Stephen S. Lavenberg

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.

On the analytical modeling of database concurrency control

The Concurrency Control (CC) scheme employed can profoundly affect the performance of transaction-processing systems. In this paper, a simple unified approximate analysis methodology to model the effect on system performance of data contention under different CC schemes and for different system structures is developed. This paper concentrates on modeling data contention and then, as others have done in other papers, the solutions of the data contention model are coupled with a standard hardware resource contention model through an iteration. The methodology goes beyond previously published methods for analyzing CC schemes in terms of the generality of CC schemes and system structures that are handled. The methodology is applied to analyze the performance of centralized transaction processing systems using various optimistic- and pessimistic-type CC schemes and for both fixed-length and variable-length transactions. The accuracy of the analysis is demonstrated by comparison with simulations. It is also shown how the methodology can be applied to analyze the performance of distributed transaction-processing systems with replicated data.

Statistical Results on Control Variables with Application to Queueing Network Simulation

The development and application of control variables for variance reduction in the simulation of a wide class of closed queueing networks is discussed. These networks allow multiple types of customers, priorities and blocking. Alternative methods of generating confidence intervals from independent replications of a simulation are investigated. A result is given which quantifies the loss in variance reduction caused by the estimation of the optimum control coefficients. This loss is an increasing function of the number of control variables. Good variance reduction is obtained providing that the number of control variables remains small.

A perspective on queueing models of computer performance

Abstract Analytical modeling plays an important role in evaluating computer system performance during the design, development and configuration of a system. We will survey analytical computer performance modeling with an emphasis on developments of practical importance. In doing so the symbiotic relationship between computer performance modeling and queueing theory, in particular queueing networks, will be made evident. The survey will proceed historically, starting with developments in the mid-1960s, when the first published results on queueing models of multiprogramming and time sharing systems appeared, and continuing to include current areas of research. The computer systems we will consider include conventional single processor systems as well as highly parallel multiprocessor systems. Both subsystem models and overall system models will be discussed. It is intended that in addition to being of interest to the computer science community this paper will expose queueing theorists and applied queueing analysts to the practical queueing analysis problems that arise in computer performance modeling.

Mean value analysis by chain of product form queueing networks

A computational algorithm is developed for closed multichain product-form queueing networks. For networks that consist of only single-server fixed rate and infinite-server service centers, it involves only mean performance measures. The algorithm, called mean value analysis by chain (MVAC), is based on a recursion that is quite different in form from the recursion used in the well-known mean value analysis (MVA) algorithm and has quite different computational and storage costs. For networks with few service centers and many chains, MVAC typically has much lower costs than MVA, although it becomes more costly than MVA as the number of service centers increases. The MVAC recursion is similar in structure to a recursion involving normalizing constants that was derived by A.E. Conway and N.D. Georganas (1986). That recursion formed the basis for their recursion by chain (RECAL) algorithm for computing the normalizing constant and from it the mean performance measures. The computational and storage costs for MVAC are shown to be similar to those for RECAL. >

Introduction to regenerative simulation

A recently developed method for estimating confidence intervals when simulating stochastic systems having a regenerative structure is reviewed. The paper is basically tutorial, but also considers the pragmatic issue of the simulation duration required to obtain valid estimates. The method is illustrated in terms of simulating the M/G/1 queue. Analytic results for the M/G/1 queue are used to determine the validity of the simulation results.

Calculating joint queue-length distributions in product-form queuing networks

A new computational algorithm called distribution analysis by chain (DAC) is developed. This algorithm computes joint queue-length distributions for product-form queuing networks with single-server fixed rate, infinite server, and queue-dependent service centers. Joint distributions are essential in problems such as the calculation of availability measures using queuing network models. The algorithm is efficient since the cost to evaluate joint queue-length probabilities is of the same order as the number of these probabilities. This contrasts with the cost of evaluating these probabilities using previous algorithms. The DAC algorithm also computes mean queue lengths and throughputs more efficiently than the recently proposed RECAL and MVAC algorithms. Furthermore, the algorithm is numerically stable and its recursion is surprisingly simple.

A simple analysis of exclusive and shared lock contention in a database system

We consider a probabilistic model of locking in a database system in which an arriving transaction is blocked and lost when its lock requests conflict with the locks held by currently executing transactions. Both exclusive and shared locks are considered. We derive a simple asymptotic expression for the probability of blocking which is exact to order 1/N where N is the number of lockable items in the database. This expression reduces to one recently derived by Mitra and Weinberger for the special case where all locks are exclusive.

Concomitant Control Variables Applied to the Regenerative Simulation of Queuing Systems

We investigate using multiple concomitant control variables to reduce the width of confidence intervals when estimating steady-state response variables via the regenerative method of simulation. A concomitant control variable is an estimator of a known quantity, defined with respect to the system being simulated, that is believed to be correlated with the response variable estimator. We give examples of such control variables for two regenerative queuing systems, the stable GI/G/1 queue and a closed queuing system. An estimator that uses multiple control variables involves unknown coefficients; one wishes to choose these coefficients to minimize the variance of the estimator. We establish the asymptotic validity of confidence intervals constructed using control variables when the coefficients themselves are estimated via regenerative simulation. For the response variables and control variables in our examples we compute the variance reduction that could be obtained if the optimum coefficients were known and empirically investigate the variance reduction obtained in practice using various methods for estimating the coefficients. We find that when the coefficients are estimated from a small fraction of the simulated tours the controlled estimators yield confidence intervals whose width is less than and whose coverage is comparable to that obtained without using control variables.

Regenerative simulation of a queuing model of an automated tape library

Recently, techniques have been developed for estimating confidence intervals when simulating stochastic systems having a regenerative structure. These techniques are applied to the simulation of a queuing model of a computer systems automated tape library. Theoretical and practical issues related to the application of these techniques are addressed. An interesting feature of the automated tape library represented in the queuing model is that certain queues have finite capacity; when these queues are filled to capacity certain services are prevented from occurring. The regenerative techniques are used in conjunction with multiple comparison procedures to make statistically valid statements about the effect of the finite queue capacities on performance.