**5. Conclusions**

In this Chapter, under the assumption that unencumbered service time is exponentially distributed, a set of novel general-algebraic equations that examines the relationships between cell dwell time and residual cell dwell time as well as between cell dwell time and new and handoff channel holding times was derived. This work includes relevant new analytical results and insights into the dependence of channel holding time characteristics on the cell dwell time probability distribution. For instance, we found that when cell dwell time is Coxian or hyper-exponentially distributed, channel holding times are also Coxian or hyper-exponentially distributed, respectively. Also, our analytical results showed that the mean and coefficient of variation of the new and handoff call channel times depend on Laplace transform and first derivative of the Laplace transform of the probability density function of cell dwell time evaluated at the inverse of the mean unencumbered service time as well as on the mean of both cell dwell time and unencumbered service time. Additionally, we derive the condition upon which the mean new call channel holding time is greater than the mean handoff call channel holding time. Similarly, the condition upon which the mean residual cell dwell time is greater than the mean cell dwell time was also derived. To the best authors' knowledge, this phenomenon that may seem to be counterintuitive has been explained and mathematically formulated in this Chapter. We believe that the study presented here is important for planning, designing, dimensioning, and optimizing of mobile cellular networks.
