Martin Reiser

Mean-Value Analysis of Closed Multichain Queuing Networks

It is shown that mean queue sizes, mean waiting times, and throughputs in closed multiple-chain queuing networks which have product-form solution can be computed recursively without computing product terms and normalization constants. The resulting computational procedures have improved properties (avoidance of numerical problems and, in some cases, fewer operations) compared to previous algorithms. Furthermore, the new algorithms have a physically meaningful interpretation which provides the basis for heuristic extensions that allow the approximate solution of networks with a very large number of closed chains, and which is shown to be asymptotically valid for large chain populations.

A Queueing Network Analysis of Computer Communication Networks with Window Flow Control

A computer communication network with window flow control is modeled by a closed multichain queueing network. The severe computational limitation of previous solution algorithms is overcome with a heuristic derived from the recently found mean value analysis. A large numerical example is given.

Queuing networks with multiple closed chains: theory and computational algorithms

In this paper a recent result of Baskett, Chandy, Muntz, and Palacios is generalized to the case in which customer transitions are characterized by more than one closed Markov chain. Generating functions are used to derive closed-form solutions to stability, normalization constant, and marginal distributions. For such a system with N servers and L chains the solutions are considerably more complicated than those for systems with one subchain only. It is shown how open and closed subchains interact with each other in such systems. Efficient algorithms are then derived from our generating function representation.

Mean-value analysis and convolution method for queue-dependent servers in closed queueing networks

Abstract In this paper, we formulate a recursive relation for the marginal probabilities of a closed network with K customers in terms of the same network with K − 1 customers. Mean-value analysis (MVA) is an application of this relation, together with Littles formula. It is shown that the convolution method, too, can be based on the same recursive result. This leads to a new convolution algorithm called normalized convolution algorithm (NCA), which like MVA works entirely with probabilities and throughputs rather than with quantities such as normalization contacts. NCA avoids a difficult problem, the occurrence of floating-point over-flows in the original convolution algorithm. We shall also solve a numerical stability problem found in MVA. Finally, we show how MVA and the convolution algorithm can be combined in the same problem to yield a hybrid method retaining the best properties of both methods.

Congestion Control of Store-and-Forward Networks by Input Buffer Limits--An Analysis

The use of input buffer limits for congestion control of store-and-forward networks is investigated. An analytic model is formulated. Based upon the analytic results, strategies are proposed for the design of input buffer limits to achieve the maximum network throughput as well as to provide a safety margin for uncertainties in traffic assumptions. A useful capacity law is discovered. Major conclusions drawn from the analysis are supported by simulation results for a fournode homogeneous network. These results indicate that input buffer limits which satisfy the capacity law are a simple and effective means of network congestion control. Further simulation studies are underway to investigate methods of implementation in a general network.

A Queueing Model with Finite Waiting Room and Blocking

A two-stage queueing network with feedback and a finite intermediate waiting room is studied. The first-stage server is blocked whenever M requests are enqueued in the second stage. The analysis of this system under exponential assumptions is carried out. An algorithm to calculate the stationary state probabilities is given and some special cases are considered.

A two-dimensional numerical FET model for DC, AC, and large-signal analysis

A numerical model is presented allowing calculation of the dc, ac, and large-signal parameters of field-effect transistors (FETs). The numerical procedure is based on finite-difference approximations to the full time-dependent set of equations. The scheme presented uses centered difference quotients and an implicit treatment of the continuity equation. It is shown to be absolutely stable and accurate for time steps below 1 ps. A set of numerical data calculated for one typical example is compared systematically with experimental values. Excellent agreement between measured and computed values is found for the dc characteristics. Small-signal solutions, obtained by Fourier transform methods are also close to the empirical values. The good fit between experiment and numerical simulation is a thorough validation of both the physical model and the numerical procedure.

Performance Evaluation: Origins and Directions

Position Paper.- Performance Evaluation in Industry: A Personal Perspective.- Topical Area Papers.- Mainframe Systems.- Performance Analysis of Storage Systems.- Ad Hoc, Wireless, Mobile Networks: The Role of Performance Modeling and Evaluation.- Trace-Driven Memory Simulation: A Survey.- Performance Issues in Parallel Processing Systems.- Measurement-Based Analysis of Networked System Availability.- Performance of Client/Server Systems.- Performance Characteristics of the World Wide Web.- Parallel Job Scheduling: A Performance Perspective.- Scheduling of Real-Time Tasks with Complex Constraints.- Software Performance Evaluation by Models.- Performance Analysis of Database Systems.- Performance Analysis of Concurrency Control Methods.- Numerical Analysis Methods.- Product Form Queueing Networks.- Stochastic Modeling Formalisms for Dependability, Performance and Performability.- Analysis and Application of Polling Models.- Discrete-Event Simulation in Performance Evaluation.- Workload Characterization Issues and Methodologies.- Personal Accounts of Key Contributors.- From the Central Server Model to BEST/1(c).- Mean Value Analysis: A Personal Account.- The Early Days of GSPNs.- The Discovery of Self-Similar Traffic.

Finite Capacity Queuing Systems with Applications in Computer Modeling

A queuing system with a buffer of unlimited capacity in front of a cyclic arrangement of two exponential server queues is analyzed. The main feature of the system is blocking, i.e., when the population in the two queues attains a maximum value M, say, new arrivals are held back in the buffer. The solution is given in form of polynomial equations which require the roots of a characteristic equation. A solution algorithm is provided. The stability condition is given in terms of these roots and also in explicit form. Limiting cases which are of practical interest are discussed. These limiting cases lead to a better understanding of some popular approximation techniques.

Internet performance modeling: the state of the art at the turn of the century

Abstract Seemingly overnight, the Internet has gone from an academic experiment to a worldwide information matrix. Along the way, computer scientists have come to realize that understanding the performance of the Internet is a remarkably challenging and subtle problem. This challenge is all the more important because of the increasingly significant role the Internet has come to play in society. To take stock of the field of Internet performance modeling, the authors organized a workshop at Schlos Dagstuhl. This paper summarizes the results of discussions, both plenary and in small groups, that took place during the four-day workshop. It identifies successes, points to areas where more work is needed, and poses “Grand Challenges” for the performance evaluation community with respect to the Internet.