Telecommunication Systems 16:3,4, 335–345, 2001  2001 Kluwer Academic Publishers. Manufactured in The Netherlands. Modeling Packet Delay in Multiplexed Video Traffic CHARLES THOMPSON, KAVITHA CHANDRA ∗ , SUDHA MULPUR ∗∗ and JIMMIE DAVIS ∗∗∗ Center for Advanced Computation and Telecommunications University of Massachusetts-Lowell, Lowell, MA 01854, USA Abstract. In this paper a Markov chain based characterization of a single video source is used to model multiplexed video traffic and the resulting packet delay. The multiplexed video stream of statistically identi- cal sources is represented using a reduced order approximation of the superposed Markov generator matrix. It is shown that inadequate spectral content in the single source generator matrix is manifested as an un- derestimate of the packet delay probabilities for the multiplexed stream. A new method for simplifying the generator matrix for the multiplexed video stream that amply models its spectral content is given. The simulated and calculated results using the aforementioned model are shown be in good agreement. Keywords: fluid buffer, VBR, multiplexer 1. Introduction Variable bit rate (VBR) video traffic sources can be successfully modeled by finite state, discrete time Markov chains [2,3,16]. The state structure, in conjunction with a rate process attributed to each state, allows modeling of the short-time correlation in traffic generated by a video-coder. The impact of temporal correlation in the output rate of a VBR video source on the queue response has been examined in [8] and it has been shown that macro-level correlations can be modeled by Markov chain based models. Long-range dependence seen in VBR video has also been examined and the queueing results have been compared to those obtained using a Markov chain based discrete au- toregressive model [7]. It was concluded that for moderate buffer sizes, the short-range correlations obtained using Markov chain models are sufficient to estimate the buffer characteristics. Traffic analysis [2,3] of H.261 and MPEG-2 coders has shown that typically 15–20 states are required to faithfully model the queue behavior of moderate to high activity video sources. Single source models form the basis for determining the queueing delay and loss distributions for multiplexed video sources. The distribution of the queueing de- lay is considered to be the sum of two components: one resulting from packet-level (cell- level) and the other from burst-level queueing [12]. In packet-level (cell-level) queues, the arrival packet stream is modeled as a periodic process with random displacements in the starting epoch [11,13]. Burst-level queues have been analyzed using the fluid buffer ∗ Partially supported by NSF CAREER grant NCR-9734585. ∗∗ Currently at Tellabs, Willington, MA 01887. ∗∗∗ Supported by Lucent Technologies Cooperative Research Fellowship Program.