Khosrow Sohraby

Congestion control for high speed packet switched networks

The authors suggest and investigate a general input congestion control scheme that takes into account a broad spectrum of network issues. As a preventive congestion control strategy, a leaky-bucket-type scheme operating on a session basis that limits the sessions average rate and the burstiness is proposed. This restrictive control is combined with an optimistic bandwidth usage scheme which works by marking packets into two different colors, green and red. The packets are marked so that the average green packet rate entering the network is at the reserved average rate. The average red packet rate represents traffic in excess of this guaranteed average rate and is sent to further utilize unused bandwidth in the network. Both types of packets are further filtered by a spacer which limits the peak rate at which the packets enter the network. The marked packets are then sent into the network, where they are treated according to their color, using at each intermediate node a simple threshold policy.<<ETX>>

On the asymptotic behavior of heterogeneous statistical multiplexer with applications

The author combines a heterogeneous statistical multiplexer in heavy traffic with different characteristics in discrete time which is representative of the asynchronous transfer mode (ATM) environment at the cell level. An exact formulation of the queuing model for the multiplexer is presented. Using spectral decomposition method and asymptotic analysis, it is shown that for fixed source average utilization and peak rate, as the burst size of the individual sources increase the tail behavior of the distribution of the number of cells queued in the multiplexer has a simple characterization. This characterization provides a simple approximation of the queuing behavior of the multiplexer, where the impact of each source is quite evident. The accuracy of this approximation is examined. Some applications are considered where both buffer sizing and admission control are discussed.<<ETX>>

On the theory of general on-off sources with applications in high-speed networks

A general theory of on-off sources is provided. The basic source model is characterized by alternating independent on (burst) and off (silence) periods, which may have general distributions. Other more complex sources are constructed, and their behavior is characterized in terms of the basic source model. Heterogeneous and homogeneous statistical multiplexers fed by such sources are considered. In the heterogeneous environment, a simple result on the tail behavior of the multiplexer queue length distribution in the heavy traffic is provided. In the homogeneous environment, asymptotic results on the tail behavior of the queue length distribution are provided for all levels of utilization. The results for the heterogeneous environment suggest a new call admission control policy for general on-off sources in high-speed networks, which depends only on the first two moments of the on and off periods of individual sources and their respective peak rates.<<ETX>>

On the performance of bursty and correlated sources subject to leaky bucket rate-based access control schemes

The analysis of a rate-based access control scheme in high speed environments that is based on a buffered leaky bucket algorithm is presented. The analysis is carried out in discrete time, which is representative of asynchronous transfer mode environments. For the cell arrivals to the leaky bucket, a general discrete Markovian arrival process is considered which models bursty and correlated sources. The introduction of the deficit function allows the reduction of the original problem to a more standard discrete time queuing system with the same arrival process. As an important special case, the detailed analysis of the binary Markov source throttled by such rate-based access control schemes is presented. Along with explicit recursions for computation of state probabilities and simple characterization of the asymptotic behavior of the queue buildup, some guidelines for the parameter selection of these schemes is provided.<<ETX>>

An invariant subspace approach in m/g/l and g/m/l type markov chains

Let , be a sequence ofmtimes;mnonnegative matrices and let be such that A(1) is an irreducible stochastic matrix. The unique power-bounded solution of the nonlinear matrix equation has been shown to play a key role in the analysis of Markov chains of M/G/l type. Assuming that the matrix A(z) is rational, we show that the solution of this matrix equation reduces to finding an invariant subspace of a certain matrix. We present an iterative method for computing this subspace which is globally convergent. Moreover, the method can be implemented with quadratic or higher convergence rate matrix sign function iterations, which brings in a new dimension to the analysis of M/G/l type Markov chains for which the existing algorithms may suffer from low linear convergence rates. The method can be viewed as a “ bridge ” between the matrix analytic methods and transform techniques whereas it circumvents the requirement for a large number of iterations which may be encountered in the methods of the former type and the r...

An analysis of the effects of mobility on bandwidth allocation strategies in multi-class cellular wireless networks

In this paper we present a multi-cell analytic model for multi-class cellular networks. We investigate the effects subscriber mobility has on bandwidth control strategies when the network supports multiple classes of subscribers having different bandwidth requirements. We introduce control strategies from non-mobile networks and examine them in a mobile environment. The expressions for call blocking using these control strategies have product form solutions. This allows us to develop a multi-cell, multi-class, model by generalizing on the Erlang fixed point approximation using generalized multi-rate, multi-class, Erlang loss formulas for each class of traffic. We produce expressions for originating calls lost, hand-off calls lost, forced-termination, and mean channel occupancy for each class of traffic in each cell for different control strategies. The multicell analytic model allows us to investigate the effects of asymmetric loads and mobility patterns in the network. The analytic results are supported by simulation.

Pseudo-isochronous cell forwarding

Abstract This paper shows how to design a packet switched network, for real-time traffic, such that under full network load: (i) the end-to-end delay bound of a low-rate voice connection is minimized, (ii) the bound on the delay uncertainty or jitter is a fixed network parameter – independent of the network size and the connection rate, and (iii) the required buffer sizes (inside the network) to ensure congestion-free routing is minimized. In addition, this design can be generalized to accommodate either variable bit rate (VBR) traffic with statistical multiplexing or the integration of available bit rate (ABR) traffic 7 , 12 . The isochronous timing information (can be provided by the global positioning system (GPS) [1] ) is used for pacing the packet/cell forwarding inside the network. This means that a cell is forwarded from one switch to another not at a specific time but within a time frame of a relatively long duration as compared with the cell transmission time. This time frame is an independent network parameter, which determines the delay and jitter bounds inside the network. A study of the blocking probability of this approach is presented. (Blocking is defined as the impossibility of allocating bandwidth for a new connection while capacity is still available, but not in the proper time frames.) The study includes both analytical and simulation results, which demonstrate an important trade-off between the blocking probability and the end-to-end delay bound.

Jitter calculus in ATM networks: single node case

The authors formulate and analyse the jitter process in an ATM environment. The jitter analysis is presented for a tagged renewal stream. The queueing model consists of the superposition of the tagged renewal stream and background traffic. In the case of periodic tagged stream, the correlated background traffic is also considered. A solution methodology is developed which can be utilized in solving a large class of problems. They investigate the impact of various traffic parameters (e.g. the background traffic load and burstiness, the interarrival time of the renewal stream, etc.) on the jitter of the tagged stream. Numerical examples provide insight into the behavior of the system. They observe that the variance of the jitter behaves (almost) linearly with the variance of the background traffic. Some interesting heavy traffic results are also provided when the background traffic consists of number of identical two state ON-OFF sources.<<ETX>>

On the Exact Analysis of a Discrete-Time Queueing System with Autoregressive Inputs

In this paper, we provide an exact analysis of a discrete-time queueing system driven by a discrete autoregressive model of order 1 (DAR(1)) characterized by an arbitrary marginal batch size distribution and a correlation coefficient. Closed-form expressions for the probability generating function and mean queue length are derived. It is shown that the system performance is quite sensitive to the correlation of the arrival process. In addition, a comparison with traditional Markovian processes shows that arrival processes of DAR(1) type exhibit larger queue length as compared with the traditional Markovian processes when the marginal densities and correlation coefficients are matched.

Matrix-geometric solutions of M/G/1-type Markov chains: a unifying generalized state-space approach

We present an algorithmic approach to find the stationary probability distribution of M/G/1-type Markov chains which arise frequently in performance analysis of computer and communication networks. The approach unifies finite- and infinite-level Markov chains of this type through a generalized state-space representation for the probability generating function of the stationary solution. When the underlying probability generating matrices are rational, the solution vector for level k, x/sub k/, is shown to be in the matrix-geometric form x/sub k+1/=gF/sup k/H, k/spl ges/0, for the infinite-level case, whereas it takes the modified form x/sub k+1/=g/sub 1/F/sup k//sub 1/H/sub 1/+g/sub 2/F/sup K-k-1//sub 2/H/sub 2/, 0/spl les/k/spl les/K, for the finite-level case. The matrix parameters in the above two expressions can be obtained by decomposing the generalized system into forward and backward subsystems, or, equivalently, by finding bases for certain generalized invariant subspaces of a regular pencil /spl lambda/E-A. We note that the computation of such bases can efficiently be carried out using advanced numerical linear algebra techniques including matrix-sign function iterations with quadratic convergence rates or ordered generalized Schur decomposition. The simplicity of the matrix-geometric form of the solution allows one to obtain various performance measures of interest easily, e.g., overflow probabilities and the moments of the level distribution, which is a significant advantage over conventional recursive methods.