Computational algorithms for state-dependent queueing networks

Abstract

IBMQueueing networks are important as performance models of computer and communication systems.Exact numerical solution of a queueing network is usually only feasible if the network has a product form solution in the sense of Jackson. Product form networks allow a rich variety of forms of statedependent behavior. However, efficient computational algorithms have not been developed for several of the allowed forms of state-dependent behavior. This paper develops the two most important computational algorithms. Convolution and Mean Value Analysis, to apply to forms of state-dependent behavior allowed in product form networks. It is demonstrated that these two algorithms are of equal generality, contrary to common belief.

A note on stable flow-equivalent aggregation in closed networks

“…, n M,C ) at the flow-equivalent server M . This case is known to be prohibitively expensive because an additional nested recursion is required to evaluate each state of the underlying Markov process [9]. Because of the different structure imposed by the nested recursion, the mean value analysis does find application to this case [9] which is therefore outside the scope of this work.…”

“…Real systems with features such as finite capacity constraints, memory swapping, or high-variability in service times violate the underlying assumptions of product-form networks, but still can be approximated accurately by these models using the flow-equivalent aggregation technique [3,6] (also known as the Norton's theorem for queueing networks or the Chandy-Herzog-Woo method). In the flow-equivalent aggregation approach, the real system is modeled by a load-dependent queue, called flow-equivalent server, whose service rate equals in any feasible state of the network the observed throughput of the system; after this step, the resulting load-dependent model is solved by the load-dependent Mean Value Analysis (MVA) algorithm [7,9].…”

“…, µ(N ). The following quantities derived from (1) are also considered throughout the derivations, see [2,7,9] for proofs. The marginal probability that j ≥ 1 jobs are enqueued at station i is…”

Mean Value Analysis Approximation for multiple server queueing networks

“…The basic concept of mean value analysis is the application of an iterative procedure to calculate mean residence time, system throughput, and the mean number of jobs. A number of studies about mean value analysis has been published in the last few years [1,3,6,7,[10][11][12][13][14][15][17][18][19][20][21]. The principle advantage to mean value analysis lies in its ability to effectively compute the performance measures without computing the normalization constants.…”

A computational complexity-aware model for performance analysis of software servers

“…Most existing work on load-dependent servers looks at the number of requests at the server and queue, and not the entire population [4,7,10]. In this paper, we extend the basic client-server closed queueing network model [6,11] to one that takes into account the complexity of algorithms (in terms of the population N ) that constitute the processing of a request.…”