time distribution considering the busy-line effect. In this paper, we develop an analytical model to investigate the busy-line effect on the interservice time distribution. Closed-form analytical formulas for the interservice time are derived. A numerical study shows that a big discrepancy exists between the interarrival time and the interservice time. Based on the analytical results for the interservice time, the impact of the busy-line effect on modeling of portable movements in PCS networks is further evaluated. An analytical result for the distribution of the number of cell-boundary crossings during the interservice time is obtained. Both analytical results and numerical examples indicate that the busy-line effect has influence on the distribution of the number of cell-boundary crossings during the interservice time. Therefore, cost analysis for location management without considering the busy-line effect may lead to unreliable results. The results presented in this paper pave the way for modeling location management and portable movements in PCS networks.