Providing heterogeneous quality of service bounds for correlated video traffic at a multiplexor

Abstract

Network support for variable bit-rate video needs to consider (i) properties of workload induced (e.g., significant auto-correlations into far lags and heterogeneous marginal distributions), and (ii) application specific bounds on delay-jitter and statistical cell-loss probabilities. The objective of this paper is to present a quality-of-service solution for such traffic at each multiplexing point in a network. Heterogeneity in both offered workload and quality-of-service requirements are addressed.

A per-virtual-circuit framing structure and a pseudo earliest-due-date cell dispatcher are introduced to provide guaranteed delay-jitter bounds. Heterogeneous jitter-bounds are supported through software controlled frame-sizes which may be independently set for each virtual-circuit. The framing structure is a generalization of per-link framing introduced by Golestani. The proposed framing structure eliminates correcting for phase mismatches between incoming frames and outgoing frames, necessary in per-link framing. This results in reduction in end-to-end delay bound and buffer requirements, and a simpler implementation.

Strong auto-correlations typically seen in video traffic make equivalent bandwidth computations for heterogeneous cell-loss bounds intractable. To address this, the framing strategy is combined with an active cell-discard mechanism with prioritized cell-dropping, the latter utilizing the history of dropped cells and target cell-loss bounds for each virtual circuit. Upper bounds on the equivalent bandwidth needed to support a given workload with a target quality of service are developed. These are validated through numerical and simulation results from variable bit-rate MPEG-I video traces.

Introduction

The objective of this paper is to present a solution for providing (i) heterogeneous delay-jitter bounds, and (ii) heterogeneous statistical cell-loss bounds to different classes of variable bit-rate traffic at individual multiplexing points. The network is assumed to be cell-switched with virtual circuits similar to that in ATM networks.

Studies on a range of video applications indicate that there exists a slowly decaying auto-correlation structure in the underlying stochastic processes that constitute VBR video applications [3], [7], [8], [20]. It appears that different compression schemes can change this correlation structure somewhat; however, the dominant dependence structures imposed by applications are likely to persist. Studies in [8], [13] have suggested that VBR video can be modeled as a fractionally differenced autoregressive integrated moving average process.

A significant number of VBR video applications are expected to require guaranteed maximum-delay and delay-jitter bound for cells that are delivered, and low cell-loss probabilities. Further, quality of service guarantees for different applications are likely to belong to one of several classes. In order to provide dependable quality of service, a multiplexing point in the network must have the capacity available when it is needed. Providing quality of service guarantees for real-time traffic is an active area of research, see for instance [6], [10], [15], [26]. However, providing guarantees on maximum-delay, delay-jitter, and cell-loss probabilities (or some other measure of cell-loss) in the presence of a slowly decaying auto-correlation structure in traffic is non-trivial, especially if the coefficient of variation of the marginal distribution (or the distribution tail) is large. This is because such traffic significantly increases queue length statistics at a multiplexor [1], [5], [8], [16], [17], [18], [19].

Fig. 1 shows mean cell-loss versus number of frame-buffers for three traffic correlation structures with approximately the same coefficient of variation (∼0.24). A frame-buffer is the maximum number of cells that can be transmitted by the output channel in a given time interval (frame-time). The solid line showing a slow decay is for a long-memory input traffic sequence. The dashed line in the middle is for traffic with short memory. The line with the smallest mean cell-loss corresponds to a white noise (uncorrelated) input stream. Notice that mean cell-loss decays very slowly with increasing buffer size for traffic with a slowly decaying auto-correlation function.

While the above observations are not new, they offer a compelling reason to re-think how to meet strict bounds on delay-jitter, maximum-delay, and cell-loss probabilities for variable bit-rate video traffic. The problem is exacerbated by the fact that these bounds may need to be different for different applications (e.g., medical imaging versus video-conferencing). Also, the offered load may be heterogeneous, both in the auto-correlation structures and in marginal distributions.

The contribution of this paper is an architecture and associated algorithms for guaranteeing heterogeneous delay-jitter bounds and heterogeneous cell-loss bounds for such traffic.

A high-level view of the proposed architecture is as follows:

• A framing structure on a per-VC basis. To provide heterogeneous delay-jitter bounds, a framing structure is induced on virtual circuits, similar to that in [9], [10], [11]. (Differences between the two approaches are described later.) Consider a virtual circuit (VC), i, with a desired delay-jitter bound M_i. The frame structure splits time for this virtual circuit into juxtaposed intervals of length M_i at each multiplexing point. Cells from VC i that arrive in a given frame at a multiplexor are buffered, and not transmitted until the beginning of the next frame-time. If sufficient capacity is available to transmit these cells in the next interval, all cells arrive at the next hop within an interval of length M_i. This way, they are guaranteed to meet a delay-jitter bound of M_i. Also, if H_i is the number of hops for virtual circuit i, and D_i is a bound on the one-way propagation and processing delay, all cells that make it to the receiver are guaranteed an end-to-end delay bound of H_iM_i+D_i.

• Priority scheduling. Cells at an output queue that are ready to go contend for bandwidth and have competing delay-jitter bounds and cell-loss probability bounds. A priority scheduler addresses these concerns. For delay-jitter bounds, the scheduler follows an earliest due-date principle with modifications to enhance algorithmic efficiency. For cell-loss bounds, it uses a minimum guaranteed capacity, C_i cells/frame for virtual circuit i, with the rest of the cells if any, scheduled on a non-guaranteed basis. C_i is based on (i) marginal distribution of number of cells/frame, (ii) maximum acceptable probability of cell-loss in a frame, and (iii) the equivalent bandwidth of all virtual circuits in this jitter-class. The C_i’s are computed by the equivalent-bandwidth unit described in Item (4) below.

• An active cell-discard unit. If there are excess cells leftover from a frame at the multiplexor after the corresponding frame-time is over, it is likely that this is due to persistence in the arrival process as suggested by the solid lines in Figs. 1(a) and (b). These cells are likely to cause increased delay for cells in successive frames. Since buffering does not reduce cell-loss significantly for persistent traffic, we may elect to either toss them right away or mark them as low-priority cells and discard them on demand.

  The active cell-discard unit reclaims (or marks as old ) cells that do not get transmitted in their frame time. It is activated at the end of each frame.

  An important side-effect of using the active cell-discard unit is that it simplifies computation of equivalent bandwidth for correlated traffic (especially for heterogeneous cell-loss bounds), while achieving high utilization through statistical multiplexing.

• Appropriate equivalent bandwidth algorithms. Algorithms for computing upper-bounds on equivalent bandwidth are developed. They address heterogeneous cell-loss probabilities and heterogeneous jitter-classes.

• Miscellaneous.

  • Frames may be implemented on a per-VC basis. Frames from different VCs need not be synchronized.

  • Per-VC framing and active cell-discard may be implemented efficiently through associative matching of cell tags similar to that in processor pipelines (Section 2.2).

  • The frame-size for each virtual circuit is software set-able, so delay-jitter bounds may be negotiated over a continuum (at the granularity of cell transmission time). Also, unlike per-link framing (see Section 1.4), the frame size of a given virtual circuit is not constrained by frame-sizes of other active virtual circuits.

  • The minimum capacity guarantee per frame, C_i for each VC i, provides protection from misbehaving or malfunctioning VCs.

  • A call admission unit will use the equivalent bandwidth algorithms to determine if a specific call can be admitted without violating quality of service guarantees of other calls (or if an important call must be admitted, which calls to disconnect). The call-admission unit is not discussed in this paper.

Per-VC framing has been derived from Stop-and-Go queuing described in [9], [10], [11]. The primary enhancements are as follows:

• Framing is induced on a per-virtual circuit basis instead of a per-output-link basis, see Fig. 2, Fig. 3. Per-VC framing eliminates the need for correcting for phase mismatches between incoming frames and outgoing frames at a multiplexor, and significantly simplifies its implementation. As we shall see in Section 3, per-VC framing also reduces the maximum queuing delay by half and cuts buffer requirements by 1/3 at a switch, while retaining the same delay-jitter bound of per-link framing.

• Once cells from a frame become active (i.e., not dormant, waiting for their next frame-time), they compete with active cells from other virtual circuits for the output link. The algorithms that decide on which active cells to transmit and when, and which cells to drop, are necessitated by the need to meet heterogeneous cell-loss bounds and heterogeneous delay-jitter bounds simultaneously. They also provide a firewall across connections (protection from misbehaving sources). These algorithms are new.

  In [9], the objective was to support no-loss transmission with heterogeneous delay-jitter bounds. The latter were integral multiples of the smallest jitter-bound supported. Golestani showed that a pre-emptive priority scheduler with highest priority to the smallest jitter-class could meet all jitter bounds if sufficient capacity was available. In [11], Golestani also presented a solution that allowed for cell-losses for a single jitter-class (fixed delay-jitter bound).

  In the general case of meeting heterogeneous delay-jitter bounds with potential cell-losses, however, the scheduler needs to follow (i) an earliest due-date principle, and (ii) a cell-drop policy that takes into account current observations on dropped-cells per VC, and heterogeneous cell-loss bounds across VCs. See Section 2.3.

• The original Stop-and-Go queuing requirement that a traffic stream declare its (r,T)¹-smooth parameter is dropped. This trades-off higher utilization for a loss-less network. For a long-memory input stream, the average rate over a small interval, T, can be significantly higher (or lower) than its overall average rate, so r would need to be the peak rate for loss-less transmission, and would result in significantly low utilizations. In the current proposal, cell losses, while allowed, will be reduced through statistical multiplexing across virtual circuits and controlled through equivalent bandwidth computations.

• No-loss transmission can be guaranteed in the proposed architecture if desired, see Section 4.3. However, the emphasis is on efficient statistical multiplexing that can also guarantee specified cell-loss bounds.

The rest of the paper is organized as follows. Section 2 presents the proposed architecture. It includes (i) per VC framing with active cell-discard, and (ii) cell dispatching to meet heterogeneous delay-jitter and cell-loss guarantees for heterogeneous virtual circuits (with heterogeneous marginal distributions and auto-correlation structures). Section 3 presents maximum-delay bound, delay-jitter bound, and buffer requirements for per-VC framing, and compares the results with per-link framing. Section 4 addresses upper-bounds on equivalent bandwidth needed to meet heterogeneous delay-jitter requirements and heterogeneous cell-loss probability bounds, presents numerical and simulation examples, and shows that loss-free transmission may be achieved for desired virtual circuits. Section 5 presents related work. Section 6 presents our conclusions.