Recent studies have shown that the superposition of packet sequences generated by packetized voice sources with speech detection exhibit high burstiness due to inherent correlations between successive interarrival times in the superposition stream. In a packet voice multiplexer without bit dropping, these correlations tend to cause significantly larger queueing delays and packet losses than would be predicted for a Poisson input stream. In this paper, we examine the performance of a packet voice multiplexer queue in which the less significant bits on voice packets are dropped during states of congestion in the multiplexer. Using the results of simulation and analytical modeling, it is illustrated that bit dropping on voice packets significantly smooths the superposition packet voice traffic by speeding up the packet service rate during critical periods of congestion in the queue. This phenomenon renders it possible to approximate the superposition process by a Poisson process for analyzing a packet voice multiplexer with bit dropping. The multiplexer is modeled using an M/D/l/K model in which D denotes the deterministic but state dependent nature of service. By comparison with a simulation, this model is shown to produce quite accurate performance predictions.
Significant effort is currently being devoted to the development of packet oriented technologies for integrated multiplexing
and switching of voice and data1,2,3,4,5,6
. Packetization of voice makes it possible to carry voice along with data on a single integrated packet-switched network. The advantages of integrated packet voice/data networks are many, e.g. the efficient sharing of transmission and switching facilities, the capacity advantage due to statistical multiplexing, and the potential evolution toward a fully integrated network which would provide image and video services as well. Some recent studies7,8,9
have also focused on hybrid multiplexing schemes in which voice is serviced using synchronous time division multiplexing while data is serviced asynchronously through packet queues. In this memorandum, we concentrate on integrated networks in which voice packets are also queued and therefore served asynchronously. However, generally voice packets would be given priority over data so as to ensure a low delay for voice. Voice packets
, however, do get jittered in time due to the variable queueing delays at the access interface as well as inside the network at the switching nodes enroute. A suitable delay build-out strategy is employed at the receiver to eliminate the delay jitter before playing out the voice to the listener10
In order to traffic engineer an integrated voice/data network, it is first necessary to understand the characteristics of the packet traffic generated by voice and data sources. In particular, it is of interest to know a way to characterize the superposition of packet arrival streams generated by a number of voice and/or data sources. Several recent studies have dealt with this issue in some deiail11,12,13,14,15,16,17. The work reported here is a continuation of the authors' previous studies11,12 and, in particular, this memorandum investigates the smoothing effects on the superposition traffic in a packet voice multiplexer with bit dropping for congestion control. The bit dropping scheme, based on an embedded voice coding technique18,19,20,21,22,23 takes advantage of the fact that voice is tolerant to bit dropping to a certain extent. Based on subjective quality consideration, it is well recognized that it is better to drop bits on voice packets rather than drop whole packets24,25 (for a given ratio of carried over offered information).
Recent studies have shown that the superposition of packet sequences generated by packetized voice sources with speech detection exhibit high burstiness (relative to a Poisson process) due to inherent correlations between successive interarrival times in the superposition stream. In the papers by Sriram and Whitt11 and Heffes and Lucantoni12, the burstiness due to correlations has been investigated by using the indices of dispersion for counts and intervals. In a packet voice multiplexer without bit dropping, these correlations tend to cause significantly larger queueing delays and packet losses than would be predicted by a Poisson model. In this paper, we examine the performance of a packet voice multiplexer in which the less significant bits in voice packets are dropped during states of congestion in the multiplexer. It is illustrated here that bit dropping on voice packets significantly smooths the superposition packet voice process by speeding up the packet service rate during critical periods of congestion in the queue. In fact, this paper seeks to establish a very significant hypothesis, namely, in a packet voice multiplexer with bit dropping, the superposition packet arrivals can be viewed as a Poisson process from a packet delay and queue length perspective. The hypothesis is conjectured first by looking at the structure of correlations in the superposition arrival process characterized by the index of dispersion for intervals (see Section 3). Then it is verified by comparing the results of exact simulations of the multiplexer with those of analytical modeling. The importance of the hypothesis is due to fact that the virtual sm90thing of the packet arrival process as a result of bit dropping on the voice packets has significant implications in terms of effecting delay and buffer overflow reductions in packet voice/data multiplexers. This result (i.e. traffic smoothing due to bit dropping) also makes it easier to develop tractable analytical models for the multiplexer for the general mixed voice/data scenarios, and helps avoid undue conservatism in traffic engineering.
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