Performance Analysis of a Priority based ATM Multiplexer with Correlated Arrivals Reza Jafari and Khosrow Sohraby Computer Science Telecommunications University of Missouri zyxwv - Kansas City 5100 Rockhill Road Kansas City, MO 64110, USA zyxw (rja zyxwvuts f ari, sohraby)@cstp.umkc.edu Abstract-In this paper, we consider the performance anal- ysis of an ATM multiplexer supporting both delay sensitive (e.g., silence detected voice) and loss sensitive (e.g., data) traffic flows. The delay sensitive cells are stored in a finite (relatively small) buffer and are given service priority over loss sensitive cells in each slot. In our formulation, we al- low both classes to have a general (Markovian) correlation structure. A simple matrix geometric solution for the state proba- bility of the system is provided allowing simple computation of any desired performance metric such as loss probability and buffer requirements of high and low priority classes, respectively. We provide number of numerical results. In particular, we consider the superposition zyxwvutsr of Bernoulli ON-OFF sources of- ten used to model silence detected packetized voice-like traf- fic as high priority class. The example for low priority traffic is taken to be i.i.d batches of geometric distribution and two- state correlated batches. Our numerical results show that both the loss behavior and the buffer requirements are quite sensitive to the (average) burst size of high priority traffic. In particular, it is demonstrated that for any level of uti- lization, the buffer requirements for both classes appear to be almost proportional to the burst size of the high priority class. The performance of low priority traffic is shown to be quite sensitive to its correlation structure. This class suffers most if both low and high priority traffic are very bursty. zyxwvut Key Words: Priority Queueing Systems with Finite Buffer. M/G/l-Type structure, Matrix Geometric Solu- tion. I. INTRODUCTION Modern telecommunications networks are expected to provide diverse type of services such as data, voice, and video which may share common resources for transmis- sion. ATM (Asynchronous Transfer Mode) is a promising transfer technology for supporting the modern telecommu- nications needs. Different classes of service may require different degree of Quality-of-Service (QoS). For example, voice traffic is very sensitive to delay or delay jitter while data traffic is loss sensitive. In an ATM network, packets are broken into fixed size cells which are statistically multiplexed over the high speed links. Statistical multiplexing of the cells generated from diverse traffic sources with possibly very different charac- teristics on an ATM link introduces considerable flexibility and potential saving in the allocation of network resources. However, if the network is not properly designed, dimen- sioned and controlled, extensive cell delay, cell loss and cell delay variation (CDV) deteriorate the performance of the network to an unacceptable level. In order to provide an acceptable performance to both loss and delay sensitive services, we may give priority to loss sensitive traffic. This is easily achieved by (logical) partitioning of buffer at the ATM switching fabrics where in each slot, the delay sensitive cells are transmitted first. In this paper, we concentrate on the loss behavior of delay sensitive (high priority) class and the buffer require- ment of the loss sensitive class (low priority). Fig. 1 depicts the system under consideration. To fully capture the im- pact of correlation of both traffic sources, we model them as general Markovian arrival processes. In addition, our model allows an arbitrary large number of cells arriving from the low priority sources in any slot, where a general rational “probability generating matrix” for the arrival pro- cess of this stream is considered. We also provide a (mod- ified) matrix geometric solution for the buffer fill distribu- tion for low priority class. Moreover, our model is exact in the sense that we do not use truncation in the computation of various performance measures in the system. Our work departs sharply from the existing works in the literature such as [3], [lo], [6]. First, we do not assume infi- nite buffer for the delay sensitive traffic, since a small buffer may be sufficient to support this service. Examples of dis- crete time priority queueing systems where both sources enter an infinite buffer are given in [3],[10]. In zy [7], [6], 191, the authors use the probability generating function (p.g.f) approach in the analysis which requires root finding and z-transform inversion for the distribution of cells in each buffer. In [4], correlated traffic is considered for a special case of a two-state Markovian source. In [lo], the work in [4] is generalized by assuming a more general source for the high-priority source. However, independent arrivals are assumed for the low-priority source. The matrix analytic approach of Neuts [5] is used which may require extensive memory and possibly truncation if the support of the dis- tribution (i.e., the maximal value) of low-priority of cells arriving in each slot is infinite (large). In [ll], the authors consider only the analysis of the finite high-priority system. In their model, they solve a finite M/G/l-Type chain by utilizing its structure. In this paper, we assume a finite buffer for high-priority class. The cell arrival process of this source is assumed to be a general batch Markovian process. The arrivals of the low-priority cells are also assumed to be a gen- eral batch Markovian process. Our formulation is general and does not make any specific assumption on either pro- cesses. Moreover, the rational (as compared with polyno- mial) probability generating matrix (p.g.m) which is as- sumed for the low priority traffic, allowing an accurate nu- merical calculations with very modest computational com- plexity. Our algorithmic approach follows closely the new methodology in [l] which finds a matrix geometric solution 0-7803-5417-6/99/$10.00 01 999 zyxwvuts IEEE. 10 36