article Free Access Share on Corrigendum: `` Mean-Value Analysis of Closed Multichain Queuing Networks'' Authors: M. Reiser View Profile , S. S. Lavenberg View Profile Authors Info & Claims Journal of the ACMVolume 28Issue 301 July 1981https://doi.org/10.1145/322261.322275Published:01 July 1981Publication History 6citation363DownloadsMetricsTotal Citations6Total Downloads363Last 12 Months6Last 6 weeks1 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

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.

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 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.

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.

Research into queuing networks and their applications to computer systems is in a state of prosperity. The object of this paper is to discuss the computational aspect of separable queuing networks. Separable networks constitute that class of models for which a solution can be computed efficiently for fairly large problems. Open networks do not pose any computational problem. It is the case of closed networks where the subject of numerical algorithms becomes an issue.

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.

The finite capacity of storage has a significant effect on the performance of a contemporary computer system. Yet it is difficult to formulate this problem and analyze it by existing queueing network models.