The mathematics of nonlinear programming
The mathematics of nonlinear programming
The Dependence of Sojourn Times in Closed Queueing Networks
Proceedings of the International Workshop on Computer Performance and Reliability
Asymptotic analysis of closed queueing networks with bottlenecks
Proceedings of the IFIP WG 7.3 International Conference on Performance of Distributed Systems and Integrated Communication Networks
Dimensioning bandwidth for elastic traffic in high-speed data networks
IEEE/ACM Transactions on Networking (TON)
A practical bottleneck detection method
Proceedings of the 33nd conference on Winter simulation
Throughput limits from the asymptotic profile of cyclic networks with state-dependent service rates
Queueing Systems: Theory and Applications
A unified framework for the bottleneck analysis of multiclass queueing networks
Performance Evaluation
Closed Queueing Networks Under Congestion: Nonbottleneck Independence and Bottleneck Convergence
Mathematics of Operations Research
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Asymptotic behavior of queues is studied for large closed multi-class queueing networks consisting of one infinite server station with K classes and M processor sharing (PS) stations. A simple numerical procedure is derived that allows us to identify all bottleneck PS stations. The bottleneck station is defined asymptotically as the station where the number of customers grows proportionally to the total number of customers in the network, as the latter increases simultaneously with service rates at PS stations. For the case when K=M=2, the set of network parameters is identified that corresponds to each of the three possible types of behavior in heavy traffic: both PS stations are bottlenecks, only one PS station is a bottleneck, and a group of two PS stations is a bottleneck while neither PS station forms a bottleneck by itself. In the last case both PS stations are equally loaded by each customer class and their individual queue lengths, normalized by the large parameter, converge to uniformly distributed random variables. These results are directly generalized for arbitrary K=M. Generalizations for K \neq M are also indicated. The case of two bottlenecks is illustrated by its application to the problem of dimensioning bandwidth for different data sources in packet-switched communication networks. An engineering rule is provided for determining the link rates such that a service objective on a per-class throughput is satisfied.