To evaluate the performance of both the DYVR-M and DYVR-A algorithms at a large scale which is not feasible experimentally, we performed extensive simulations. The sim- ulation environment mimics the characteristics of real networks that we observed through
0 0.1 0.2 0.3 0.4 0.5 Channel Fading Probability 6 7 8 9 10 11 12 13 Utility DYVR-M DYVR-A Prediction-based Oracle-based Oracle-based-window (a) 0 0.1 0.2 0.3 0.4 0.5
Channel Fading Probability 0 1 2 3 4 5 Lost Segments (%) DYVR-M DYVR-A Prediction-based Oracle-based Oracle-based-window (b) 0 0.1 0.2 0.3 0.4 0.5
Channel Fading Probability 0 1 2 3 4 Buffer Underflows (%) DYVR-M DYVR-A Prediction-based Oracle-based Oracle-based-window (c) 0 0.1 0.2 0.3 0.4 0.5
Channel Fading Probability 0
20 40 60 80
Video Rate Switches (%)
DYVR-M DYVR-A Prediction-based Oracle-based Oracle-based-window (d)
Figure 4.2: Simulation results for uniform channel conditions with varying channel fading probabili- ties (a) average utility achieved, (b) percentage of lost segments, (c) percentage of buffer underflows, and (d) percentage of video rate switches.
10 20 30 40 50 Number of Receivers 0 10 20 30 40 50 Utility DYVR-M DYVR-A Prediction-based Oracle-based Oracle-based-window (a) 10 20 30 40 50 Number of Receivers 0 0.5 1 1.5 2 2.5 3 Lost Segments (%) DYVR-M DYVR-A Prediction-based Oracle-based Oracle-based-window (b) 10 20 30 40 50 Number of Receivers 0 0.5 1 1.5 2 2.5 3 Buffer Underflows (%) DYVR-M DYVR-A Prediction-based Oracle-based Oracle-based-window (c) 10 20 30 40 50 Number of Receivers 0 10 20 30 40 50 60 70
Video Rate Switches (%)
DYVR-M DYVR-A Prediction-based Oracle-based Oracle-based-window (d)
Figure 4.3: Simulation results for fast changing channel conditions with varying number of receivers: (a) average utility achieved, (b) percentage of lost segments, (c) percentage of buffer underflows, and (d) percentage of video rate switches.
experimental measurements and of those reported in [99, 109, 174].
We assume that DYVR-M and DYVR-A can estimate the channel conditions at the receivers at the beginning of each slot. More specifically, we assume that the probability distribution of the state of the system is known at the beginning of each slot. DYVR-M and DYVR-A do not have any knowledge about the long-term channel state.
We compare the performance of DYVR-M and DYVR-A to the following buffer/virtual queue independent algorithms:
(i) Oracle: The Oracle Algorithm has exact knowledge of the channel conditions for each time slot up to a maximum window of wnd slots. At the beginning of each slot, it sets the transmission rate rtto be the maximum rate at which a fixed fraction f of the receivers can
generally very high. For a fair comparison, we tune f such that the Oracle Algorithm leads to similar number of segments lost as DYVR . Further, Oracle sets the video rate as the average of transmission rates over wnd, vt = wnd1 Pt+wndτ =t rτ to avoid frequent video rate
switches.
We consider two variants of Oracle with wnd = 1 called Oracle-Based and a large wnd called Oracle-Based-Window. Oracle-Based provides a loose upper bound on the achievable utility with more video rate switches and underflows. Oracle-Based-Window provides a more realistic comparison to DYVR where the number of video rate switches and underflows are close to DYVR. We choose wnd values for Oracle-Based-Window such that the number of video rate switches and buffer underflows are close to that of DYVR.
(ii) Prediction-Based: The Prediction-Based Algorithm has the same knowledge of the channel conditions as the DYVR algorithms. More specifically, it knows pi
t(r), the proba-
bility of successful reception at each receiver i and at each rate r. At the beginning of each time slot, it selects rt such that an expected fraction f of receivers will successfully receive
the video segments. Similar to Oracle, we choose f such that the number of segments lost is close to DYVR and a window-based mechanism to set the video rate vt= wnd1 Pt+wndτ =t rτ.
We simulate a variety of environments with different channel state distributions, receiver mobility patterns, and varying number of receivers. We assume that the transmission and video rate values can be chosen from sets of 8 different values each. The channel state characteristics of the simulated environments mimic those of real networks obtained through experimental measurements and existing literature. For our measurements, we conducted experiments with Nexus 7 tablets and an ASUS WiFi AP in indoor settings over a 5GHz channel for 802.11a transmissions. We measured the probability of successful packet reception at the receiver at different locations for different values of transmission rates for 5 experimental runs of 500s each. We observed that packet losses are bursty, the amount of losses is stable for the duration of a few seconds for stationary receivers, and there are atypical events that can lead to high losses for short durations of time. These observations agree with measurements in existing literature [109, 174]. Accordingly, the simulation scenarios and the assumptions are as follows:
(i) Uniform: The maximum transmission rate for which a receiver i can successfully receive a segment, ri
t, is chosen uniformly at random at beginning and remains same at all
times. However, for certain randomly chosen slots, the maximum ri
tdrops to a lower value.
This assumption models the channel fading effect we experimentally observed. We assume that the DYVR and Prediction-Based algorithms only know the probability of these fading events, while the Oracle Algorithm can predict a fading event in advance.
(ii) Mobility: The state of the system changes slowly over a period of time. We simulate a condition when the ri
t value for each receiver change according to a discrete Markov
Chain with 8 states corresponding to 8 channel states . Markov channel models have been extensively studied before [216, 231]4. We consider a variety of transition probabilities to
simulate the effect of higher mobility.
We developed a custom simulation tool based on the above observations. For various simulation scenarios, we ran 5 instances each 2,500 slots long.
Fig. 4.2 shows the performance of different algorithms in the Uniform scenario. Each simulation consisted of 10 receivers. We set the QoE parameters α = β = γ = 0.02. Fig. 4.2(a) shows the average utility achieved for different algorithms. The utility achieved by DYVR-A is marginally better than by DYVR-M and the average utility reduces as the fading probability increases. The utility achieved by both DYVR algorithms is close to that of of the Oracle-Based-Window Algorithm but higher than the utility of the Prediction- Based Algorithm.
Figs. 4.2(b), 4.2(c), and 4.2(d) show the average percentage of segments lost, percentage of slots with buffer underflows, and percentage of slots with video rate switches, respec- tively. We observe that both DYVR algorithms achieve performance as dictated by QoE requirements. While DYVR-A achieved marginally higher utility than DYVR-M, it also leads to marginally higher number of segments lost due to looser constraints on the number of segments lost.
4While significant effort has been dedicated to modeling mobility (e.g., [33, 58] and subsequent literature
consider Markovian mobility models), we use a simplistic mobility model since our focus is on the algorithmic performance evaluation rather than on mobility patterns.
Since the parameters of Oracle-Based-Window and Prediction-Based algorithms were tuned to yield performance close to DYVR, they satisfy the QoE requirements. It should be noted that the parameters of Oracle-Based-Window and Prediction-Based algorithms were obtained by rigorous trial and error. In practice, these parameters will change in different environments and it is infeasible to tune these parameters in realistic environments. The Oracle-Based Algorithm does not result in any segments lost and buffer underflows, due to knowledge of channel states. However, it results in large number of video rate switches.
Fig. 4.3 shows the performance of different algorithms in the Mobility scenario as a function of the number of receivers in the system. As expected, the average utility as shown in Fig. 4.3(a) grows for each algorithm with the number of receivers. Both DYVR-A and DYVR-M achieve higher utility than Prediction-Based but lower than the Oracle-Based and Oracle-Based-Window algorithms. Further, the gap between the performance of Oracle, DYVR, and Prediction-Based algorithms grows larger with increasing number of receivers. Figs. 4.3(b), 4.3(c), and 4.3(d) show the average number of segments lost, number of buffer of underflows, and video rate switches, respectively. Even in the challenging mobil- ity scenario, the DYVR-M and DYVR-A algorithms satisfy the required QoE constrains. Moreoever, the number of lost segments, buffer underflows, and video rate switches are less than 2%. The Prediction-Based and Oracle-Based-Window algorithms satisfy the QoE requirements by design but Oracle-Based results in high number of video rate switches.
In summary, the simulations demonstrate that both the DYVR-A and DYVR-M algo- rithms can provide close to optimal utility while satisfying the QoE requirements.