In this paper, we present simple performance bounds for multiplexed regulated traffic streams, which are leaky-bucket regulated with peak, mean rate and burst size constraints. We consider independent, heterogeneous streams, which are multiplexed in a common buffer. We derive bounds on the mean delay in the deterministic context and we then obtain a simple stochastic bound, which is exact when the number of sources increases. A byproduct is a characterization of the worst case sources for mean delay, when they are leaky bucket regulated.

In this paper we consider a multi-buffered system consisting of N buffers accessed by heterogeneous long-tailed sessions and served according to the generalized processor sharing (GPS) discipline with weights {/spl phi//sub i/}. We assume that sessions arrive according to a Poisson process. A session of type i transmits at rate r/sub i/ and has a duration whose distribution is longtailed of the form P(/spl tau//sub i/>t)/spl sim//spl alpha//sub i/t/sup -(1+/spl beta/i)/ where /spl alpha//sub i/, /spl beta//sub i/>0. We obtain the large buffer asymptotics under very general stability hypotheses. In particular we show that recent results on the GPS asymptotics obtained by Borst, Boxma and Jelenkovic (see IEEE INFOCOM, vol.2, p.912-21, 2000) can be recovered and there are important cases for which we obtain exact asymptotes for which the previous results do not apply. The methodology exploits the sample-path description of the workload evolution under GPS as well as the marked Poisson structure of the inputs.

In this paper we consider a generalization of the so-called M/G//spl infin/ model where M types of long-tailed sessions enter a buffer. The instantaneous rates of the sessions are functions of the occupancy of an M/G//spl infin/ system with long-tailed G distributions. In particular we assume that a session of type i transmits r/sub i/ cells per unit time and lasts for a random time r with long-tailed distribution given by P(/spl tau/>x)/spl sim//spl alpha//sub i/x(-(1+/spl beta//sub i/)) where /spl beta//sub i/>0. We derive the mean cell loss asymptotics for large buffer size as well as the complementary distribution of the buffer occupancy exceeding a high level. When specialized to the homogeneous case we show that recent results on large buffer asymptotics, which have been shown under more restrictive assumptions, hold more generally. In the heterogeneous case, we show that the asymptotics are not necessarily governed by the sources with the smallest /spl beta//sub i/ but also depend on the rates r/sub i/ and it is the ratio of /spl beta//sub i/ to r/sub i/ which is important. Finally it is a simple observation that light-tailed (exponential tails for example) sources have no influence on the asymptotics except that they contribute to reducing the capacity available to heavy-tailed sources by their mean load.

We derive asymptotically exact expressions for buffer overflow probabilities and cell loss probabilities for a finite buffer which is fed by a large number of independent and stationary sources. The technique is based on scaling, measure change and local limit theorems and extends the results of Courcoubetis and Weber (see J. Appl. Prob., vol.33, no.3, p.886-903, 1996) on buffer overflow asymptotics. We discuss the cases when the buffers are of the same order as the transmission bandwidth as well as the case of bufferless multiplexers. Moreover we show that the results hold for a wide variety of traffic sources including on/off sources with heavy-tailed distributed on periods which are typical candidates for so-called "self-similar" inputs showing that the asymptotic cell loss probability behaves in much the same manner for such sources as for Markovian type of sources which has important implications for statistical multiplexing. The paper concludes with comparison of the theoretical results with simulations.

In this paper we consider the problem of calculation of cell loss probabilities when M classes of stationary ON-OFF sources access a given multiplexer of large capacity. We show that when the number of sources of each type is large and scaled according to the capacity we can obtain an explicit analytic formula (O(1) in complexity) in terms of the parameters of the sources. This is based on a measure change technique combined with the use of uniform local limit theorems which gives estimates with a precise notion of the order of errors. We compare our results with standard Gaussian approximations which have been reported showing the improvement in the ATM context where cell loss probabilities are typically of the order 10/sup -9/.

Random multiple access (RMA) protocols comprise an important class for the accessing/signaling stage in multimedia ATM wireless networks. Within the RMA class, the ALOHA algorithm is most widely used at this point in time, while, as is well known, the latter algorithm becomes unstable, as the user population increases. In this paper, we consider the part-and-try algorithm, instead, for a system with different priorities. Based on this algorithm, we construct a mixed priority protocol whose total throughput-for all priorities combined-equals 0.487. In the special and important for ATM case of two, low, and high priorities, with respective Poisson intensities /spl lambda//sub L/ and /spl lambda//sub H/. We also present an analytical methodology which allows the computation of the average packet delays as functions of the rates /spl lambda//sub L/ and /spl lambda//sub H/.>

Random multiple access (RMA) protocols comprise an important class for the accessing/signaling stage in multimedia ATM wireless networks. Within the RMA class, the ALOHA algorithm is most widely used, while, as is well known, the latter algorithm becomes unstable, as the user population increases. We consider the part-and-try algorithm, instead, for a system with different priorities. Based on this algorithm, we construct a mixed priority protocol whose total throughput for all priorities combined equals 0.487. In the special and important ATM case of two, low- and high-priorities, with respective Poisson intensities /spl lambda//sub L/ and /spl lambda//sub H/. We also present an analytical methodology which allows the computation of the average packet delays as the functions of the rates /spl lambda//sub L/ and /spl lambda//sub H/.

The effect that large propagation delay has on the problem of network access is explored for the infinite population model with success-idle-collision feedback information, where the feedback information suffers a large propagation delay N. A simple lower bound is given on the probability that a packet is not successfully transmitted within N/2 time units (not including the forward propagation delay), where N is the station-to-station propagation delay. The bound implies a lower bound on the mean access delay. We also display an algorithm for which the transmission delay is within a factor of three of the lower bound, for moderate traffic loads and asymptotically large propagation delay.>