A diagram of the proposed QoS mapping framework is presented in Figure 3.1. In our framework, service differentiation is done in terms of the loss rate and delay performance of network service. (We are assuming that the traffic-conditioning entities of the DiffServ network are taking care of the throughput negotiation.)

Figure 3.1. Overall QoS mapping framework based on RPI and network DS levels.

Each video flow of a user application must be classified according to its importance to receive low-delay or low-loss packet delivery service from the network. For example, low delay is more important to a video conference application than to a streaming video application. Moreover, each packet is associated with the RPI, which is composed of two normalized indices, the RLI and the RDI. These indices are described in detail in Section 3.3. RLI and RDI are basically indices that indicate the impact of a data segment’s loss and delay, respectively, on the quality of the application. Therefore, these indices specify the data segment’s importance in terms of receiving good service quality from the network layer.

The packets associated with the RPI are categorized into intermediate DS traffic categories (i.e., traffic aggregates with different source traffic priorities) in a fine-grained manner by the application. We use the term “intermediate DS traffic categories” because these categories may change as the packet enters the DS domain. The marking of codepoints in the packets in accordance with these intermediate DS traffic categories is a “pre-marking” [17] from the viewpoint of the DS domain. We allow the application to do such a pre-marking on the basis of the application’s knowledge of the packet’s content without it knowing the status of the network or SLA between the application’s domain and the DS domain. Then, pre-marked (i.e., RPI-categorized) packets are conveyed into the DiffServ-aware node for QoS mapping, which takes into account the SLA with the DS domain, and in the case of dynamic QoS mapping, also the network status. Such QoS mapping can be implemented at the end-system itself, at a DiffServ boundary node, or at both. Thus, given a video application and the responding DiffServ network, the QoS mapping is accomplished by mapping (i.e., marking) the relative prioritized packets to maximize end-to-end video quality under a given cost constraint. Then, at the DiffServ junction (i.e., a DiffServ boundary node), the packets are classified, conditioned, and re-marked to certain network DS levels by considering the traffic profile based on the SLA and current network status. (The QoS mapping implemented at the DiffServ boundary node can be designed to consider the SLA and global view of all the aggregate traffic coming from multiple applications.) Finally, the packets with DS-level mapping are forwarded toward the destination through a packet-forwarding mechanism, which mainly comprises queue management and a scheduling scheme.

In this chapter, we consider the case in which the DS domain provides proportional DiffServ through its packet-forwarding mechanisms. The desired differentiation in queuing may be realized by adopting multiple queues with several drop curves such as multiple RED and RIO [42], [97]. Furthermore, if different weighting factors are adopted, a modified version of WFQ scheduling can be used to complement queue management to provide the desired loss-rate/delay differentiation.

The above QoS mapping framework can be applied to multimedia rate-adaptive transport mechanisms. The framework can be used with a futuristic differentiated service with a pricing mechanism that charges different prices for different classes. Since a video codec has several options for trading compression efficiency for flexible delay manipulation, error resilience, and network friendliness, the QoS coordination has to provide a simplified QoS mapping process between the video encoder and target network. The purpose of introducing RPI is to abstract and isolate coding details from the network adaptation. By assigning RPI to each packet in an appropriate manner (i.e., keeping the fine granularity as much as possible), the proposed delivery system can accommodate the demand of each packet to achieve the best end-to-end performance in adapting to network fluctuations.

A typical DiffServ architecture defines a simple forwarding mechanism at interior network nodes while pushing most of the complexity to network boundaries [17], [98]. The traffic conditioner (composed of the meter, marker, shaper, and dropper) is placed at the boundary of the network. Given this functionality at the boundary, interior nodes use a packet-forwarding mechanism with queue management and scheduling for incoming packets to deliver differentiated services to various packets. This DiffServ architecture can bring benefits to both the end-user and ISP by providing better service quality for CM applications if they are willing to pay more for higher quality. Thus, the design principles for QoS mapping should consider the interests of both the end users and the ISPs. That is, an end-user should benefit from a DiffServ-aware application through having the option of obtaining higher service quality, while an ISP should enjoy the benefit of flexible charging based on the end-user’s preferences. To handle this negotiation, we need to measure the QoS demand of CM applications and the QoS supply of DiffServ networks in terms of pre-defined granularity. With pre-defined granularity, service differentiation can be demanded by marking differently at the end-system to request targeted DS levels. The service level may then be adjusted (i.e., through re-marking) in the DiffServ network and handled (i.e., forwarded) accordingly.

Each DS level is identified by the ToS or DS byte (i.e., the DSCP) defined in the IP header. The DiffServ working group also defines PHBs using the DS byte to specify the required forwarding behavior for packets in accordance with DS levels. Among initial PHBs being standardized are the EF PHB for DiffServ PS [24] and the AF PHB for DiffServ AS [23]. The EF PHB group specifies a forwarding behavior in which packets experience very small losses and queuing delays. EF PHB, based on priority queueing, better suits latency-stringent applications at the cost of a higher price. The AF PHB group specifies a forwarding behavior to preferentially drop best-effort (BE) and/or out-of-profile packets when congestion occurs. By limiting the volume of AF flows and managing the BE traffic appropriately, network nodes can ensure better loss behavior for AF-marked packets. As a result, the DiffServ framework provides DS levels with different losses and delays. For example, one EF queue, four AF queues with three drop preferences, and one BE queue may be defined as depicted on the network side in Figure 3.2. We can draw three equivalent cost lines in Figure 3.2, imagining several pricing model possibilities for the ISP. Line (a) considers only loss rate, while Line (c) depends only on delay. Line (b) relies on both loss rate and delay, and it is flexible. That is, at the same cost, it provides various service combinations such as higher delay with a lower loss rate, and vice versa.

Figure 3.2. QoS mapping from source RPI into network DS levels.

Different DS levels are to be provided based on the marking (on the DS byte) of an application packet, and different amounts of loss and delay are expected based on the requested DS level. Thus, it is natural to think of associating a packet with both loss and delay priorities (i.e., RLI/RDI) rather than with loss alone, albeit in a fine-grained manner. For streaming video applications, the RLI association of each packet should reflect the loss impact of each packet on the video quality. For RDI, classification of video streams depends more on application context (e.g., video conferencing or video-on-demand) than on video content within a stream. For example, as shown on the source side of Figure 3.2, the quality request of two video applications, (A) and (B), are clearly distinguishable in terms of RDI depending on application usage, with added variability expressed by RLI.

For delay differentiation within a stream, Tan and Zakhor [99] considered frame-encoding modes. In this case, the highest delay sensitivity is given to the intra-coded frames (I frames), the next priority is assigned to the predicted frames (P frames), and the bi-directional, interpolated frames (B frames) have the lowest priority based on the encoding and decoding order of each frame type. This implies, however, that within a stream, the RLI and RDI attributes of packets are not completely orthogonal, which makes a reasonable classification somewhat difficult (this is discussed further in Section 3.3). Considering the complexity involved in varying RDI for each packet, we believe an appropriately fixed RDI with varying RLI is more than sufficient. Thus, in this work, we assign a fixed RDI for all packets of an application, as shown in Figure 3.2, and try to establish a satisfactory range of DS levels for the given RDI.

Given the RPI of each packet, our goal is to identify the best QoS mapping for video packets with content-aware forwarding under a cost constraint. At the end-system, an RPI is assigned to each packet, and it is then categorized into the kth category among K DS traffic categories. However, it is still up to a specific deploying environment to determine where the QoS mapping will be conducted. If the QoS mapping is conducted at the network adaptation unit of the end-system, an application can take advantage of its content-awareness (i.e., original RPI) to the extreme. Also, it can cover the early stage of DiffServ deployment, since it does not require any additional supporting network node except for prioritized DS levels. However, it lacks knowledge of the dynamics of the network and of the aggregation effect of competing flows, which can impede the efficiency of mapping because of the lack of a proper feedback mechanism. To provide a better fit into the access network scenario shared by multiple DiffServ-aware applications, it might be worthwhile to introduce a special version of a DiffServ boundary node to handle the proposed QoS mapping. With this, we could treat effective QoS mapping between aggregated CM packets and network DS levels (with fluctuating, but bounded service levels) under the TCA in the SLA. By adjusting the QoS mapping dynamically through coordinated interaction with end-systems, we could expect to achieve sophisticated exploitation of the DiffServ advantage.

However, note that in this chapter, we promote the futuristic concept of a proposed QoS mapping framework while deferring the discussion of practical issues such as dynamic QoS mapping and its aggregation effect.^[3] By focusing on the QoS mapping problem of each single flow, we have intensively investigated the potential of the proposed framework. In particular, we will discuss how to create the required building components, such as the RPI association/categorization, the persistent packet-forwarding mechanism desired, and the practical formulation of QoS mapping. Thus, with several DiffServ network deployment scenarios and corresponding QoS mappings to consider, both network and end-to-end video performances of the proposed mapping framework are evaluated for end-to-end streaming video over simulated DiffServ networks.

In our approach, the importance to an end-user of obtaining a low packet loss rate or reduced delay is determined based on the following criteria. First, the decision focuses on relative and fine-grained priorities inside an application, which rely on a linkage to an absolute metric related to the application’s contents. When initially marked in the DS field with RLI/RDI, video application packets at the user end have limited knowledge of the dynamic status of the network and of competing applications within the same boundary. The assigned relative priority for each packet is supposed to be interpreted at the DiffServ-aware node. Next, because more assured (but not guaranteed) service is to be provided, the video application needs to be able to cope with possible packet losses and delays. The assigned RLI/RDI parameters basically assume that the video stream has already been generated with error-resilience features so that the loss or delay of each packet can be tolerated to a certain degree. Finally, the resulting prioritization should exhibit some kind of clustering behavior in the RLI/RDI space so that it can keep its distinction when mapped to the limited DS byte.

As discussed previously, the degree of a video stream’s importance for receiving low-delay network service depends heavily on the application’s context. If we consider different degrees of importance for receiving low delay for different packets within a stream, we find that varying demands for delay quality are usually connected with the layered coding of video compression. For example, the I, P, and B frames of ISO/IEC MPEG-1/2/4 frames have varying demands with regard to delay as well as loss. The situation is similar for the spatial-scalable, SNR-scalable, and data-partitioned layers of MPEG or H.261/H.263, with the exception of the temporal-scalable layer. However, as a video application becomes network-aware, the trend seems to move gradually toward delay variation, even within a stream. A good example is the asynchronous media transmission scenario, where flexible delay margins can be exploited throughout transmission. This idea has been denoted as delay-cognizant video coding in [101], which applied an extended form of region-based scalability to H.263 video. Multiple-region layers within a stream were constructed in [101], where varying delay requirements were associated by perceiving a motion event such as nodding, gesturing, or maintaining lip synchronization. To be more specific, cognizant video coding assigns the lowest delay to the most visually significant region, and vice versa. Since packets assigned a longer delay may arrive late, this presents the opportunity for the network service to route packets through less congested but longer routes and charge lower prices. Another example is packets of the MPEG-4 system that encompass multiple elementary streams with different demands under one umbrella. This kind of integrated stream can justify the demand for inter-media RDI/RLI differentiation. Thus, we propose to distinguish a packet based on the loss rate and delay tuple, leaving flexibility to subsequent stages. Note, however, that only fixed RDI for a flow is employed currently.

The MB-level corruption model described in the previous section indicates the level of importance, for each MB, of not losing the MB. Thus, RLI can be defined on the basis of such a corruption model. However, determining the importance of not losing a particular MB requires an estimation window as data history, which induces some delay before marking RLI per packet. In this section, a simple and practical version is presented for online RPI generation. This RLI is calculated from video factors such as initial error, motion vector, and MB encoding type. Such a simplified MB-based corruption model provides RPI association to approximate the actual loss impact in MSE.

Under packetized video transmission, the RLI assignment for a packet is best when it can precisely represent its error propagation impact on the receiving video quality. However, the specific method for RLI prioritization is totally application- (and furthermore, video compression scheme-) dependent. Thus, we have chosen ITU-T H.263+ video [96] as the evaluation codec, considering its wide acceptance for low-latency video conferencing and its potential for video streaming. Note that with regard to this RLI association, there is not much difference among the motion-compensated prediction codecs, which include both MPEGs and H.261/H.263.

Given frame size and target bit rate, each packet has a different loss effect on end-to-end video quality due to inter-frame prediction. The impact of packet loss may spread within a frame up to the next re-synchronization (e.g., the picture or GOB headers) due to differential coding, run-length coding, and variable-length coding. This is referred to as spatial error propagation, and it can damage any type of frame. For temporal error propagation, damaged MBs affect the non-intra-coded MBs in subsequent frames, which use corrupted MBs as references. Recent research on the corruption model [106] has attempted to model this loss effect. The corruption model is a tool used to estimate the packet loss impact on the overall received video quality. However, most modelling efforts have focused on the statistical side of the loss effect, while a dynamic solution was sought in our approach. Instead of computationally complex options, we devised ways to associate RLI to H.263 packets with a simple and online calculation.

Basically, we use the error-resilient H.263+ stream, compressed at a target rate of 384 kilobits per second (kbps), for a common intermediate format (CIF) test sequence with 10 frames per second (fps). Several error resilience and compression efficiency options (“Annexes D, F, I, J, and T” with random intra-refresh) are used in the generation of the so-called “Anchor” (i.e., GOB) mode stream. The random intra-refresh rate is set to 5% to cover the network packet loss. It is then packetized by one or more packets per GOB, which is dependent on the maximum transfer unit (MTU) size of the IP network. Thus, we propose a simple yet effective RLI association scheme for this H.263+ video stream, which is calculated for each GOB packet.

Various video factors are taken into consideration for the proposed RLI association. First, the magnitude and direction of the motion vector for each MB are included to reflect the loss strength and temporal loss propagation due to motion. Then, the encoding types (intra, intra-refreshed, inter, etc.) are considered. In other words, the refreshing effect is added by counting the number of intra-coded MBs in a packet. Finally, the initial error due to packet loss is considered, assuming the normative error concealment adopted at the decoder. To better explain this, sample distributions of these three video factors are depicted in Figure 3.6. The RLI for a packet may take into account all of these video factors by summarizing the normalized video factors with an appropriate weighting as

Equation 3.10. 

where N_VF is the total number of video factors considered, NVFⁿ stands for the normalized video factors, and Wⁿ stands for the corresponding weight factors. The normalization is done with an online version such as through updating the sampling mean at an ith update time.

Figure 3.6. Video factors (VFs) for RLI with “Foreman” sequence: (a) motion vector magnitude; (b) number of I-coded MBs in each packet; and (c) initial error due to packet loss.

Figure 3.7 shows an example of the resulting RLI assignment for a “Foreman” sequence. This model provides a much more accurate estimated MSE, but it needs forehead information in a particular window range to allow calculation of the propagation effect. For our purpose of QoS mapping, we do not need an accurate MSE amount because the relative priority order and relative quantity are enough. Eq. (3.10) is simple and can be generated easily as an online version with the sampling mean. A more accurately estimated RLI based on a corruption model is proposed in [107], but it needs the history information of several subsequent frames to make such an estimate, which is somewhat of a trade off. As shown in Figure 3.8(d), using 20 frame history windows to calculate RLI has more correlation with actual measured MSE than the process shown in Figure 3.8(c).

Figure 3.7. RLI for “Foreman” sequence obtained by applying Wⁿ’s (0.15, 0.15, and 1.75) for the three video factors of Figure 3.6.

Figure 3.8. A comparison of: (a) the actually measured MSE coming from loss of each GOB packet; (b) the proposed RLI pattern for a “Foreman” sequence; (c) the correlation distribution between actual MSE and proposed RLI of the same GOB packet number; and (d) the correlation distribution between actual MSE and corruption model-based RLI in [107].

To show that proposed RLI approximates actual loss propagation, the actually measured MSE from each GOB packet is calculated and compared with the proposed RLI pattern in Figure 3.8. The simple RLI shows a pattern similar to the actual MSE, and there is general correlation between two. This is enough for our goal of differentiating video packets in a stream for prioritization marking according to their importance since the QoS mapping is needed from only several source categories and the network DS levels are few in number.

Finally, RLIs are categorized into K DS traffic categories to enable mapping to limited DS field space (or eventually to be ready for mapping to more limited network DS levels). In our approach, simple non-uniform quantization of RLI is performed for this categorization. That is, as shown in Figure 3.9, categorization is done with gradually increasing steps as category k increases. Another possible approach is to categorize packets into an equal number (i.e., uniform distribution). After categorization, all packets belonging to category k may be represented by their average RLI value, .

Figure 3.9. Packet distribution and average RLI of each video DS category for a “Foreman” sequence.

Higher RLI thus represents more potential damage to visual quality. To verify the clustering behavior of RLI association, we observed RLI distribution for several video sequences. As shown in Figure 3.10, the RLI distribution varied according to a scene’s characteristics. Since it affects the QoS mapping, we will explore the impact of RLI distribution patterns in Section 3.4.2. Finally, RLIs are categorized to enable mapping to limited DS field space (or eventually to be ready for mapping to more limited network DS levels), which is represented by source category k among K categories. In our approach, simple, uniform quantization of RLI is performed for this categorization. After categorization, all packets belonging to category k may be represented by their average RLI value, .

Figure 3.10. Different RLI (cumulative) distributions for several video sequences.

QoS mapping a relative prioritized packet onto a DS level can be formulated into the following optimization problem for a single flow. Each packet i of the flow, mapped to a certain network DS level q (∊{0, 1, . . . , Q-1}), gets an average packet loss rate by paying unit price p_q. (DS level refers to a DiffServ class or traffic aggregate in IETF terminology, that is, a DS level is associated with a particular DSCP.) For the sake of simplicity, fixed RDI per flow is used to limit the allowed range of [q_min, q_max] to which packets can be mapped without violating the delay requirement. Then, the problem only needs to address the RLI-based optimization as follows. Each packet i of flow f assigned to a certain network DS level q will get an average packet loss rate by paying unit price p_q. Given the acceptable total cost P(f), the effort to achieve the best end-to-end quality for flow f can be formulated by minimizing the generalized quality degradation QD^(f):

Equation 3.11. 

where N^(f) is the total number of packets in flow f. The QoS mapping is denoted by vector

and q(i) is the DS level to which the ith packet is mapped.

If we fix the mapping decision for all packets that belong to category k, Eq. (3.11) is simplified to Eq. (3.12). Note that the QD in Eq. (3.12) is an expected QD, where the loss effect of a packet belonging to category k is represented by the average loss effect :

Equation 3.12. 

where is the number of packets belonging to category k for flow f. Note that . The QoS mapping decision is denoted by the K-dimensional vector , where K is the number of the source’s packet categories.

To solve the above optimization problem, consider the following factors. First, in a real situation, we must limit the resource allocation based on the TCA specified in the SLA with the DiffServ network. Thus, the above formulation must be constrained further by the traffic conditioning agreement before practical utilization. Next, the cost function given above may better reflect a real situation if the added complexity and out-of-order arrival handling cost due to dynamically scattered packets over multiple DS levels are included. These factors are assumed negligible at the current stage. Finally, p_q(k) depends on DiffServ provisioning, which will be decided by the service provider and negotiated in the SLA.

To use this as a guiding solution, we assume that a DS domain provides a proportional DiffServ and maintains the specified proportionality persistently in a wide range of time scales. The optimal solution in such an idealized situation can be derived as follows. In an idealized, proportional, and differentiated service, the packet loss rate can be specified as a particular monotonically decreasing function of the DS level q. (In an proportional DiffServ, the actual value of the loss rates experienced can be a certain factor times the function, and the multiplicative factor varies with time.) We consider the case that the loss rate is inversely proportional to the DS level q.^[4] If unit price p_q is assumed to be proportional to DS level q, the optimal mapping solution to (3.12) can serve as a guide for the mapping decision to be practiced. We can use the Lagrangian technique [108] for both constrained optimization problems (3.11) and (3.12).

Let us assume for simplicity that the value of q(k) can be taken from a continuum. We can then replace the inequality constraint of Eq. (3.12) with an equality constraint because the optimal solution obviously will have to spend all of the allowable cost P(f). According to the Lagrangian principle, there is a useful sufficiency condition that states that if a value λ can be found such that a value of , say (λ), minimizing

Equation 3.13. 

satisfies the equality constraint

Equation 3.14. 

then solves Eq. (3.12). Thus, we can guess a value of λ that minimizes Eq. (3.13). If the minimum point satisfies the equality constraint (3.14), then the solution is found. Otherwise, we can adjust the value λ and minimize Eq. (3.13) again. Furthermore, Eq. (3.13) is separable, so we can separately minimize

Equation 3.15. 

for each k. This minimizing value of q(k) can be found by drawing a line with slope -λ that is tangent to the convex hull of curve QD_k versus cost. The cost p_q(k) corresponding to the contact point of the tangent line is the cost of q(k) that minimizes J_k(λ) for the given λ. Figure 3.11 illustrates such minimizing values of q(k) for different values of k for a given λ. (Note that we are assuming that cost p_q(k) is proportional to q(k).)

Figure 3.11. Illustration for mapping from RLI to the DS level. (Given the relationship for RLI categorization, the loss rate per DS level, and the pricing strategy, the Lagrangian formulation leads to optimal mapping.)

With the assumption of loss rate function l_q(i) = L / q(i) and unit price function P_l · q(i) (as illustrated by two of the curves in Figure 3.12(b)), the Lagrangian formula for Eq. (3.11) for each i becomes

Equation 3.16. 

Then, by searching around the convex hull of the graph of QD versus cost, we can obtain the optimal mapping solution for a particular value of λ. Also, we can obtain a closed-form solution by searching for stationary points where and applying equality constraint p_q(i) = P^(f). For a given operating λ, the minimum can be computed independently for each packet. The point on the QD versus cost characteristic that minimizes J_i(λ) is the point at which the line of absolute slope λ is tangent to the convex hull of the QD versus cost curve. The resulting closed-form solution is expressed by and

Further assuming knowledge of the video source’s RLI distribution, we can finally obtain a solution to Eq. (3.11). For this, we approximate the RPI distribution of sequences shown in Figure 3.10 as one of the three different RLI patterns shown in Figure 3.12(a): C₁ U(i)² for “Akiyo,” C₂ U(i) for “Hall,” and for the “Stefan” and “Foreman” sequences.

Figure 3.12. (a) RLI pattern with typical categorized video types; (b)an example of the packet loss rate and unit cost of DS level q.

This closed-form solution usually matches the actual numeric solutions depicted in Figure 3.13 for “Akiyo,” “Hall,” and “Stefan,” respectively. Note that the mapping distribution resembles that of Figure 3.10, which is again represented by patterns C₁ U(i)², C₂ U(i), and , respectively. We can get some QoS mapping guidance from types such as RLI_i, which represent C₁ U(i)², C₂ U(i), and as the ascending order for source category k shown in Figure 3.12(a). The loss rate function of each DS level l_q(i) is assumed to be two typical types, such as or , which are shown in Figure 3.12(b).

Figure 3.13. Effective QoS mappings for different RLI source patterns in the loss rate of (a) (b) .

One Lagrangian formula of Eq. (3.16) is for the case of an RLI using C₂ U(i). Now,

Equation 3.17. 

We can get a closed form in case of using and the equality constraint. Then, we can obtain the solution q(i), an optimal QoS mapping with the λ determined by total cost constraint, as follows:

Equation 3.18. 

If RLI_i has another pattern, such as C₁ U(i)², , then an optimal QoS mapping takes the forms that are proportional to U(i) and , respectively. It matches the actual numeric solutions of the video test sequences of “Akiyo,” “Hall,” and “Stefan,” which are patterns similar to C₁ U(i)², C₂ U(i), and , respectively. The numeric solutions under the same total cost constraint (i.e., all k is assigned to q = 4) are shown in Figure 3.13(a) as a categorized source version.

Now, let us consider the case in which the loss rate is a linear function of q and the cost p_q is also a linear function of q (e.g., p_q = P_l · q for some P_l). In such a case, the expected quality degradation caused by packet i, is a linear function of price p_q.

Let us now narrow our scope further and consider the case in which source packets have been grouped into a small number of categories K, as assumed by Eq. (3.12). We denote the category of packet i by k(i). denotes the average RLI value of category k(i) or k. Figure 3.14 illustrates that the expected quality degradation measures, QDs, caused by packets i and j, are both linear functions of price. The slope of the line for packet i (or j) is affected by . Figure 3.14 also illustrates how to optimally map the grouped source categories k with different to network DS levels q.

Figure 3.14. Optimization process with linear loss rate function.

Now, let us see how the optimal QoS mapping is determined in this linear loss rate case. In the example case in Figure 3.14, category k(i)’s QD is more sensitive to the price of q than category k(j)’s because the absolute value of is greater than that of .

As a simple illustration, let us suppose that we map both packets i and j to the same DS level that incurs cost p₀. Next, we insert a perturbation of the QoS mapping. Now, say that we reduce the cost of packet i by amount p₀–p₁ and increase the cost of packet j by p₂–p₀ while preserving the total cost. This can be done by choosing p₁ and p₂ in such a way that p₀–p₁ = p₂–p₀. (For conceptual illustration, we are currently assuming that q is in a continuum.) After such a perturbation of QoS mapping, the resulting total of the expected degradation is reduced, while the total cost remains the same. Thus, for any pair of packets belonging to different categories k, we can keep adjusting their DS levels (prices) while keeping the total cost unchanged. If this process is continued, the resulting optimal mapping q(i) has monotonicity with respect to k(i). (The higher k(i), the higher q(i).) Furthermore, the majority of packets are mapped to the extreme values of q. In other words, most packets are mapped to the highest DS class or lowest DS class. The numerical solution in Figure 3.13(b) illustrates this.

We evaluated simple and online-capable RPI (exactly RLI) in Section 3.3 through an ideal setting in which each DS level q had a different but exact packet loss rate pre-assigned by a given manipulated packet loss curve versus q. Each packet loss rate of q randomly experiences a packet loss rate from the state of the two-state Markov chain known as the Gilbert model, shown in Figure 3.15. The transition probabilities from “Bad” (i.e., packet loss) to “Good” as q = 0.9 and give a little bit of burst to the packet losses. The average packet loss rate varies between 0% and 20%.

The Markov model is popular for capturing temporal loss dependency [109], [110], [111]. It is simple to understand and implement in monitoring applications. In Figure 3.15, p is the probability that the next packet will be lost, provided the previous one has arrived. q is the opposite. 1 – q is the conditional loss probability. Normally, p + q < 1. If p + q = 1, the Gilbert model reduces to a Bernoulli model.

Figure 3.15. Network topology model for the simulation.

First, the proposed RPI performance is evaluated with H.263+ video streams under the ideal network condition of Figure 3.12(b). The result shows the effectiveness of packet-/session-based differentiation (performed by QoS mapping) over several typical video sequences. The idealized packet loss rate for each DS level is simulated by a two-state Markov model known as the Gilbert model with transition probabilities from “Bad” (i.e., packet loss) to “Good” as q = 0.9 (a somewhat large value), which gives slightly bursty packet losses. If we set q as a small probability value, it causes relatively longer bursty packet loss (i.e., a large loss-correlation effect).

The phenomenon of bursty packet loss is found easily, but the bursty loss period depends on various network load conditions. A result [112] shows that a short bursty loss causes a greater extent of video degradation in comparison with a long bursty loss since the former occurs more frequently than the latter under the same packet loss probability. In this experiment, we wanted to show the performance comparison in the case of short bursty packet loss under severe network load conditions.

Figure 3.16 shows the performance comparison between RPI-aware and RPI-blind mapping under total cost constraint. The loss rate and cost curve per DS level are assumed as the curves for p_q(i) and shown in Figure 3.12(b). It is interesting to note that the gain in PSNR varies somewhat depending on the video sequences. For “Akiyo,” the gain is smaller than with other sequences, which is partly due to the small movement involved in this scene. However, for other sequences, we can observe a clear advantage of packet-based differentiation. Overall, this result verifies the obvious benefit of RPI-aware QoS mapping in DiffServ networks.

Figure 3.16. Average objective video quality (expressed in PSNR) for several video sequences under the loss/cost assumption of Figure 3.12(b).