VirtualClock: a new traffic control algorithm for packet-switched networks
ACM Transactions on Computer Systems (TOCS)
IEEE INFOCOM '92 Proceedings of the eleventh annual joint conference of the IEEE computer and communications societies on One world through communications (Vol. 2)
Hierarchical packet fair queueing algorithms
Conference proceedings on Applications, technologies, architectures, and protocols for computer communications
Start-time fair queueing: a scheduling algorithm for integrated services packet switching networks
IEEE/ACM Transactions on Networking (TON)
Rate-proportional servers: a design methodology for fair queueing algorithms
IEEE/ACM Transactions on Networking (TON)
Efficient fair queueing algorithms for packet-switched networks
IEEE/ACM Transactions on Networking (TON)
Latency-rate servers: a general model for analysis of traffic scheduling algorithms
INFOCOM'96 Proceedings of the Fifteenth annual joint conference of the IEEE computer and communications societies conference on The conference on computer communications - Volume 1
Analysis of temporal and throughput fair scheduling in multirate WLANs
Computer Networks: The International Journal of Computer and Telecommunications Networking
A comprehensive analytical model for weighted fair queuing under multi-class self-similar traffic
ICC'09 Proceedings of the 2009 IEEE international conference on Communications
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This paper presents two fundamental theorems that show that the O(N) complexity for updating the virtual time in a weighted fair queuing (WFQ) scheduler with N sessions is caused mainly by simultaneous departures of packets, and not by iterated deletion as was previously claimed. Iterated deletion is caused by an 'avalanche' of consecutive, but not necessarily simultaneous, departures that incur more departures due to increments in available bandwidth from idling sessions. Iterated deletion potentially leads to large numbers of consecutive departures within a given time period. The number of departures is, however, a function of such implementation details as the resolution of the time-stamp and the scheduler clock. On the other hand, the problem of simultaneous time-stamps cannot be solved by any increase in the time resolution of virtual-time update. Essentially, all equal time-stamps must be processed during a single virtual-time update operation. We present a proof to show that O(N) simultaneous departures can occur during a single virtual-time update. We also show that this is a fundamental property of WFQ that holds even under the most restrictive conditions, viz. all packets arrive serially to the scheduler (no simultaneous arrivals), and the input bit-rate does not exceed the output bit-rate.