For the performance analysis of ATM networks carrying Variable Bit Rate (VBR) MPEG video sequences there is a need for appropriate video traffic models. In this paper, we discuss Markov chain models for this specific type of traffic with respect to several statistical properties and their ability to predict cell losses at buffers of ATM multiplexers. We intentionally selected a simple model class to check for its appropriateness to model a complex traffic type. The results of this paper show that Markov chain models can be used efficiently for MPEG video traffic under the following conditions. The Group of Pictures (GOP) generation process should be modeled rather than the frame process. If the performance measures depend on the correlation properties of the video traffic the scene process should also be considered in the course of the model development. 1 Introduction In B-ISDNs on the basis of the ATM, a major part of the traffic will be generated by multimedia sources like teleco...

We investigate function classes h#Pi f which are defined as the closure of #P under the operation f and a set of known closure properties of #P, e.g. summation over an exponential range. First, we examine operations f under which #P is closed (i.e., h#Pi f = #P) in every relativization. We obtain the following complete characterization of these operations: #P is closed under f in every relativization if and only if f is a finite sum of binomial coefficients over constants. Second, we characterize operations f with respect to their power in the counting context in the unrelativized case. For closure properties f of #P, we have h#Pi f = #P. The other end of the range is marked by operations f for which h#Pi f corresponds to the counting hierarchy. We call these operations counting hard and give general criteria for hardness. For many operations f we show that h#Pi f corresponds to some subclass C of the counting hierarchy. This will then imply that #P is closed under f if and only if ...

A great number of complexity classes between P and PSPACE can be defined via leaf languages for computation trees of nondeterministic polynomial time machines. Jenner, McKenzie, and Th'erien (Proceedings of the 9th Conference on Structure in Complexity Theory, 1994) raised the issue of whether considering balanced or unbalanced trees makes any difference. For a number of leaf language classes, coincidence of both models was shown, but for the very prominent example of leaf language classes from the alternating logarithmic time hierarchy the question was left open. It was only proved that in the balanced case these classes exactly characterize the classes from the polynomial time hierarchy. Here, we show that balanced trees apparently make a difference: In the unbalanced case, a class from the logarithmic time hierarchy characterizes the corresponding class from the polynomial time hierarchy with a PP-oracle. Along the way, we get an interesting normal form for PP computations.

In ATM network environments, congestion control plays an important role to support different quality of service guarantees for a large variety of traffic types. While for real-time communications, like CBR and VBR services, a preventive open-loop congestion control mechanism is applied, a reactive closed-loop mechanism has been suggested for the ABR service class, which was introduced mainly for data communications. This paper presents an analysis to evaluate the performance of the rate-based congestion control mechanism developed by the ATM Forum. We derive formulae to compute the evolution of the allowed cell rate and the resulting buffer content during steady state. Therefore, we focus on traffic scenarios consisting of single sources as well as of homogeneous mixes of ABR sources. From numerical examples we can conclude that an appropriate setting of the control parameters is important to achieve a reasonable performance of the rate-based control mechanism, especially to obtain low...

: This study investigates the properties of arti#cial recurrent neural networks. Particular attention is paid to the question of how these nets can be applied to the identi#cation and control of non-linear dynamic processes. Since these kind of processes can only insu#ciently be modelled by conventional methods, di#erent approaches are required. Neural networks are considered to be useful for this purpose due to their ability to approximate a wide class of continuous functions. Among the numerous network structures, especially the recurrentmulti-layer perceptron #RMLP# architecture is promising from application point of view. This network architecture has the wellknown properties of multi layer perceptrons and moreover these nets have the ability to incorporate temporal behavior. Departing from the original process description the applicability of RMLPs is investigated and di#erent learning algorithms for this network class are outlined. Furthermore, besides the conventional...

The investigation of feedback controls for telecommunication networks has recently gained considerable interest. The reason is the definition of a new ATM service category, the so-called Available Bit Rate service, whose primary goal is the economical support of applications with vague requirements for throughputs and delays. One class of possible feedback controls is formed by the rate-based mechanisms. Feedback from the network switches to the end systems gives users the information necessary to appropriately adjust their transmission rates. This type of control has been investigated to some extent in the existing literature, assuming a constant transmission rate on a bottleneck link. In this paper, we present a discrete-time analysis of a feedback control policy, taking into account a bottleneck link capacity that varies according to a general probability distribution. The control policy we look at belongs to the class of explicit rate control mechanisms considered for the Available...

In this paper we develop an analysis of the so-called Dual Cell Spacer. In contrast to a conventional spacer, which shapes a traffic stream only according to a given Peak Cell Rate, the Dual Cell Spacer takes into account the Peak Cell Rate as well as the Sustainable Cell Rate with the corresponding Burst Tolerance. The analysis is carried out in the discrete-time domain. Performance measures such as the cell rejection probability, the cell delay distribution and the cell inter-departure time distribution are derived. All results are of an exact nature. Numerical examples that compare the performance of the Dual Cell Spacer with that of a conventional spacer show a similar performance in terms of cell delay and cell loss for relatively small values of the Burst Tolerance. Using our analysis, both the Sustainable Cell Rate and the Burst Tolerance, which are used for traffic shaping in the Dual Cell Spacer, can be chosen adequately to achieve a given target cell rejection probability or ...

This study deals with the enforcement of source parameters in ATM networks. An algorithm for monitoring the cell rate of a connection is the so-called generic cell rate algorithm. At the moment, only peak cell rate policing is standardized, but there are discussions in the standard commissions to introduce a second source parameter, the sustainable cell rate in conjunction with a burst tolerance. These source parameters are defined at the physical layer service access point where ATM connections behave like ON/OFF-sources due to the preceding cell spacer. In this paper, we present an algorithm to derive the exact cell rejection probability of the generic cell rate algorithm if ON/OFFsources are monitored. This is done by an iterative algorithm based on a discrete-time analysis technique. Using the cell rejection probability, the parameters for the monitor algorithm can be chosen to meet desired performance objectives, e.g. the conformance of a connection. Numerical results show that th...

Well investigated are growing context-sensitive languages (GCSL), i. e. languages defined by grammars that have only growing rules, where the left side of a growing rule is shorter than its right side. GCSL is characterized by quasi growing context-sensitive grammars (QGCSG), i. e. the rules therein are growing only with respect to a valuation of all the strings by a homomorphism to natural numbers with addition. In this paper we introduce weak growing context-sensitive grammars (WGCSG), i. e. grammars that are growing with a weighted valuation of all strings, where the weights are the values of a position valuation. Here we evaluate a string by summing up every product of a symbol value with its position value. For every position valuation which does not agree with the beginning of any exponential function, the corresponding class of WGCSGs characterizes CSL, shown by a somehow tricky proof. Such a valuation function is called unsteady. On the other hand all WGCSG related to steady ...

: Recently, many companies have realized that their organization needs to be improved in order to enhance flexibility, efficiency, and effectiveness. Business Process Re-engineering has become the new organization paradigm to reconstitute profitability and competitiveness. Additionally, workflow management systems promise to provide a conceptual framework to describe and automate workflow. Analysts are asking for methods to evaluate alternative process designs for performance objectives, such as cycle time and throughput. These measures are dependent on the dynamic behavior of a process and can hardly be derived by traditional methods. In this paper we will outline an approach to model the dynamic behavior of business processes by Stochastic Petri nets. Our aim is to provide workflow management systems with an analytical evaluation component. We will summarize the problems we encountered following our approach to give directions for further research. Keywords: Business process re-en...