## 3 Numerical Examples
Figure 4: Energy consumption by varying the session arrival rate (small values of \(T_{E}\) and \(T_{W}\)). Figure 5: Energy consumption by varying the session arrival rate (large values of \(T_{E}\) and \(T_{W}\)). Figure 6: Cumulative average delay by varying the session arrival rate (small values of \(T_{E}\) and \(T_{W}\)). Figure 7: Cumulative average delay by varying the session arrival rate (large values of \(T_{E}\) and \(T_{W}\)). Figure 6 and Figure 7 show the cumulative average delay by varying the values of the inactivity timer \(T_{I}\) and the rate of data session arrival \(\lambda_{r}\), with the same parameter settings as those of Figure 2 and Figure 3, respectively, except for \(D_{off}=10(s)\) and \(D_{on}=1(s)\). The shapes of the cumulative average delay in Figure 6 and Figure 7 are very similar to each other, but the delay in Figure 6 has higher values, since the probability of the sleep state is higher in Figure 6. The cumulative average delay decreases as the values of the inactivity timer increase, since the probability of the idle state increases, which has a smaller delay than the sleep state. For a fixed value of the inactivity timer, the cumulative average delay increases as the rate of data session arrival increases. For small values of the inactivity timer, the effect of long delay in the sleep state is more dominant. Otherwise, the effect of short delay in the idle state is more dominant. Figure 8 and Figure 9 show the cost by varying the values of the inactivity timer \(T_{I}\) and the rate of data session arrival \(\lambda_{r}\), with the same parameter settings as those of Figure 2 and Figure 3, respectively, except for \(D_{off}=10(s)\), \(D_{on}=1(s)\), \(w_{energy}=20\) and \(w_{delay}=1\). The cost of Figure 8 increases as the values of the inactivity timer increase, since the effect of energy consumption is more dominant in the considered setting of weight factors, and the energy consumption of femto BSs decreases, as the values of the inactivity timer increase, as shown in Figure 4. On the other hand, the cost of Figure 9 decreases as the values of the inactivity timer increase, since the effect of energy consumption is more dominant in the considered setting of weight factors, and the energy consumption of femto BSs increases, as the values of the inactivity timer increase, as shown in Figure 2:0 For a fixed value of the inactivity timer, the cost increases as the rate of session arrival increases, in both Figure 8 and Figure 9, since higher data session arrivals cause more energy consumptions and cumulative average delays. From the results, we can see that an appropriate value for the inactivity timer should be selected to reduce the cost, depending on the energy consumption in the sleep entering and waking up states. Figure 2:1 Cost by varying session the arrival rate (small values of \(T_{E}\) and \(T_{W}\)). Figure 2:2 Low-power radio signaling load by varying the session arrival rate (small values of \(T_{E}\) and \(T_{W}\)). Figure 2:3 Cost by varying the session arrival rate (large values of \(T_{E}\) and \(T_{W}\)). tradeoff. In our further works, the power saving of MSs should be considered together with that of BSs, and thus, the integrated power saving of MSs and BSs will be analyzed.